Supporting Information
1. Mechanism of Friedel-Crafts alkylation1
(a) Initiation: aluminum chloride reacts with impurities like water to form a complex,
which reacts further with unsaturated compounds (styrene in our work) forming
the initial carbocation.
AlCl3  H 2 O   AlCl3OH  H 


(AlCl3OH)  H   R  CH = CH 2  (R  C H  CH 3 ) (AlCl3OH) 
(b) Chain scission of POE: the initial carbocation attacks POE, forming a
moacrocarbocation, PE+, which undergoes a chain scission through electron
rearrangement. The short branch of POE is not drawn.

R    CH 2  CH 2  CH 2  CH 2   RH +  CH 2  CH 2  C H  CH 2 


CH 2  CH 2  C H  CH 2    C H 2 + H 2C = CH  CH 2 
(c) Grafting: the fragments of POE chain can substitute for a proton from the benzene
ring of PS, forming a POE-g-PS copolymer.
AlCl3
R  CH  CH 2  PS 
 POE-g -PS


 AlCl3X 
R  C H 2  PS 
 POE-g -PS
2. Comparisons between model fittings and experiments
Figure S1. Storage modulus, loss modulus and complex viscosity of PS/POE 20/80
physical blend (a) and 50/50 physical blend (b) at 180oC. The solid lines in (a) denote
the fit of Palierne model with Rv=0.37µm and =1mN/m. The solid lines in (b) denote
the fit of YZZ model with lc=4.82µm and=1mN/m.
Figure S2. Storage modulus, loss modulus and complex viscosity of PS/POE 20/80
reactive blend (a) and 50/50 reactive blend (b) at 180oC. The solid lines in (a) denote
the prediction of Palierne model with Rv=0.20µm and =0=1mN/m and the additional
contributions from micelles is calculated by Yu-Zhou model. The solid lines in (b)
denote the prediction of YZZ model with lc=0.67µm and =0=1mN/m and the
additional contributions from micelles is calculated by Yu-Zhou model. The micelles
are assumed to be “unswollen” and m=0.20=0.2mN/m. The radius of unswollen
micelle particles is taken as 20nm.
Figure S3. Storage modulus, loss modulus and complex viscosity of PS/POE 20/80
reactive blend (a) and 50/50 reactive blend (b) at 180oC. The solid lines in (a) denote
the prediction of Palierne model with Rv=0.20µm and =0=1mN/m and the additional
contributions from micelles is calculated by Yu-Zhou model. The solid lines in (b)
denote the prediction of YZZ model with lc=0.67µm and =0=1mN/m and the
additional contributions from micelles is calculated by Yu-Zhou model. The micelles
are assumed to be swollen and m=0.20=0.2mN/m. The radius of swollen micelle
particles is taken as 30nm.
3. Fitting by anisotropic Palierne model
The loss modulus and complex viscosity of reactive blends are shown in Fig. S4.
The dynamic moduli of 20/80 physical blend and reactive blend were fitted using
Palierne model2, which is expressed as
Gb*    Gm*  
1  3 H  
1  2 H  
(S1)
H   
4   RV   2Gm*    5Gd*    Gd*    Gm*   16Gm*    19Gd*    E  
40   RV  Gm*    Gd*     2Gd*    3Gm*   16Gm*    19Gd*    D  
(S2)
E   
   
RV
 23Gd*    16Gm*   
2   
     

24     2  16   
RV
RV2
D   
RV
13Gd*    8Gm*  
2    
4   
 23Gd*    32Gm*   
13Gd*    12Gm*  
RV
RV 
     

48    2  32   
RV
RV2
(S3)
(S4)
where  is the volume fraction of droplets,  is the interfacial tension, Rv is the volume
average radius and  is the angular frequency. Gm* , Gd* and Gb* are complex
modulus of matrix, droplet and blend, respectively.   and   are interfacial
dilatation modulus and interfacial shear modulus, respectively. In the case of physical
blend,   and   are zero, which corresponds to isotropic version of Palierne
model. In reactive blend, when copolymers stay at the interface, it is usually assumed
that they can induce additional interfacial viscosity.   and   are often assumed
to obey Maxwell equation
 '(")    10 20
iif 1 2 
1  iif 1 2
(S5)
In the fitting,   is taken as zero and if 2 is assumed to be infinity, which
results in    20 . Both the fitting results using isotropic Palierne model (Eq. S1-S2
with E    D    0 ) and anisotropic Palierne model (Eq. S1-S5 with non-zero  20 )
for 20/80 physical blend and reactive blend are shown in Fig. S5. As shown in Fig. S5b,
considering interfacial elasticity in Palierne model only slightly increases G’ at low
frequency, which are still much smaller than experimental data.
Figure S4. The loss modulus (a) and complex viscosity (b) of reactive blends.
Figure S5. Fitting of the dynamic moduli of PS/POE 20/80 physical blend (a) and
reactive blend (b) using Palierne model. The solid lines are fitting results using isotropic
Palierne model with Rv=0.20µm and =1mN/m. The dash line in (b) is the fitting result
using anisotropic Palierne model with 2=0.001mN/m.
Reference
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Crafts alkylation. J. Appl. Polym. Sci. 1997; 65: 1385-1393
2. Jacobs U, Fahrländer M, Winterhalter J, Friedrich C. Analysis of Palierne’s emulsion
model in the case of viscoelastic interfacial properties. J. Rheol. 1999; 43: 14951509