Supporting Information
Porous exfoliated poly(ε-caprolactone)-clay nanocomposites: preparation, structure and
properties
Oana Istrate, Biqiong Chen*
1. Calculation of mass fraction of clay platelets in porous polymer/clay
nanocomposites
Mass of blowing agent-treated clay (mc)
mc 
m p c
1  c
(1)
where µc represents the mass fraction of blowing agent-treated organoclay in polymer/clay
nanocomposites and mp represents the mass of polymer.
Mass of clay platelets (mcp)
2
mcp 
mc
c o
mc   b m p
(2)
where µb and µc0 represent the mass fractions of blowing agent and of clay platelets in
organoclay.
Mass of polymer/clay nanocomposite solid (ms)
ms  m p  mc  mc
b m p
g
mc   b m p
(3)
where µg depicts the mass fraction of gas released by the blowing agent determined by TGA
as 0.37 for SB and 0.99 for ADC.
Mass fraction of clay platelets in porous polymer/blowing agent-treated clay nanocomposites
cp 
mcp
ms
1
(4)
2. Calculation of the density of the solid nanocomposite that constructs the cell
struts in the porous nanocomposite
Volume of the fully exfoliated solid nanocomposite (Vse)
Vse 
mcp
 cp

mp
(5)
p
where  represents the density, for which the subscripts cp and p refer to the clay platelets and
polymer.
Volume of the intercalated-exfoliated solid nanocomposite (Vsie)
Vsie 
mcp (1  f i )
 cp

 c f i mc m p

c
p
(6)
where c represents the density of the clay, while fi depicts the fraction of intercalated clay
platelets.
Density of the solid nanocomposite (ρs)
s 
ms
Vs
where ms and Vs represent the mass and volume of the solid nanocomposite
2
(7)
3. Calculation of the modulus of the solid nanocomposite that constructs the cell
struts in the porous nanocomposite1
Radius of gyration (Rg)
Mn  2


 M l
m 

Rg 
6
(8)
where M n represents the number average molecular weight of the polymer, i.e. 80,000, Mm is
the molecular weight of the monomer and l is the end-to-end length of the monomer taking
the bond lengths of C–C and C–O as 0.154 nm and 0.143 nm 2.
The effective volume fraction of the reinforcement (r) in an exfoliated nanocomposite:
 c  c0  s
r 
(1  kRg AT  cp )
 cp
(9)
where AT is the total specific surface area of the clay platelets (i.e. AT = 658 m2g-1) and k is
the fraction of absorbed polymer on the clay layer that behaves like clay (i.e. 0.2 for
Clay(SB)).
The volume fraction of exfoliated clay platelets (er) present in the intercalated-exfoliated
nanocomposites:
er 
 c  c0  s (1  f i )
(1  kRg AT  cp )
 cp
(10)
The volume fraction of clay platelets (cp) in a clay tactoid:
c p 
d1 ( N  1)  h
d 2 ( N  1)  h
(11)
where h, d1 and d2 are the single layer thickness (i.e. 0.98 nm), and the basal spacings for the
blowing agent-treated clay and for the intercalated structures (i.e. 1.85 nm and 2.9 nm). N is
the number of platelets in a tactoid (i.e. 2).
The density of polymer inside the clay tactoid (pi):
 pi 
s
As (d 2  h)
3
(12)
where s is the polymer uptake (i.e. 0.23) and As is the specific gallery area (i.e. 310 m2∙g-1).
The modulus of the solid polymer located inside the clay gallery (Epf) was determined by
assuming that the polymer produces a porous structure inside the clay gallery.
  ip

E p   p
E pf




2
(13)
where Ep represents the solid modulus of the polymer.
The modulus of the clay tactoid with polymer inside the basal spacing was calculated
according to the Christensen equation for platelet-filled composites (Equation 14) 1,3.
Et   c E cp  (1  c ) E 
p
p
f
p
c p (1  c p ) E cp E pf ( cp   p ) 2
c p E cp (1   cp 2 )  (1  c p ) E pf (1   p 2 )
(14)
where Ecp represents the modulus of clay platelets, υ represents the Poisson’s ratio and the
subscripts cp and p refer to the clay platelets (i.e. 0.28) and polymer (i.e. 0.47) 4,5.
The volume fraction of intercalated reinforcement (ir):
ir 
 s c f i [d 2 ( N  1)  h]
 cp [d1 ( N  1)  h]
(15)
The modulus of solid polymer/clay nanocomposites was calculated using the Mori-Tanaka
model 6,7
1
E  Ep
1
[2 cp A3  (1   cp ) A4  (1   cp ) A5 A]
(16)
2A
where A, A3, A4 and A5 are Mori-Tanaka components,6,7 which are dependent on the
Eshelby’s tensors7 and are calculated considering disc-shaped spheroidal inclusions, and 
represents the volume fraction of reinforcement.
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References
1. Chen, B.; Evans, J. R. G., Macromolecules 2006, 39, 1790.
2. Bower, D. I.; Cambridge University Press: Cambridge, 2002.
3. Christensen, R. M., J Eng Mater Technol 1979, 101, 299.
4. Rezgui, F.; Swistek, M.; Hiver, J. M.; G'Sell, C.; Sadoun, T., Polymer 2005, 46, 7370.
5. Chen, B.; Evans, J. R. G., Macromolecules 2006, 39, 747.
6. Mori, T.; Tanaka, K., Acta Metall 1973, 21, 571.
7. Tandon, G. P.; Weng, G. J., Polym Compos 1984, 5, 327.
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