Supporting Information for
Aggregation behavior of polystyrene-based amphiphilic diblock
copolymers in organic media
Tomoe Arai, Makoto Masaoka, Tomohiro Michitaka, Yosuke Watanabe, Akihito
Hashidzume* and Takahiro Sato
Department of Macromolecular Science, Graduate School of Science, Osaka University, 1-1
Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
Correspondence: A. Hashidzume, Department of Macromolecular Science, Graduate School of
Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
E-mail: akihito@chem.sci.osaka-u.ac.jp
1
Specific refractive index increment and specific density increment.
The specific refractive
index increments n/c and the specific density increments /c for several samples of
PS(x)-PA(y) and PS(x)-PV(y) were determined in DMF to estimate n/c and the partial specific
volume for PA, PV, and both chain ends. Those quantities are necessary to analyze the structure
of the reverse micelle and also the composition distribution effect on the molar mass estimated by
light scattering.
The specific refractive index increment for PS(x)-PA(y) with the degrees of polymerization of
the PS block x and of the PA block y, and molecular weight M are written as
M
n
 n 
 n 
 n 
 M 0,S x    M 0,A y     M I  M T   
c
 c S
 c A
 c end
(S1)
where M0,S (M0,A) and (n/c)S [(n/c)A] are the molar mass of the monomer unit and specific
refractive index increment of the PS (PA) block, respectively, and MI + MT and (n/c)end are the
corresponding quantities of the chain ends.
The value of (n/c)S in DMF was reported to be 0.17
cm3 g-1.
Figure S1a shows the plot of Mn(n/c) – M0,Sx(n/c)S against y obtained from experimental
Mn and (n/c) for PS(x)-PA(y) in DMF (unfilled circles).
indicated, we obtained (n/c)A and (n/c)end.
figure by filled circles.
From the intercept and slope of the line
The same plot for PS(x)-PV(y) is also shown in the
Although the data points are slightly scattered, we estimated (n/c)V from
the line indicated. The results of n/c are listed in Table S1.
The same analysis was made on the specific density increments /c.
Although /c for PS
in DMF was not reported, partial specific volumes  of PS in various solvents were reported so
far.
It is known that  is insensitive to the solvent, and we assume  of PS in DMF to be equal
2
to the average value (0.92 cm3 g-1) of reported  in several solvents.S1
The value of (/c)S for
PS can be calculated to be 0.13 from the equation
 c  1  s
where s is the solvent density (= 0.944 g/cm3 for DMF).
(S2)
From the plot in Figure S1b, we have
determined (/c)A, (/c)A and (/c)end for PA, PV, and chain ends in DMF, and moreover 
of each component using eq S2.
The  values in DCE may be identified with the results in
DMF.
(a)
(b)
Figure S1. Analyses of (a) (n/c) and (b) (/c) data of PS(x)-PA(y) and PS(x)-PV(y) in DMF.
We need n/c for each component in DCE to analyze the composition distribution effect on
the molar mass in DCE estimated by light scattering.
The specific refractive index increment of
component i can be written asS2
 n c i  i  ni  ns 
3
(S3)
where ni and ns are the refractive indices of component i and solvent.
have calculated (n/c)i in DCE.
Using this equation, we
All the results of (n/c)i, (n/c)i, and i are listed in Table
S1.
Table S1. Results of n/c, /c, and  for the components PS, PA, PV, and chain ends
a
i
i
(n/c)i a in DMF
(n/c)i a in DCE
(/c)i a in DMF
S
0.17 b
0.16
0.13
0.92 c
A
0.079
0.070
0.34
0.70
V
0.106
0.095
0.25
0.80
end
0.17
0.17
0.26
0.78
In units of cm3 g-1.
b
Taken from ref. S2.
c
a
An assumed value.
Composition distribution effect on the molar mass estimated by light scattering.
If an AB
diblock copolymer sample has dispersities in the degrees of polymerization of both block chains
and the specific refractive index increments of the two blocks are different, light scattering does not
give the true weight average molar mass of the sample.
Here, we consider the dispersity effect on
the molar mass obtained by light scattering.
The molar mass Mk of species k in the copolymer sample is given by
M k  M A,k  M B,k  M e
4
(S4)
where MA, MB, and Me are the molar masses of the block chains A, B, and chain ends in species k,
respectively.
Using the mole fraction n(MA,k, MB,k) of species k in the copolymer sample, the true
number and weight average molar masses (Mn and Mw) are calculated by
M n  k M k n(M A,k , M B,k ), M w  M n 1 k M k 2 n(M A,k , M B,k )
(S5)
Similarly, the weight average molar masses of the A block chain MA,w and B block chain MB,w are
given by
M A,w   k
M A,k 2
wA M n
n( M A,k , M B,k ), M B,w   k
M B,k 2
wB M n
n( M A,k , M B,k )
(S6)
where wA and wB are the weight fractions of the A and B block chains in the sample given by
wA 
1
Mn
1
 k M A,k n(M A,k , M B,k ), wB  M  k M B,k n(M A,k , M B,k )
(S7)
n
When specific refractive index increments of the A block chain, B block chain, and chain ends
are denoted as (n/c)A, (n/c)B, and (n/c)e, respectively, the specific refractive index increment
n/c for the overall block copolymer chain is given by
n c  wA  n c A  wB  n c B   M e M n   n c e
(S8)
According to the light scattering theory,S3 the excess Rayleigh ratio R0 at the zero scattering angle
divided by the optical constant K and the copolymer mass concentration c (or the apparent weight
average molar mass Mw,app) is written as
R0
 M w,app
Kc
(S9)




Me 
Me 
  A B  M w   2 
 M e    A   B   A wA M A,w   B wB M B,w    2   e
 e M e
Mn 
Mn 




where
 A   n c A  n c  ,  B   n c B  n c  ,  e   n c e  n c 
5
(S10)
When copolymer chains aggregate in solution, the dispersity in the aggregation number also
affects Mw,app obtained by light scattering.
However, if the aggregation number is independent of
the species of the copolymer chain, the correction factor Mw,app/Mw is identical with that in the
non-aggregating case, given by eq S9.
We estimate the correction factor Mw,app/Mw for PS(x)-PV(y) and PS(x)-PA(y) samples
examined by light scattering.
The calculation of Mw,app/Mw using eq S9 needs the distribution
function n(MA, MB). Here we assume that MA and MB have no correlation and each of MA and MB
obeys the log normal distribution.
Then we have

 

n(M A , M B )dM A dM B  1   exp  xA 2 exp  xB2 dxA dxB
(S11)
where xA and xB are defined as
M A  M A,n M A,w exp  A xA  , M B  M B,n M B,w exp  B xB 
(S12)
 A2  2ln  M A,w M A,n  ,  B2  2ln  M B,w M B,n 
(S13)
with
and MA,n and MB,n are calculated from x and y estimated by 1H NMR.
Although we have no data
of MA,w/MA,n and MB,w/MB,n, we may expect that they are not so large.
Assuming that MA,w/MA,n = MB,w/MB,n = 1.2 and 1.5, we have calculated the correction factors
Mw,app/Mw for PS(x)-PV(y) and PS(x)-PA(y) samples examined by light scattering.
listed in Table S2.
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The results are
Table S2. Results of Mw,app/Mw for PS(x)-PV(y) and PS(x)-PA(y) samples examined by light
scattering
Mw,app/Mw
sample
x
y
MA,w/MA,n = MB,w/MB,n = 1.2
MA,w/MA,n = MB,w/MB,n = 1.5
PS(23)-PV(7)
23
7
0.98
0.96
PS(55)-PV(10)
55
10
0.99
0.97
PS(69)-PV(12)
69
12
0.99
0.97
PS(37)-PV(6)
37
6
0.99
0.97
PS(30)-PV(4)
30
4
0.99
0.97
PS(23)-PV(3)
23
3
0.98
0.97
PS(41)-PA(4)
41
4
0.98
0.96
PS(41)-PA(3)
41
3
0.98
0.97
REFERENCES
S1. Lechner, M. D., Nordmeier, L. & Steinmeier, D. G. In Polymer handbook (ed. Brandrup, J.,
Immergut, E. H. & Grulke, E. A.), VII/85-VII/213 (Wiley & Sons, 1999).
S2. Mächtle, V. W. & Fischer, H. Zum spezifischen brechungsinkrement von homo- und
copolymerlösungen. Angew. Makromol. Chem., 7, 147-180 (1969).
S3. Benoit, H. & Froelich D. In Light Scattering from Polymer Solutions (ed. Huglin, M. B.), Ch.
11 (Academic Press, 1972).
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