Self-Assembly of Synthetic and Biological Polymeric Systems of ...

Self-Assembly of OCH2CH(C6H5)-OCH2CH2 Block Copolymers Langmuir, Vol. 24, No. 14, 2008 7113
Figure 7. TEM micrograhs of micelles formed by copolymers (a) E137S18E137 and (b) E10S10E10.
Figure 8. Aqueous solutions of copolymer E137S18E137. (a) Temperature
dependence of (9) storage (G′) and (O) loss (G″) moduli for aqueous
hard gel at 50% (w/v), frequency, f ) 1 Hz, and strain amplitude, A )
0.5%. (b) Temperature dependence of storage (G′) (9), and loss (G″),
(O), moduli at 10% (w/v), f ) 1 Hz, and A ) 0.5%.
They have used yield stress (σy) and modulus (storage and loss,
G′ and G″) to define three convenient subdivisions of the range
of behaviors observed: immobile hard gel (high σy and G′, G′
> G″), mobile soft gel (low σy and G′, G′ > G″), and mobile
sol (null σy and very low G′, G′ < G″).
Temperature Dependence of Copolymer E137S18E137. The solhard
gel boundary was already determined by tube inversion and
rheology previously, 39 but additional measurements were done
to complete its phase diagram. Figure 8a shows an example of
a temperature scan of the logarithm of the elastic modulus for
a concentrated solution above the critical gel concentration (cgc)
for this copolymer (19% (w/v), derived from the expression cgc
) 10 2 Faφc/δt, where φc ) 0.68 is the volume fraction of spherical
micelles packed in a body-centered structure. 39 On the basis of
a critical value of G″ ) 1 kPa for a hard gel, the 50% (w/v)
(38) Almgrem, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273, 2–15.
(39) Hamley, I. W.; Castelletto, V.; Ricardo, N. P. M. S.; Pinho, M. E. N.;
Booth, C.; Attwood, D.; Yang, Z. Polym. Int. 2007, 56, 88–92.
Figure 9. Phase diagram of copolymer E137S18E137 from (0) tube inversion
and (9, b) rheology showing the sol, soft gel, and hard gel regions.
copolymer solution is a hard gel in the whole range, with a
maximum value of G′ ≈ 16 kPa, and G′ > G″ throughout the
whole experiment. In Figure 8b, a temperature scan of G′ and
G″ at a concentration below the hard-gel boundary (10% w/v)
is also shown as an example. Other polymer concentrations in
this region below the cgc display the same profile (not shown).
Using the conditions described above, we found that at
temperatures at which G′ (1 Hz) exceeds 10 Pa the solutions are
soft gels, otherwise sols. 36–38 As illustrated, within the region of
raised modulus G′ was higher than G″, which justifies the
convenient term “soft gel” for the fluid to distinguish it from sol.
A complete phase diagram of the regions of sol, soft gel, and
hard gel defined by rheometry and tube inversion for copolymer
E137S18E137 is shown in Figure 9. These sol-gel diagrams follow
the general pattern as those published previously for other EO/
SO block copolymers. 1,2 The upper limit to the soft gel region
for the copolymer is not reached within the temperature range
investigated, consistent with the stability at high temperature of
the hard gels of this copolymer.
Frequency Dependence of Copolymer E137S18E137. To get a
more detailed picture about the rheological behavior of both
hard and soft gels, frequency scans of solution of E137S18E137
block copolymer were performed. Figure 10a shows the frequency
scan obtained for the 15% (w/v) solution of copolymer E137S18E137
at 25 °C. This type of soft gel at temperatures and concentrations
relatively near the hard-gel boundary can be assigned as defective
versions of the cubic packed hard gels (i.e., small structured
domains in an overall fluid matrix). These soft gels are
109