5. PIB x -b-PMAA y Diblock Copolymers: Self-Assembly in Aqueous Media
5.3 Results and Discussion
5.3.4 Dynamic Light Scattering
The distance between the cores of the PIBx-b-PMAAy micelles in the cryo-TEM images (Figure 5.4) can also be compared to apparent hydrodynamic radius,Rh, of such assemblies obtained by means of DLS at more diluted concentrations of cP ol.
= 0.02 wt-%. The data are collected in Table 5.3.
Fig. 5.6: The angular dependence ofRhobtained from DLS of PIB30-b-PMAA170micelles, at () cN aCl = 0.1 M, (
•
) cN aCl = 0.5 M, cT RIS = 0.01 M (pH = 9) and of PIB75-b-PMAA1600 micelles at pH = 5, cN aCl = 0.1 M (), cP ol. = 0.02 wt-%.Figure 5.6 shows the angular dependence ofRh of the PIB30-b-PMAA170 at two considerably different salt concentrations at pH = 9. The absence of an angular dependence in both cases cannot be seen for all other polymers investigated in this work. Especially, the copolymers with longer PMAA blocks like PIB75-b-PMAA615
show that the values of Rh decrease with increasing scattering angle. This can be attributed to the influence of the hydrodynamic form factor. CONTIN analysis revealed that mostly one type of micellar aggregates can be seen in DLS. Therefore, for selected polymers, Cumulant Analysis was applied. Therefrom PDIs of the aggregates of approximately 0.08 to 0.10 for the samples shown in Figure 5.6 were evaluated.
This can be seen at all salt concentrations used for pH-values in the range from 4 to 9, representing almost uncharged up to fully ionized PMAA block. In Figure
5. PIBx-b-PMAAy Diblock Copolymers: Self-Assembly in Aqueous Media 69
Fig. 5.7: The pH-dependence of Rh for the PIB75-b-PMAA1600 micelles, cN aCl = 0.1 M, Θ = 90◦, cP ol. = 0.02 wt-%.
5.6 PIB75-b-PMAA1600 at pH = 5 is depicted as a representative example for this behavior. The pronounced increase of the size of the PIB75-b-PMAA1600 micelles observed with increasing pH in Figure 5.7 is obviously attributed to the stretching of the arms of the micelle due to increasing charge density of the PMAA block caused by ionization of the COOH-groups. The corresponding change of the average aggregation number of the micelles,Nagg, as will be shown later in the SLS and SANS sections, also takes place.
In case of changing ionic strength in solutions of star-like equilibrium micelles, Borisov et al. [23] report on two countervailing effects. On the one hand, the Nagg
increases upon raising salt concentration cs, according to Nagg ∼ NB10/11
(α4NA)3/11c6/11s (5.2) with NA being the DPn of the hydrophilic block and NB being the DPn of the hydrophobic block. On the other hand, the effect of repulsion of charges is screened by increasing the ionic strength in the system (Figure 5.8). This leads to shrinking of PMAA blocks and consequently to lower values of Rh for star-like equlilibrium micelles according to
Rh ∼(NA3α)2/11NB2/11c−s1/11. (5.3) For almost all PIBx-b-PMAAy micelles examined, the same trend is observed: the values of Rh decrease with rising salt concentration. The effect is most pronounced for the PIBx-b-PMAAy copolymers with the longer PMAA blocks (cf. Table 5.3).
Schuch et al. also investigated PIBx-b-PMAAy micelles [11] with a x:y block length ratio of 1:1. In that paper they report thatRh of the micelles of the
copoly-mers with DPn of the PMAA blocks of 50 and 70 is around 15 nm (CONTIN plot at Θ = 90◦), comparable to the contour length, Lc, of a totally stretched PMAA block. Comparing this result to our micelles with DPn of PMAA blocks equal to 170 and 190, the micellar radius coincides with the Lc calculated for the micelles formed by the copolymers used in this work, which are between 43 nm and 48 nm (Rh = 40 nm; PIB30-b-PMAA190, PIB31-b-PMAA170, PIB75-b-PMAA190), pointing to a degree of stretching of the PMAA chain of ca. 80 to 90 %.
Pergushov et al. also reported on solutions of PIB20-b-PMAAy micelles with y varying from 100 up to 425 [10]. The apparent hydrodynamic radius was determined to be approximately 20 nm for micelles formed by the shortest PIB20-b-PMAA100
copolymer at concentrations of NaCl from 0.1 up to 1.0 M NaCl. The smaller size of the micellar assemblies compared to those found in this paper can be explained shorter PIB block of those copolymers. The shorter the PIB block is, the smaller is the core of the micelle and consequently the smaller is the Nagg of the micellar assemblies formed. This can be stated by a comparison of the values ofNagg obtained for micelles of those copolymers with the values ofNagg obtained for PIBx-b-PMAAy
micelles examined in this work (see section 5.3.5).
Fig. 5.8: Double-logarithmic plot of Rh of PIB30-b-PMAA170 (), PIB75-b-PMAA1600 (
•
) and PIB25-b-PMAA2600 () micelles on concentration of NaCl at pH = 9,cT RIS = 0.01M, Θ = 90◦.In Figure 5.8 a double-logarithmic plot of hydrodynamic radius against salt con-centration is shown. As the core size of our star-like micelles is rather small compared to the corona thickness, we can also compare it to the results shown below. It was reported that the slope of the double-logarithmic plot of corona thickness Dcorona of equilibrium star-like micelles (Rcore << Dcorona) against salt concentration is a
5. PIBx-b-PMAAy Diblock Copolymers: Self-Assembly in Aqueous Media 71
measure of the shrinkage of the corona [5]. This can also be seen from equations above.
F¨orster et al.[28] reported that at salt concentrations above 0.05 M the micelles are in the salted-brush regime, e.g. the concentration of salt in bulk solution is higher than the salt concentration within the micellar corona. In their work they obtained a Dcorona ∼ c−0.13 dependence for poly(ethylethylene)-b-polystyrene sulfonic acid (PEE-b-PSSH) micelles. Also Guenoun et al. [29] reported on c−0.14 and c−0.11 dependences for poly(tert-butylstyrene)x-b-poly(sodium styrenesulfonate)y (PtBSx -b-PSSNay) micelles withx/ybeing 26/404 and 27/757, respectively. For the micelles of the PIBx-b-PMAAy copolymers examined in this work the scaling exponent values are in the same range, except of PIB30-b-PMAA170, as shown in Figure 5.8. For PIB25-b-PMAA2600 a slope of -0.12 is found while for PIB75-b-PMAA1600 it is -0.15 and therefore in nice agreement with the theoretical predictions by Borisov (cf.
Equation 5.3). The distinct deviation of the scaling exponent (-0.07) for the micelles of the copolymer with the shortest PMAA block (DPn = 170) from the theoretical predictions might be due to the finite size of the micellar core and a state of not perfect equilibrium.