10. Appendix
10.4. Appendix to Chapter 2.4, and Chapter 5 – Interaction of Multivalent
Presence of multivalent counterions can lead to a collapse and finally to a phase separation of the stars even at constant ionic strength. This was shown by turbidimetric titrations of (PMETAI170)18 solutions with hexacyanocobaltate(III) ([Co(CN)6]3-).
0,0 0,2 0,4 0,6 0,8 1,0 1,2
0,0 0,2 0,4 0,6 0,8 1,0
0,0 0,2 0,4 0,6 0,8 1,0 1,2
0,0 0,2 0,4 0,6 0,8 1,0
0,0 0,2 0,4 0,6 0,8 1,0 1,2
γ Iv/I0
Figure 10. 9: Turbidimetric Titration of (PMETAI180)17 (0.5 g/L: black full line; 0,05 g/L: black dashed line) in 0.1 n NaCl solution with 0.0167 n K3[Co(CN)6] as titer (relative transmitted intensity against charge compensation γ of PE star with trivalent counterions); lines in light grey design the onset of precipitation
We see from Figure 10. 9 that basically the ratio γ of charge concentrations once due to multivalent counterions and due to the macroion (γ = z⋅c([M(CN)l]z−) cmonomerunit ) determines the interstellar interactions. Close to the point where all charges of the macrocations are compensated by the charges of the trivalent anions the system becomes macroscopically immiscible yielding a phase with high polymer content and an almost polymer free aqueous phase. It seems that there is slight dependence on the macroion’s concentration, i.e. at higher star densities the precipitation is facilitated (Figure 10. 9). This might be caused by stronger interactions due to decreased mean interparticle distances.
Figure 10. 9 also implies that the charge compensation ratio defines the conformation of the star-shaped polyelectrolyte in solution. This was investigated by dynamic light scattering usually at 90°. At constant ionic strength the hydrodynamic radius was investigated in
dependence of multivalent counterion concentration. The results are summarized in Figure 10.
10. We directly see that the hydrodynamic radius Rh decreases with increasing concentration of multivalent counterions though the ionic strength is kept constant for each single run. If only Debye-Hückel law15 would hold true for this system, the hydrodynamic radius would not change with increasing cyanometalate concentration. But the intrastellar exchange of a considerable part of monovalent counterions with multivalent counterions leads to a pronounced drop in osmotic pressure within the star and to an increase in the counterion’s entropy. This is the actual driving force for this transition, seen in the arm’s collapse due to lowered osmotic pressure inside the star.
Figure 10. 10: Collapse of hydrodynamic radius Rh of cationic polyelectrolyte star (PMETAI180)17 in respect to concentration ratio of multivalent to monovalent counterions; left hand side: polyelectrolyte concentration effect (0.1 n NaCl solution titrated with 0.0167 n K3[Co(CN)6]; : 0.5 g/L (PMETAI180)17; : 0.2 g/L; the grey bars depict a factor in the concentration ratio of 2.25); right hand side: effect on counterion valency (^: 0.1 n NaCl solution titrated with 0.033 n K2[Ni(CN)4]; 0.5 g/L of (PMETAI180)17) and ionic strength (H: 0.2 n NaCl solution titrated with 0.033n K3[Co(CN)6]; 1.0 g/L of (PMETAI180)17) and for comparison (:0.1 n NaCl solution titrated with 0.0167 n K3[Co(CN)6]; 0.5 g/L (PMETAI180)17; dashed lines depict Rh, measured without multivalent counterions); circles depict the samples which were used for cryo-TEM
On the left hand side of Figure 10. 10 we see the comparison of the collapse curves with different polyelectrolyte concentrations and constant ionic strength. This implies that the majority of the trivalent counterions are incorporated by the cationic star-shaped macroion, as the collapse curves are shifted by almost the factor which is given by the ratio of the two differing polyelectrolyte concentrations (see grey bar in Figure 10. 10). This is consistent with the results of the turbidimetric titration (see Figure 10. 9).
The influence of ionic strength is given on the right hand side of Figure 10. 10. To compare collapse curves with different ionic strengths in the same type of presentation as given in Figure 10. 10, one needs to increase also the polyelectrolyte concentration. The reason: the
x-1E-4 1E-3
axis is coupled to the ionic strength, determined by the NaCl concentration. As seen in Figure 10. 10 the collapse seems to take place at slightly lower [Co(CN)6]3--concentration when the ionic strength is increased. This appears to be contra-intuitive, but since the number density of stars has increased, the bulk volume (volume not occupied by stars) has decreased. This is believed to accelerate the incorporation as the volume for free trivalent counterions is diminished.
The influence of counterions charge at constant ionic strength is also depicted on the right hand side of Figure 10. 10. Usage of tetracyanonickelate(II) ([Ni(CN)4]2-) as divalent counterion needs a higher counterion concentration for the collapse compared to trivalent counterions ([Co(CN)6]3-). Since divalent counterions bear lower charge the charge compensation takes place at higher counterion concentration. But when plotting the results of Figure 10. 10 against charge compensation ratio γ it becomes obvious that the collapse still goes on even when the macroions charge has already been compensated by divalent counterions (Figure 10. 11). This is in accordance with molecular dynamics simulations showing that the binding of divalent counterions to a macroion is of intermediate nature.16 Also this system precipitates at higher divalent counterion concentrations.
Figure 10. 11: results of Figure 10. 10 depicted against charge compensation ratio γ (for assignment see Figure 10. 10)
Cryo-TEM did also reveal differences in the star structures with and without trivalent counterions. Without trivalent counterions, the stars appeared fuzzier, whereas the trivalent counterions lead to a more compact structure. Same was seen by AFM (see chapter 5).
0,01 0,1 1
Figure 10. 12: Cryo-TEM images of 0.5 g/L (PMETAI180)17 in 0.1 n NaCl (left hand side: c([Co(CN)6]3-) = 1.0 10-5 n; right hand side: 3.3 10-4 n; scale bar 100 nm)
For the low concentration of trivalent salt the polyelectrolyte star’s structure seem to be quite diffuse. One can discern some black dots, which are believed to be the core of the stars (diameter in the range of 3nm; silsesquioxane core) and some shadows around the cores, which corresponds to the decreasing segment density around the star’s cores. It is hard to discern the star’s diameter. At high concentrations of cobaltate the structures appear much more compact (visible diameter in the range of 20 nm), which is in accordance with the incorporation of the trivalent counterion.
By use of [Co(CN)6]3-, we can reverse this contraction by simple UV-irradiation (chapter 5).17, 18 Light exchanges one cyano ligand with water and the charge of the counterion is reduced (photoaquation). One counterion is decomposed into two counterions. This leads again to an increase in osmotic pressure inside the star and the star’s arms stretch. Due to the resemblance to real flowers we called those stars “nanoblossoms”. Figure 2.8. (Chapter 2. 4) shows the hydrodynamic radius after uninterrupted illumination. The intensity weighted size distributions according to CONTIN analysis were then monomodal for most measurements, even if the light scattering experiment was repeated hours later. If one interrupts the illumination (e.g. for DLS measurement) and continues the illumination afterwards a small fraction of aggregates (around 100 nm) appears in the intensity weighted size distributions after 11 min of UV-illumination (and 3 interruptions). Those aggregates were not visible for uninterrupted illumination with same irradiation time. With interruptions the Rh of the single stars is after 45 min close to the expected 18 nm. But since the aggregates might slightly
influence the Rh of the single stars during CONTIN analysis and since we do not understand the mechanism of the development of species with long diffusion times, we do not further discuss the interrupted illumination.
Chapter 5 also describes a way of dissolving the polymer-counterion complex by UV-irradiation (see chapter 5 for details). The solution turns slightly turbid after one day by keeping the already photodissolved solution in darkness. A precipitate was observed after one week. The supernatant solutions stayed yellowish but the precipitate can be redissolved by UV illumination. This behavior is not yet understood. Maybe the photoaquation process is slightly reversible slowly producing trivalent counterions after irradiation. However the photoaquation of [Co(CN)6]3- is reported to be irreversible.17, 18 Also partial hydrolysis of the polymer’s quaternary amine moiety by developed hydroxide could lead to an ampholytic polymer with changed solubility.