Block copolymers are polymers consisting of two chemically different polymeric blocks that are coval — Analytical Chemistry Chemistry Question
Self-assembly of Amphiphilic Block Copolymers
Block copolymers are polymers consisting of two chemically different polymeric blocks that are covalently attached one to the other. Amphiphilic block copolymers consist of a hydrophilic and a hydrophobic block. Such molecules behave in analogy to low-molecular mass surfactants, but they can form larger aggregates in a size range from 5 nm to several µm, so that they allow further applications.
Block copolymers can vary in the relative lengths of their blocks. In the illustration below, the hydrophobic parts are black and the hydrophilic parts are grey. Note that the polymers are flexible chains.
[VISUAL] Which of these block copolymers do you expect to form spherical micelles, vesicles (bilayers), or which of them will show phase separations when given into a) water and b) toluene?
Model Answer
in water:
I: spherical micelles
II: phase separation
in toluene:
I: phase separation
II: spherical micelles
Two block copolymers consisting of poly(vinylpyridine) (PVP) and polystyrene (PS), PVP23-b-PS122 (A) and PVP45-b-PS122 (B), form ”inverse” spherical micelles in toluene (PVP inside, PS outside). Aggregation numbers are determined via membrane osmometry. The solutions contain only micelles while monomers have been removed (which is possible for block copolymers). Here, we regard the solutions as ideal so that the van´t Hoff equation is valid:
Π V = n R T.
Π is the osmotic pressure.
The soutions of A and B, both with concentrations of of c = 8.000 g dm–3 are analyzed. The heights of the solvent columns above the solvent in osmotic equilibrium with the polymer-containing solutions are 11.02 mm and 2.48 mm for polymer A and polymer B, respectively.
(ρ(solvent) = 0.866 g cm–3 and T = 298.15 K).
What are the aggregation numbers N of the two samples?
Model Answer
M(PVP-monomer) = 105.15 g mol-1
M(PS-monomer) = 104.16 g mol-1
M(A) = 15125.97 g mol-1
M(B) = 17439.27 g mol-1
The molar mass of the micelles M(micelle) can be obtained from the osmosis experiment. Notice that the molar concentration cmo (mol dm–3) refers to the mass concentration cma (g dm–3):
cmo = cma / M(micelle) and cmo = n / V , n = cmo · V
Π V = n R T ⇒ Π = cmo RT ⇒ M(micelle) = cma RT / Π
The osmotic pressure is counterbalanced by the pressure of the solvent column above the solution, thus Π = ρ g h.
M(micelle) = cma RT / (ρ g h)
For micelle A: h = 11.02 mm ⇒ Π = 93.62 Pa
M(micelle A) = 211820 g mol-1
For micelle B: h = 2.48 mm ⇒ Π = 21.07 Pa
M(micelle B) = 941231 g mol-1
The aggregation number N is obtained from the molar mass of the micelles and block copolymers:
N(A) = M(micelle A) / M(A) = 211820 / 15125.97 = 14
N(B) = M(micelle B) / M(B) = 941231 / 17439.27 = 54
Colloidal metal particles are of high interest due to their special optical, electric and magnetic properties, applications as catalysts etc. Block copolymer micelles in organic solvent can be used as confined reaction compartments (”nanoreactors”) for the preparation of such small metallic particles.
Two polymers C and D in toluene have the following properties (R is the micelle radius and N is the aggregation number):
C: PVP123-b-PS118 with R = 25 nm, N = 310
D: PVP63-b-PS122 with R = 21 nm, N = 123
Tetrachlorogoldacid-tri-hydrate (HAuCl4·3 H2O, ”gold acid”) is added to the polymer solution and the mixture is stirred for several hours. While the gold compound is normally insoluble in toluene, the yellow colour of the solution indicates that it has solubilized within the micelles.
Two experiments are made with each polymer: a) the addition of 0.01 g and b) the addition of 0.05 g of HAuCl4·3 H2O to 10 cm3 of polymer solution (c(polymer) = 10 g dm–3).
In all cases, the total amount of added HAuCl4·3 H2O is solubilized.
In a second step, a reducing agent such as hydrazine or sodium borohydride (sodium boranate) is added. The solution turns red or blue indicating the formation of metallic gold nanoparticles.
The micelle size does not change after the solubilization of HAuCl4·3 H2O and reduction.
Write down the reaction equations for the two reductions.
Model Answer
Reduction with hydrazine: hydrazine can react to give nitrogen or nitrogen and NH3.
4 HAuCl4·3 H2O + 3 N2H4 → 4 Au + 3 N2 + 16 HCl + 12 H2O
or
2 HAuCl4·3 H2O + 6 N2H4 → 2 Au + 3 N2 + 6 NH4Cl + 2 HCl + 6 H2O
Reduction with sodium borohydride:
8 HAuCl4·3 H2O + 3 NaBH4 → 8 Au + 3 NaB(OH)4 + 12 H2O + 32 HCl
It is observed that one gold particle is formed in each micelle. Gold particles are spherical and show a narrow size distribution. There is no redistribution of gold during the process of particle formation, but HAuCl4·3H2O that has solubilized inside one micelle (by uniform distribution among the micelles) forms one particle.
ρ(Au) = 19.3 g cm–3
Which gold particle diameters do you expect for the four experiments with the two polymers and the two given amounts of added gold acid?
Model Answer
M(C) = 25224.33 g mol-1
M(D) = 19331.97 g mol-1
M(micelle C) = N × M(C) = 7819542.3 g mol-1
M(micelle D) = N × M(D) = 2377832.31 g mol-1
cmo(micelle C) = 1.2788×10^-6 mol dm-3
cmo(micelle D) = 4.2055×10^-6 mol dm-3
When M(HAuCl4·3 H2O) = 393.84 g mol-1, the molar concentration of HAuCl4·3 H2O for the two cases a) and b) is:
a) cmo(HAuCl4·3 H2O) = 2.5391×10^-6 mol dm-3
b) cmo(HAuCl4·3 H2O) = 0.0127 mol dm-3
Hence, the equivalents of HAuCl4·3 H2O that have been added per micelle (z(Au, micelle)) is:
z(Au, micelle) = cmo(HAuCl4·3 H2O) / cmo(micelle) (I)
We obtain the gold colloid mass m(Au, colloid) and by its volume V the radius r and diameter d of the spherical gold colloid:
m(Au, micelle) = z(Au, micelle) × M(Au) / Na
m(Au, colloid) = m(Au, micelle)
V(Au, colloid) = 4/3 * pi * r^3 and V(Au, colloid) = m(Au, colloid) / rho(Au)
r = (3 * m(Au, colloid) / (4 * pi * rho(Au)))^(1/3)
d = 2 * (3 * z(Au, micelle) * M(Au) / (4 * pi * rho(Au) * Na))^(1/3) (II)
With M(Au) = 196.97 g mol-1 and ρ(Au) = 19.3 g cm-3, equations (I) and (II) lead to:
- Polymer C, a) 0.01g Au-acid: z(Au, micelle) = 1985, d = 4.0 nm
- Polymer C, b) 0.05g Au-acid: z(Au, micelle) = 9931, d = 6.8 nm
- Polymer D, a) 0.01g Au-acid: z(Au, micelle) = 604, d = 2.7 nm
- Polymer D, b) 0.05g Au-acid: z(Au, micelle) = 3019, d = 4.6 nm
Why is one gold particle per micelle preferentially formed instead of multiple smaller particles inside one micelle?
Model Answer
The surface of a gold colloid is energetically unfavourable, because the surface atoms have fewer neighbours and thus contribute less crystallization energy than inner “bulk” gold atoms (surface tension is based on the same phenomenon, so that reasoning based on surface tension is correct as well). The total surface area of larger particles is smaller. Therefore, particles tend to become as large as possible (by direct growth or coagulation) to decrease the ratio of surface area to volume.
Additional notes:
1. This is the reason why e.g. metallic gold forms as a macroscopic precipitate rather than colloids if you reduce gold ions in an aqueous solution without any additives. In the block copolymer micelles, however, growth is restricted due to compartmentalization.
2. Many small gold colloids inside one micelle can form if the inner polymer block has functional groups that attach to the surface of the gold with a gain in energy: the colloids are "stabilized". If a fast reduction creates many nuclei inside one micelle, multiple small gold colloids can be stabilized. Further, small colloids are often kinetically stabilized, because the activation energy for their coagulation is higher than the thermal energy.