Use of catalytic nanoparticles opens new ways to study and to understand catalysis. The exiting meas — Analytical Chemistry Chemistry Question
Catalytic transformation of a single molecule on a single nanoparticle
Use of catalytic nanoparticles opens new ways to study and to understand catalysis. The exiting measurements were performed at Cornell University (NY, USA). The researchers observed the catalytic transformation of single molecules on the surface of a spherical nanoparticle (d = 6 nm) formed by Au atoms.
The experimental design is shown in Fig.1.
The dissolved А was transformed into dissolved В in the presence of Au nanoparticles, adsorbed on the glass slide. The reaction product В is a fluorescent molecule while the reagent A is not. Continuous laser light producing fluorescence was focused within a small surface area containing a single Au nano-particle. The time dependence of fluorescence on the wavelength characteristic for B, adsorbed on the Au nanoparticle is shown in Fig. 2.
The fluorescence of B in the solution could not be detected under the experimental conditions. The same intensity of fluorescence was observed periodically for the time intervals τ2. The fluorescence disappeared during the time intervals τ1 between the peaks (see Fig. 2). The researchers have performed their measurements for long periods of time and for many different single Au nanoparticles. As a result the averaged values of [τ1] and [τ2] were obtained.
Answer the following questions about this experiment and the conclusions made by its authors.
Estimate the number of the Au atoms in a single nanoparticle if its density is equal the bulk density of Au, 19.32 g cm–3. What fraction of Au atoms is involved in the catalysis if catalytically active is the surface layer with the depth equal to two atomic diameters of Au (dAu = 0.350 nm)?
Model Answer
a) VAu nano = 4/3 πR3 = 1.13 ⋅ 10–19 cm3,
mAu nano = 1.13 ⋅ 10–19 cm3 × 19.32 g cm–3 = 2.18⋅10–18 g,
NAu atoms = 2.18 ⋅ 10–18 g / (196.97 / 6.02⋅1023) = 6675 atoms.
b) f = Vsurface / VAu nano = (VAu nano – Vcore) / VAu nano = 1 – (r^3(core) / r^3(Au nano)) = 1 – (3 – 0.7)^3 / 3^3 = 0.55.
The resolution of the instruments made it possible to measure the fluorescence emitted from 1 µm2 area. The number density of Au nanoparticles on the glass slide was 0.035 particle⋅µm–2. What was the probability (%) of observing fluorescence from a single Au nanoparticle?
Model Answer
Suppose you detect a signal from a particular 1µm2 area. The probability to have one particle within this area is 0.035. For two particles such probability is (0.035)^2 and for three it is equal to (0.035)^3 etc.
The probability that the detected signal originates from a single Au nanoparticle is:
p = 0.035 / (0.035 + (0.035)^2 + (0.035)^3 + ... ) = 1 - 0.035 = 0.965 = 96.5 %
The authors claimed that each peak in Fig. 2 corresponds to the fluorescence of a single molecule В adsorbed on Au nanoparticle. What was the main argument of the authors?
Model Answer
В is the only fluorescent molecule in the system. The fluorescence of B in the solution could not be detected under the experimental conditions. Thus the signal is detectable as long as B is seating on the Au nanoparticle. The consistent height of the peaks (Fig. 2) indicates that each peak comes from a single molecule. If it were from many molecules, the peaks would have variable heights depending on the number of molecules.
Consider adsorption of А on Au nanoparticles to be a fast reversible process. Let m catalytic sites exist on the surface of a single nanoparticle. The fraction of catalytic sites occupied by molecules A, is equal to θA = Kads[A] / (1 + Kads[A]).
Relate [τ1] and [τ2] to the rates of catalytic production/desorption of a single molecule B on/from a single Au nanoparticles.
Model Answer
[τ2] is an average time necessary to desorb a single molecule B from a single catalytic site on Au nanoparticle. The rate of desorption of B molecules from a single catalytic site of Au nanoparticle is
rdes = 1 / [τ2] = kdes
where kdes is the rate constant for one catalytic site.
[τ1] is the average time necessary to form a single molecule B on a single Au nanoparticle. The number of catalytic sites occupied by substrate A is
mθA = m Kads[A] / (1 + Kads[A])
All these sites equally participate in catalytic formation of a single B on a single Au nanoparticle,
rcat = 1 / [τ1] = kcat mθA = kcat m Kads[A] / (1 + Kads[A])
where kcat is the rate constant for one catalytic site.
Plot [τ1]–1 and [τ2]–1 as a function of concentration of А in the solution.
Model Answer
[τ2]–1 is independent of [A], [τ1]–1 increases with the increase of [A] and approaches constant value when Kads[A] >> 1 (see Answer 6.4)
How will [τ1]–1 and [τ2]–1 change with the increase of nanoparticle diameter from 6 to 12 nm?
Model Answer
[τ2]–1 does not vary. [τ1]–1 is proportional to the number of catalytic cites, m, which is in turn proportional to the area of the surface of Au nanoparticle. [τ1]–1 varies as the square of diameter i.e. in our case increases by a factor of 4. (See Answer 6.4)