Measurement Results of Bare Nickel Nanoparticles

which involves repeated drying and washing steps that bring the particles into close contact. Even by using strong ultrasound sonication, these agglomerates cannot be separated. By the improved fabrication method without drying steps resulting in noble metal shell coated nanorods, aggregational problems can be avoided and single particle dispersions can be obtained, which will be shown later in chapter 5.4.3.

can be assumed that the small area of the protein's cross section points toward the nanorod surface (upright oriented binding) with the result that the amount of used BSA is sucient for at least ve times full coverage of the nanorods, if hexagonal dense packing of the protein is expected. Eects related to a change of the sample viscosity upon protein addition can be neglected, as measurements with a micro-viscometer did not reveal viscosity changes within a resolution of 1%

of the measured value.¹¹

Figure 5.20.: Phase lag spectra of Ni nanorod dispersions without and with addition of BSA protein. Frequency phase lag spectra are recorded at three dierent eld magnitudes. (a) Without addition of BSA. (b) After BSA addition at a concentration of 128 nM. Measured data (dots) is tted by calculated phase spectra (solid lines).¹¹

The model ts include integration over Gaussian distributions of the plain nanorod parameters (length, diameter, and magnetic moment) and the main free parameter for tting, which is the hydrodynamic shell thickness. This shell is the sum of the PVP surfactant layer, the stagnant surface layer of immobile uid, and a layer of adhered target proteins on the nanorod surface. While the geometric nanorod parameters (mean values and standard deviation of the length and the diameter) are determined by TEM imaging (see Fig. 5.5), the magnetic moment is deduced from VSM measurements (see chapter 5.1.2). Good model ts were obtained by reducing the magnetic moment by 20 % to a value of 3.0·10^-17 Am². The reason for the reduction of the magnetic moment is that the VSM measure-ments were carried out three weeks prior to the PlasMag measuremeasure-ments and that Ni experiences a progressing surface oxidation. A decrease of the magnetic vol-ume of the Ni nanorods by 20 %, corresponds to a surface oxide layer of about 1.3 nm thickness, which agrees to reported values in the literature.¹⁵³ A standard deviation of the magnetic moment of 2.1·10^-17 Am² for the best t manifests it-self in the curvature of the phase lag spectra. The hydrodynamic shell thickness

extracted from the tting procedure as the free parameter is 12±8 nm for bare Ni nanorods and 34±24 nm after BSA addition. Thus, the addition of BSA results in an increase of the mean hydrodynamic shell thickness of 22 nm. Regarding the dimensions of the BSA molecule and its polarity, as mentioned above, this increase represents a reasonable value. The remaining dierence can be attributed to an increase of the stagnant surface layer of immobile uid.¹¹

Fig. 5.21 shows phase lag spectra of Ni nanorods with and without addition of BSA for a single eld strength of 1 mT. Absolute phase lag values of Ni nanorods are shown in black (without BSA) and grey (with BSA) and the relative phase dierence is shown in blue and corresponds to the right axis. Phase dierences of approximately 22^◦ are obtained at an external magnetic eld frequency of 330 Hz.

Therefore, protein binding can be easily detected by the PlasMag measurement method.

Figure 5.21.: Phase spectra of Ni nanorods with and without addition of protein at an external magnetic eld amplitude of 1 mT and corresponding relative phase dierence. The dots represent measured values, while the lines correspond to the calculated ts. The relative phase dierence (blue) reaches a maximum value of about 22^◦ at a frequency of 330 Hz.

Determination of bound BSA amount by electrophoretic mobility measurements

The amount of bound protein to the surface of the employed Ni nanorods has been evaluated independently by measuring the electrophoretic mobility of nanorods with and without adhered protein. Therefore, a commercial Zetasizer has been used (Malvern Zetasizer Nano ZS, Model ZEN3600). All samples were washed prior to the measurements and redispersed in ultrapure water to remove unbound

protein. The washing procedure involved a magnetic separation of the particles from the solution by using a small permanent magnet. Electrophoretic mobility measurements of 6 samples (three each with and without BSA) have been carried out. The results presented here, reect the calculated mean values. Mobility val-ues of 2.71·10^-8 m²/Vs for bare Ni nanorods and -1.05·10^-8 m²/Vs for Ni nanorods with bound BSA have been determined. The change of the sign of the mobility values upon BSA addition already indicates protein binding.¹¹ The Debye length 1/κ(see chapter 3.1) is experimentally determined from the ionic strength (IS) of the sample solution (see equation 5.1), while the ionic strength itself follows from the measured conductivity of the sample solution. The conductivity Λ amounts to about 2.0 µS/cm for all measured samples, which indicates a successful wash-ing of the nanorod dispersions. The ionic strength can be calculated under the assumption of a small salt concentration by IS[µM] ≈ 9.3·Λ[µS/cm].¹⁵⁴ This results in Debye lengths for both samples of about 70 nm.

κ⁻¹[nm] = 9.6

pIS[mM] (5.1)

The product of the inverse Debye lengthκand the hydrodynamic particle radius Rdetermines the model that can be used for interpreting electrophoretic mobility measurements and calculating the zeta potential. The radiusRcorresponds to the distance from the center of the particle to the slip plane boundary (see chapter 3.1 and Fig. 3.5 for more details on the zeta potential). For cylindrical particles, this is the hydrodynamic particle radius and corresponds to the sum of the magnetic core radius and the additional hydrodynamic shell thickness.¹⁵⁵ Therefore, the product κR amounts to 0.36 for Ni nanorods without protein (R = 13 nm + 12 nm) and 0.67 for Ni nanorods with bound protein (R = 13 nm + 34 nm).

The geometry of the used nanorod has to be considered for calculating the zeta potential from measured electrophoretic mobilities. A model that can be used here, was developed by Ohshima¹⁵⁵ and is valid for all values of the κR product and, for an arbitrary orientation of the nanorods during the measurement. This model will be discussed in more detail in the following paragraphs.¹¹

For cylindrical particles aligned perpendicular to the applied electric eld, the electrophoretic mobility µ can be expressed as^{156, 157}

µ= _r0

η ζf(κR) (5.2)

with the Henry function f(κR)which is given by¹⁵⁵ f(κR) = 1

2

1 + 1

(1 + 2.55/[κR(1 +exp(−κR))])²

, (5.3)

where _r (78.5) is the relative permittivity, ₀ is the permittivity of vacuum with a value of 8.854·10^-12, η is the uid viscosity, ζ denotes the zeta potential, κ the inverse Debye length and R the cylinder radius. The Henry function is valid for all values of the product κR and for low zeta potentials.¹⁵⁵

For an arbitrarily oriented cylinder, the mobility averaged over a random dis-tribution of orientations is of the form:

µav = 1

3µpar+ 2

3µperp, (5.4)

with µ_par the mobility for parallel orientation of the cylinder to the electric eld andµ_perp the mobility for perpendicular alignment.¹⁵⁸ This can be expressed with Henry's function as¹⁵⁵

µ_av = _r0

3η ζ(1 + 2f(κR)). (5.5)

Inserting the values ofκ,R, and the measured mobilityµ_av, mean zeta potentials ζ of +55 mV for bare Ni nanorod samples, and -21 mV for BSA coated nanorod samples are obtained. As mentioned above, the Ni nanorods possess a thin oxide layer on their surface. Nickel oxide has a point of zero charge (see equation 3.3 in chapter 3.1) at a pH value of about 8, which is above the pH value of the used Ni nanorod sample solution (pH = 5.4).¹⁵⁹ Therefore, positive values of the zeta potential are reasonable.¹¹

The surface charge density for cylindrical particles can be deduced from the zeta potential.¹⁶⁰ In general electrolyte solutions, the surface charge density of a cylindrical particle is given by

σ= r0κkBT

e I, (5.6)

with the Boltzmann constant k_B, the temperature T = 295 K, the elementary electric charge e, and a factor

I = 2 sinh y_s

2

1 + 1

β² −1

1 cosh²(y_s/4)

¹₂

, (5.7)

where

β = K₀(κR)

K₁(κR), (5.8)

which depends on modied Bessel functions K_n(z) of the second kind of order n.¹⁶⁰

Furthermore, the scaled potential y and the scaled surface potential y_s are of the form:¹⁶⁰

y= eψ

k_BT (5.9)

and

ys= eψ_s

k_BT. (5.10)

The electrical potential at a certain radial distancer is ψ(r) and the potential on the particle surface ψ_s.¹⁶⁰

Applying equation 5.6 results in surface charge densities at the slip plane of +1.23·10^-3 C/m² for Ni nanorods without bound BSA, and -0.28·10^-3 C/m² for BSA coated nanorods.

The number of elementary charges on the particle surface is n= σA

e , (5.11)

withAdenoting the particle surface area, and amounts to +280 for a bare nanorod, and to -150 for a protein coated nanorod. Therefore, the mean change upon protein binding in elementary charge per nanorod equals to a number of 430.

According to literature, every BSA molecule carries a mean charge of -3.4 at the used pH value of 5.4.¹⁶¹ Therefore, a mean number of bound protein molecules can be calculated from the above mentioned change in overall surface charges upon protein binding. This value amounts to approximately 130 and corresponds to a protein surface density of 5.8 fmol/mm², which is reasonable compared to values of bound BSA densities on various surfaces reported in the literature ranging from 0.8 fmol/mm² to 54 fmol/mm².11, 162, 163

5.4.3. Measurement Results of Noble Metal Coated Cobalt