Measuring the refractive index and sub-nanometre surface functionalisation of nanoparticles in suspension

Abstract

Direct measurements to determine the degree of surface coverage of nanoparticles by functional moieties are rare, with current strategies requiring a high level of expertise and expensive equipment. Here, a practical method to determine the ratio of the volume of the functionalisation layer to the particle volume based on measuring the refractive index of nanoparticles in suspension is proposed. As a proof of concept, this technique is applied to poly(methyl methacrylate) (PMMA) nanoparticles and semicrystalline carbon dots functionalised with different surface moieties, yielding refractive indices that are commensurate to those from previous literature and Mie theory. In doing so, it is demonstrated that this technique is able to optically detect differences in surface functionalisation or composition of nanometre-sized particles. This non-destructive and rapid method is well-suited for in situ industrial particle characterisation and biological applications.

Fig. 1. A pictorial representation of the technique. Incident light on a capillary creates a fringe pattern that shifts by Δϕ depending on the nanoparticle morphology and volume fraction. The nanoparticles in the suspension are modelled as core of radius r_c and refractive index n_c, surrounded by a shell of outer radius r_t and refractive index n_s. The full core–shell particle can be considered a single, homogeneous particle of effective refractive index n_p.

Fig. 2. A diagram reproduced from Mulkerns et al. showing the backscattering interferometer used here. A coherent laser beam is incident on a thermally stabilised capillary tube containing the nanoparticle solution, creating an interference pattern due to the reflections at the multiple interfaces of the capillary. This pattern of fringes is then imaged by the camera and transferred to a computer for analysis.

Fig. 3. A graph showing how the refractive index of the overall particle suspension varies with mass fraction for Rayleigh PMMA nanoparticles and unfunctionalised carbon dots in water using BSI. The experimental results obtained for PMMA (green squares) and the Mie theory data (orange circles) match well, indicating the ability to measure the refractive index of nanoparticles. The carbon dot data (CD, blue triangles) can be fitted and eqn (5) used to determine their refractive index. Note that error bars are present, but too small to see on this plot; a typical error on a measurement is σ ≈ 2 × 10⁻⁶ RIU.

Fig. 4. Representations of carbon dot (CD), CD-lactose (CD-Lac), and CD-lactose dendrimer (CD-Lac3) particles are shown in A. B shows a graph of the experimentally measured change in refractive index of the solution as a function of CD mass fraction. Blue triangles refer to data for unfunctionalised CDs, orange squares to CDs functionalised with lactose and green circles are data for CDs functionalised with a lactose-based tri-dendrimer. The difference in the gradients in B shows that the various surface functionalisations can be differentiated easily. The inset of B shows a magnified copy of the data at low mass fraction. Note that error bars are present on all data, but can only be seen in the inset; a typical error on a measurement is σ ≈ 2 × 10⁻⁶ RIU.