Gold Nanorods as Plasmonic Sensors for Particle Diffusion - The

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Gold Nanorods as Plasmonic Sensors for Particle Diffusion Verena Wulf, Fabian Knoch, Thomas Speck, and Carsten Sönnichsen J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02165 • Publication Date (Web): 17 Nov 2016 Downloaded from http://pubs.acs.org on November 20, 2016

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The Journal of Physical Chemistry Letters

Gold Nanorods as Plasmonic Sensors for

Particle Diffusion Verena Wulf,1 Fabian Knoch,2 Thomas Speck,2 and Carsten Sönnichsen1* 1

Institute of Physical Chemistry, University of Mainz, D-55128 Mainz, Germany 2

Institute of Physics, University of Mainz, D-55128 Mainz, Germany

*corresponding author: [email protected]

Abstract

Plasmonic gold nanoparticles are normally used as sensor to detect analytes permanently bound to their surface. If the interaction between the analyte and the nanosensor surface are negligible, it only diffuses through the sensor’s sensing volume, causing a small temporal shift of the plasmon resonance position. By using a very sensitive and fast detection scheme, we are able to detect these small fluctuations in the plasmon resonance. With the help of a theoretical model consistent with our detection geometry, we determine the analyte’s diffusion coefficient. The method is verified by observing the trends upon changing diffusor size and medium viscosity and the diffusion coefficients obtained were found to reflect reduced diffusion close to a solid interface. Our method, which we refer to as NanoPCS (for nanoscale plasmon correlation

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spectroscopy) is of practical importance for any application involving the diffusion of analytes close to nanoparticles.

TOC GRAPHIC

Measuring diffusion constants is a way to determine diffusor size1 and even reaction kinetics of inter-particle or particle-surface interaction.2-3 Diffusors are nanoparticles, colloids, or macromolecules, especially proteins. Commonly, the diffusion constant is measured by tracking the time a single diffusing particle/molecule spends in a given (small) observation volume. Most often, the diffusors are labeled with a fluorescent dye and the observation volume is defined by the focus of the excitation laser. This technique is usually referred to as fluorescence correlation spectroscopy (FCS).4-5 The observation volume and the diffusor concentration have to be small enough to ensure a measureable change of diffusor number within the observation volume over time – usually the temporal average of diffusors within the observation volume has to be between 0.1 and 1000.4 Many variations of correlation spectroscopy techniques exist, for example by creating an observation volume in total internal reflection (TIR) geometry6 or with a dark-field condenser.7,8 Apart from different illumination geometries, the labeling method can


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also be varied: Instead of fluorescent dyes the scattering of plasmonic nanoparticles can be detected.9 FCS and related techniques require attaching a (fluorescent) label to the diffusing analyte, which involves chemical modification steps and control experiments to ensure that the label does not interfere or change the system under investigation.10 Monitoring the plasmon resonance of gold nanorods offers an alternative to the fluorescence based FCS approach: the plasmon resonance changes when an analyte comes in close vicinity of the gold nanorod without the need of a label.11-13 A lot of effort is done to reduce the sensing volume of FCS methods to measure analytes in biologically relevant concentrations (micromolar or even millimolar range).14-16 In addition to the lack of labeling, plasmonic nanosensors offer an observation volume in the attoliter range,17 which allows to use such high analyte concentrations. We show in this work that it is indeed possible to use gold nanorods as an alternative to FCS by recording the plasmon resonance wavelength with high time resolution and spectral accuracy. Specifically, we monitor continuously the plasmon resonance of a single immobilized gold nanorod (referred to as nanosensor) by observing its scattered light when illuminated by a whitelight laser in TIR configuration. The nanosensors are exposed to a solvent (water) in a flow cell, which contains diffusors (either small gold or polystyrene nanoparticles). Diffusors entering and leaving the vicinity of the gold nanosensor, the ‘sensing volume’, cause a fluctuation in the plasmon resonance wavelength λres. In analogy to FCS, the autocorrelation of the plasmon resonance wavelength time trace λres(t) contains the information on the diffusion constant D. We have modified the commonly used FCS evaluation model18 to account for the geometry of the sensing volume around gold nanorods and the presence of the nanoparticle surface. Using our new theoretical model, we are able to extract diffusion constants from the measured plasmon resonance time traces λres(t). We demonstrate that the extracted diffusion constants correctly


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follow the Stokes-Einstein equation when we change diffusor-size, viscosity of the solvent and diffusor-concentration. These results show that plasmonic sensors give insights into the Brownian dynamics of unlabeled macromolecules and particles which opens the door to measure rate constants between unlabeled analytes and surfaces of coated gold nanorods.19 For our measurements, plasmonic gold nanorods are deposited randomly on a glass flow-cell resulting in a microfluidic device that allows to flush diffusors in and out.20 These nanosensors are illuminated with a supercontinuum white-light laser in total internal reflection (TIR) geometry.21

Figure 1. Nanosensor-based diffusion measurements via dark-field spectroscopy. Plasmonic gold nanorods immobilized in a microscope flow-cell scatter light under TIR-illumination (a).


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The scattered light of the nanorods can be spectrally resolved and detected with high time resolution. At each frame, the plasmon resonance wavelength λres is extracted by fitting the measured spectrum with a Lorentz curve (b). Analytes diffusing through the sensing volume of a nanorod cause fluctuations in the sensor‘s plasmon resonance wavelength λres (c). Evaluating the autocorrelation of these fluctuations with the help of a theoretical model enables to extract the diffusion coefficient D of the diffusors (d). The light elastically scattered by a single nanosensor is collected by the objective of a microscope (Figure 1a). Spectra are recorded by an electron multiplying charge-coupled device (EMCCD) coupled to a transmission spectrometer allowing to detect the spectra of the sensor with an acquisition time of 79 µs. The plasmon resonance wavelength (λres) is obtained by a Lorentzian fit to every spectrum (Figure 1b) resulting in a time series or time trace λres(t). The diffusors change the polarizability in the nearby environment of the plasmonic nanosensor, which results in a fluctuating time trace (δλres(t) = λres(t)-‹λres(t)›) (Figure 1c). To obtain the diffusion coefficient of a diffusor in the sensor’s environment, we extract information from the autocorrelations (Figure 1d) of the fluctuating signal employing a mathematical model adapted to the geometry of the nanosensors with effective volume Veff (see Supporting Information). According to this model and assuming independent diffusors, the normalized autocorrelation function G(τ) of our signal follows as: =

〈 〉 〈 〉

= ⁄∥ , ⁄

(1)

Where the concentration of the diffusors c only appears in the pre-factor. The function H describes lateral diffusion in and out of the sensing volume of the nanosensor with aspect ratio = / (with l as length and d the diameter of the nanorod). The time constant ∥ = ⁄4


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depends on the diffusion coefficient D of the diffusors and a lateral length = √ ∙ . The diffusion perpendicular to the flow-cell surface is described by the function Z with time constant

= ! ⁄ ∥ , where ! is the effective penetration depth of the sensitivity of the nanosensor (see Supporting Information for the explicit expression for both functions). For large lag times ≫ ∥ the asymptotic decay of the autocorrelation function is independent of the nanosensor geometry. We then obtain ~%

&'(

which is the same result found for FCS (Figure 2

and Supporting Information).

Figure 2. Comparison of modeling function for NanoPCS and FCS for varying geometries of the sensing volume. Theoretical lines are shown for different geometries of the sensing volumes, i.e. different ratios of ! / . In our model z0 is the decay length of the sensitivity of the nanosensor and r0 is a lateral length of the nanorod = √ ∙ with a fixed aspect ratio = / = 2.27 defined by the nanosensors used for the measurements (a). In standard FCS, the sensing volume is defined by a focused laser beam approximated with a three dimensional Gaussian decaying


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laterally with r0 and in axial direction with z0 (b). Both models show the same asymptotic behavior for longer whereas for faster both functions are dependent on the geometry of the different sensing volumes. The measured signal contains detector noise with , being the corresponding concentration of ‘spurious’ diffusors contained in the normalization resulting in an amplitude of the autocorrelation function not exclusively dependent on diffusor concentration. The detector noise has a temporal correlation that is much shorter that the resolution of the signal, leading to an apparent value < 1 of the normalized autocorrelations smaller than unity. As our signal is normalized with the variance and thus includes fast detector noise, the normalized function G apparently goes to 0 = ,/, + , . This value increases with increasing analyte concentration. For the aspect ratio α we use a fixed value (α = 2.27) that was determined from transmission electron microscopy (TEM) images (Supporting Information, Figure S1). Evaluating the calculated autocorrelations with function (1) is a three parameter fit yielding the pre-factor (, ), the decay time of the diffusors ∥ , and the ratio ! ⁄ which depends on the nanosensor’s geometry. The diffusion coefficient follows from ∥ = ⁄4. To test our system, we investigated the influence of the medium viscosity and the concentration of diffusors. While a higher viscosity of the medium slows down diffusion, a change in diffusor concentration should not affect their diffusion behavior as long as the volume fraction of the diffusors remains small. As diffusors we use small gold nanospheres with a mean particle diameter of 20 nm coated with methoxy-polyethylene glycol (Au@mPEG). The PEGcoating prevents particle aggregation and their attachment to the surface of the flow-cell as well as the sensor. The medium viscosity η was varied by an increasing amount of glycerol in water. Viscosities were measured with a rotational viscometer.


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We measured the diffusors in 5%, 15% and 25% glycerol in water, resulting in viscosities of

η5% = 1.08 mPas,

η15% = 1.50 mPas

and

η25% = 2.10 mPas,

respectively.

The

diffusor

concentration was varied in a medium containing 15% glycerol by dilution (1:1 and 1:3) resulting in particle concentrations in the nM range. The particle concentration was determined via UV-vis spectroscopy, measuring particle adsorption at 400 nm.22 For each of the parameters mentioned above, we measure about 5 different nanosensors. Each nanosensor is used to record a minimum of three time traces over 20 s, each of which is used to extract a decay time ∥ according to equation (1).

Figure 3. Diffusion time ∥ increases with increasing viscosity and is independent on diffusor concentration. Examples for single nanosensor autocorrelations are shown (a and c). Data points show the measured autocorrelation curves of single particles, solid lines are the corresponding


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fits. An increased medium viscosity (blue: η1=1.08 mPas; green: η2=1.50 mPas; red: η3=2.10 mPas) results in a change in diffusion times and the amplitude of the autocorrelation, while different relative diffusor concentrations (blue: 0.25; green: 0.5; red: 1; all in the nM range) simply change the amplitude of the autocorrelation function (c). Insets in (a) and (c) are normalized to demonstrate this effect. Mean parallel diffusion times ∥ of all sensors and their standard error quantify this results (b and d): An increased viscosity results in the expected linear increased diffusion time with a slope mainly dependent on the sensor’s dimensions while a change in diffusor concentration does not influence ∥ (trendlines in b and d). Figure 3 shows examples for the autocorrelations and the corresponding fitted lines for varying viscosities (Figure 3a) and varying diffusor concentrations (Figure 3c). An increasing medium viscosity changes the decay time ∥ and the autocorrelation amplitude. Increasing the diffusor concentration affects only the autocorrelation amplitude, which is best observed when normalizing the autocorrelations to the first value (Figure 3a and c insets). The measurements presented in Figure 3a and c were repeated at several different sensors. The mean decay times ∥ obtained for all these experiments support the above mentioned observations quantitatively: The mean decay time ∥ increases linearly with increasing medium viscosity (Figure 3b) as expected from ∥ = ⁄4 with ~1/1. The decay time should not dependent on diffusor concentration. Our results (Figure 3d) confirm this prediction. Furthermore, the ratio ! ⁄ , another fit parameter, is an intrinsic property of the nanosensors, independent on the diffusors. It should not show much variation in between measurements – and indeed, the fits yield values within a very small range: ! ⁄ = 0.076 ± 0.002. This value is consistent with the value ! ⁄ = 0.08 calculated from known particle properties: the average lateral length given by the dimensions of the nanosensors =


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√ ∙ = 56.9 78 (Supporting Information, Figure S1), and the decay length of the sensitivity of the nanorod from its surface ! = 16.1 78 determined by BEM simulations.23-24 The diffusion behavior of particles should depend solely on their size and shape, not their material or composition. As an additional test, we determine therefore the diffusion coefficients of various types of particles, differing in surface coating, size and core material. Specifically, we use methoxy-polyethylene glycol coated gold nanospheres (Au@mPEG) and carboxypolyethylene glycol coated gold nanospheres (Au@cPEG) to obtain particles with different surface chemistry but comparable hydrodynamic radii. Furthermore, we measure polystyrene nanospheres (PS-NP) with a larger hydrodynamic radius to show that our results have the expected size dependency (Figure 4a).


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Figure 4. Diffusion coefficients are solely dependent on particle size and reflect diffusion close to a solid surface. We measured diffusors with varying surface chemistry, particle core material, and varying sizes: Gold nanoparticles coated with carboxy-PEG (Au@cPEG) and methoxy-PEG (Au@mPEG) with similar hydrodynamic radii of RH,Au@mPEG = (17.33 ± 1.11) nm and RH,Au@cPEG = (18.47 ± 1.16) nm and polystyrene nanoparticles with RH,PSNP = (29.61 ± 0.52) nm, respectively (a). Normalizing the obtained diffusion coefficients for each diffusor type on the viscosity ( ∙ 1) and comparing them to the data obtained by DLS, shows the same size dependency of the diffusion coefficients for both methods. The diffusion coefficients measured in NanoPCS are consistently lower by a factor of (DDLS/DNanoPCS = 10.94 ± 0.86) due to the fact that measurements are performed close to a surface (b). Specifically, we determined the hydrodynamic radii (via dynamic light scattering) as: RH, Au@mPEG = 17.33 ± 1.11 nm, RH, Au@cPEG = 18.47 ± 1.16 nm (the small size difference is caused by a slightly longer PEG-chain in the case of cPEG), and RH, PS-NP = 29.61 ± 0.52 nm. Every type of particles was measured in the three different glycerol/water ratios used above. The diffusion coefficients D are obtained with equation (1) using the constant value of the sensor specific dimension = 56.8 78 and the relation ∥ = ⁄4. Normalizing the obtained diffusion coefficients to the viscosity of the medium (Dη) results in a constant for each particle type that only depends on their hydrodynamic radius (RH, Au@mPEG < RH, Au@cPEG < RH, PS-NP). Comparing these values to normalized diffusion coefficients obtained by dynamic light scattering (DLS), we find consistently larger values for DLS. However, there is a constant factor DDLS/DNanoPCS = 10.9 ± 0.8 (Figure 4b). This constant factor points towards an interesting effect: in DLS particles are free to diffuse in all directions whereas in our experimental setup, the measurement is close to the supporting glass surface. Simulations predict a decrease of the


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diffusion coefficient close to a solid surface in the same range as measured (Supporting Information, Figure S4). Additionally our results show that the inhomogeneous sensitivity (larger at the tip than at the sides) averages out as predicted theoretically.25 We have also addressed the question about the limits of NanoPCS towards smaller analytes, in particular macromolecules. As outlined in section G of the supporting information, using a smaller nanosensor (in combination with a stronger light source) would provide enough signal to detect fluctuations caused by macromolecules of 5 nm size or even lower. The most important technical issue would be to increase the time resolution two orders of magnitude to capture the fast fluctuations of those macromolecules. Shifting from the acquisition of full spectra to intensity changes at single frequencies could easily provide the necessary improvement.31 Using plasmonic gold nanorods as sensors to detect diffusion of particles in their near environment is a new approach for label-free sensing of analytes in their thermodynamic equilibrium. We show that this method is suitable to determine diffusion coefficients and the hydrodynamic radii of particles diffusing in solution and that these values follow the expected trends: being independent from material, surface chemistry and concentration, but dependent on the viscosity of the solution and the particles size. Our measurements allow to identify the influence of a surface on particle diffusion through its viscous drag. Although our technique, working without labels, cannot distinguish between different analytes, it offers valuable insights into the diffusion properties of particles and macromolecules at or near surfaces, which is an important first step for particle uptake by cells,26-28 drug delivery by nano-carriers29-30 and many other applications of nanotechnology.


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Supporting Information. The Supporting Information is available free of charge. Detailed information on materials, sensor and diffusor synthesis, characterization and functionalization, setup description, additional control measurements and simulations, description of the theoretical model for data evaluation (PDF) Corresponding Author *[email protected]

Acknowledgements This work was financially supported by the ERC Grant 259640 (“Single Sense”) and by the DFG through TRR 146 (F.K. and T.S.). We thank Mathias Schmitt for some help in particle synthesis and Dr. Wolfgang Schärtl for help with DLS measurements.


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Gold Nanorods as Plasmonic Sensors for Particle Diffusion - The

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