# Maximizing the Surface Sensitivity of LSPR Biosensors through Plasmon Coupling—Interparticle Gap Optimization for Dimers Using Computational Simulations

## Abstract

**:**

## 1. Introduction

## 2. Simulation Methods

_{0}) was always the longer axis, and the coupling and interparticle gap (D) were defined in the longitudinal direction. The dielectric environments were modeled with a constant refractive index (e.g., air n = 1 and water n = 1.33). The molecular layers deposited on the nanoparticles were modeled as a dielectric shell of n = 1.5, corresponding well with the equivalent refractive index used to model dense DNA monolayers in an aqueous environment [25,27,44]. The different simulation conditions are illustrated in Figure 1.

_{1}= 1 to n

_{2}= 1.33, both for single particles ($\Delta {\lambda}_{p,sp}$) and for dimers ($\Delta {\lambda}_{p,dim}$). Contrary to RIS, where the RI change affects the whole accessible volume of the plasmonic electric field, surface sensitivity measures only a fraction of the field closest to the surface of the nanoparticles [37]. The surface sensitivity was obtained as the peak shift experienced upon adding a dielectric shell with a thickness of t and an RI of n

_{l}= 1.5 in a constant dielectric environment of n = 1.33.

_{∞}, while the EF

_{t=x}form refers to an EF obtained by depositing a layer with a thickness of t = x nm on the nanoparticles. This annotation also indicates that the bulk EF is technically the same as the surface EF for a layer with a thickness of t = ∞.

## 3. Results and Discussion

_{0}) of 70 nm were used, with a 7 nm interparticle distance (D) in the case of the dimers. This interparticle distance (D/D

_{0}= 0.1) was small enough to properly excite the Σ coupled mode (in-phase bonding mode [45]) in the dimers that caused an increased peak shift upon the same RI change compared to single particles. The obtained extinction peak shifts for the bulk RI change were $\Delta {\lambda}_{p,sp}$ = 26.3 nm for a single nanosphere (RIS

_{sp}= 78.9 nm/RIU) and $\Delta {\lambda}_{p,dim}$ = 62.6 nm for the dimers (RIS

_{dim}= 187.8 nm/RIU), which yielded a bulk enhancement factor (EF

_{∞}) of 2.38. By depositing a dielectric layer of 5 nm thickness and n

_{l}= 1.5, the experienced extinction peak shifts were $\Delta {\lambda}_{p,sp}$ = 6.1 nm and $\Delta {\lambda}_{p,dim}$ = 18.2 nm (Figure 2b), corresponding to an enhancement of 2.98 (EF

_{t=5nm}).

_{0}, which corresponds well with previous results on Au, Ag, In, and Si nanospheres and nanocubes [33,35,46].

_{0}was smaller. In this sense, the initial sensitivity advantage of nano-ellipsoids practically diminishes for D/D

_{0}< 0.1.

_{l}= 1.5 in water medium, with n

_{m}= 1.33). The diameter of the particles was 70 nm, with a 10 nm interparticle gap (D/D

_{0}= 0.14). As shown in Figure 4a, dimers of the same particle type always had a larger peak shift, consistent with their increased RIS due to plasmonic coupling. In Figure 4b, the relative extinction peak shifts were calculated as the ratio of $\Delta {\lambda}_{p}/\Delta {\lambda}_{p-max}$, where $\Delta {\lambda}_{p-max}$ is defined as the peak shift upon changing the RI of the whole medium from 1.33 to 1.5 (or, in other words, coating the nanoparticles with a layer of infinite thickness, t = ∞).

_{d}) of the nanoparticles, which can be extracted from Figure 4a by using Equation (3) [37]. In our case, the three curves belonging to the single particles can be perfectly fitted with Equation (3) (R

^{2}= 0.999), resulting in decay lengths of 33 nm (c = 1, nanosphere), 27.2 nm (c = 1.5, ellipsoid), and 25.4 nm (c = 2, ellipsoid). For single particles, the calculated l

_{d}showed a negative correlation with both $\Delta {\lambda}_{p}$ and c, demonstrating that for nano-ellipsoids, the longitudinal mode focused the field, which accounted for higher peak shift and overall sensitivity.

_{t}values were 3.2, 2.4, and 2.1 for the three nanoparticle types, respectively. The practical meaning of EF

_{t}is, for example, that dimer nanospheres of 70 nm diameter and 10 nm gap provide a 3.2 times higher signal compared to uncoupled spheres of the same size with t = 5 nm layer thickness. EF

_{∞}, on the other hand, is the ratio between the RIS of dimers (228.2 nm/RIU) and single particles (124.7 nm/RIU), which was ~1.8 for these nanospheres. As shown in Figure 4d, for small layer thicknesses, EF

_{t}was higher than EF

_{∞}, which means an increased sensing performance for thin layers. Figuratively, the 3.2 vs. 1.8 difference in EF

_{t}and EF

_{∞}means that the coupled nanospheres with 228.2 nm/RIU RIS will respond to a 5 nm-thick layer as a single particle with 405.7 nm/RIU RIS would.

_{0}= 0.28 case. It can clearly be seen that the 7 nm layer occupies the most sensitive regions (with the highest field strength) that are confined between the nanoparticles. By depositing thin layers on top of the nanoparticles, we worked in the most sensitive near-field region. Again, it has to be pointed out that Figure 4c,d showed a local maximum around t = D/2 thickness when the deposited layers touched and filled the interparticle gap. Above t = D (10 nm), the EF showed an exponential decay, and EF

_{t}→ EF

_{∞}at t = ∞.

_{0}= 70 nm, and the interparticle gap was decreased, thus scaling the dimensionless D/D

_{0}. The enhancement factors were again calculated as the ratio of the presented dimers and single particles of the same size. The characteristic of the curves (exponential decay) is similar to what can be seen in Figure 3 for the bulk sensitivity tests, but a clear elevation of the left side of the curves is visible in Figure 6a,c. Based on Figure 6d, this is clearly the yield of the increased surface sensitivity. Again, please note that the curves in Figure 6b,d have a clear maximum, around D/D

_{0}= 0.1–0.15, which translates to a 7–10 nm interparticle distance, which is also in the t = D/2 range. For nanospheres, in this region, the effective utilization of the plasmon field could reach around 80% (Figure 6b).

_{0}) in the 0.08–1 range [52]. A similar excellent control over the nanoparticle arrangement on large surface areas (cm

^{2}range) was recently reported by using a template-assisted solid-state dewetting synthesis and subsequent nanoparticle transfer to a transparent polymer support [23].

_{0}trends significantly.

## 4. Conclusions

## Supplementary Materials

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Dimitriev, A. Nanoplasmonic Sensors. Integrated Analytical Systems; Springer: New York, NY, USA, 2012. [Google Scholar]
- Sepúlveda, B.; Angelomé, P.C.; Lechuga, L.M.; Liz-Marzán, L.M. LSPR-Based Nanobiosensors. Nano Today
**2009**, 4, 244–251. [Google Scholar] [CrossRef] - Sriram, M.; Zong, K.; Vivekchand, S.R.; Gooding, J.J. Single nanoparticle plasmonic sensors. Sensors
**2015**, 15, 25774–25792. [Google Scholar] [CrossRef] - Liu, J.; He, H.; Xiao, D.; Yin, S.; Ji, W.; Jiang, S.; Luo, D.; Wang, B.; Liu, Y. Recent Advances of Plasmonic Nanoparticles and Their Applications. Materials
**2018**, 11, 1833. [Google Scholar] [CrossRef] - Rodrigues, M.S.; Borges, J.; Lopes, C.; Pereira, R.M.S.; Vasilevskiy, M.I.; Vaz, F. Gas Sensors Based on Localized Surface Plasmon Resonances: Synthesis of Oxide Films with Embedded Metal Nanoparticles, Theory and Simulation, and Sensitivity Enhancement Strategies. Appl. Sci.
**2021**, 11, 5388. [Google Scholar] [CrossRef] - Unser, S.; Bruzas, I.; He, J.; Sagle, L. Localized Surface Plasmon Resonance Biosensing: Current Challenges and Approaches. Sensors
**2015**, 15, 15684–15716. [Google Scholar] [CrossRef] [PubMed] - Jiang, J.; Wang, X.; Li, S.; Ding, F.; Li, N.; Meng, S.; Li, R.; Qi, J.; Liu, Q.; Liu, G.L. Plasmonic Nano-Arrays for Ultrasensitive Bio- Sensing. Nanophotonics
**2018**, 7, 1517–1531. [Google Scholar] [CrossRef] - Hong, J.; Huh, Y.-M.; Yoon, D.S.; Yang, J. Nanobiosensors Based on Localized Surface Plasmon Resonance for Biomarker Detection. J. Nanomater.
**2012**, 2012, 1. [Google Scholar] [CrossRef] - Chen, J.-S.; Chen, P.-F.; Lin, H.T.-H.; Huang, N.-T. A Localized surface plasmon resonance (LSPR) sensor integrated automated microfluidic system for multiplex inflammatory biomarker detection. Analyst
**2020**, 145, 7654–7661. [Google Scholar] [CrossRef] [PubMed] - Keshavarz, M.; Tan, B.; Venkatakrishnan, K. Label-Free SERS Quantum Semiconductor Probe for Molecular-Level and in Vitro Cellular Detection: A Noble-Metal-Free Methodology. ACS Appl. Mater. Interfaces
**2018**, 10, 34886–34904. [Google Scholar] [CrossRef] - Fong, K.E.; Yung, L.-Y.L. Localized surface plasmon resonance: A unique property of plasmonic nanoparticles for nucleic acid detection. Nanoscale
**2013**, 5, 12043–12071. [Google Scholar] [CrossRef] [PubMed] - Bonyár, A. Label-Free Nucleic Acid Biosensing Using Nanomaterial-Based Localized Surface Plasmon Resonance Imaging: A Review. ACS Appl. Nano Mater.
**2020**, 3, 8506–8521. [Google Scholar] [CrossRef] - Liu, Z.; Liu, G.; Liu, X.; Fu, G. Plasmonic sensors with an ultrahigh figure of merit. Nanotechnology
**2020**, 31, 115208. [Google Scholar] [CrossRef] [PubMed] - Yang, J.; He, X.; Zhang, J.; Huang, J.; Chen, D.; Han, Y. Plasmonic Refractive Index Sensor with High Figure of Merit Based on Concentric-Rings Resonator. Sensors
**2018**, 18, 116. [Google Scholar] - Liu, B.; Chen, S.; Zhang, J.; Yao, X.; Zhong, J.; Lin, H.; Huang, T.; Yang, Z.; Zhu, J.; Liu, S.; et al. A Plasmonic Sensor Array with Ultrahigh Figures of Merit and Resonance Linewidths down to 3 nm. Adv. Mater.
**2018**, 30, 1706031. [Google Scholar] [CrossRef] - Tu, M.H.; Sun, T.; Grattan, K.T.V. LSPR Optical Fibre Sensors Based on Hollow Gold Nanostructures. Sens. Actuators B
**2014**, 191, 37–44. [Google Scholar] [CrossRef] - Min, J.; Wang, Y. Manipulating Bimetallic Nanostructures with Tunable Localized Surface Plasmon Resonance and Their Applications for Sensing. Front. Chem.
**2020**, 8, 441. [Google Scholar] [CrossRef] - Loiseau, A.; Zhang, L.; Hu, D.; Salmain, M.; Mazouzi, Y.; Flack, R.; Liedberg, B.; Boujday, S. Core–Shell Gold/Silver Nanoparticles for Localized Surface Plasmon Resonance-Based Naked-Eye Toxin Biosensing. ACS Appl. Mater. Interfaces
**2019**, 11, 46462–46471. [Google Scholar] [CrossRef] [PubMed] - Gartia, M.R.; Hsiao, A.; Pokhriyal, A.; Seo, S.; Kulsharova, G.; Cunningham, B.T.; Bond, T.C.; Liu, G.L. Colorimetric Plasmon Resonance Imaging Using Nano Lycurgus Cup Arrays. Adv. Opt. Mater.
**2013**, 1, 68–76. [Google Scholar] [CrossRef] - Guo, L.; Jackman, J.A.; Yang, H.; Chen, P.; Cho, N.; Kim, D. Strategies for enhancing the sensitivity of plasmonic nanosensors. Nano Today
**2015**, 10, 213–239. [Google Scholar] [CrossRef] - Svedendahl, M.; Chen, S.; Dmitriev, A.; Käll, M. Refractometric Sensing Using Propagating versus Localized Surface Plasmons: A Direct Comparison. Nano Lett.
**2009**, 9, 4428–4433. [Google Scholar] [CrossRef] - Kabashin, A.V.; Evans, P.; Pastkovsky, S.; Hendren, W.; Wurtz, G.A.; Atkinson, R.; Pollard, R.; Podolskiy, V.A.; Zayats, A.V. Plasmonic Nanorod Metamaterials for Biosensing. Nat. Mater.
**2009**, 8, 867–871. [Google Scholar] [CrossRef] [PubMed] - Lednický, T.; Bonyár, A. Large Scale Fabrication of Ordered Gold Nanoparticle-Epoxy Surface Nanocomposites and Their Application as Label-Free Plasmonic DNA Biosensors. ACS Appl. Mater. Interfaces
**2020**, 12, 4804–4814. [Google Scholar] [CrossRef] [PubMed] - Klinghammer, S.; Uhlig, T.; Patrovsky, F.; Böhm, M.; Schütt, J.; Pütz, N.; Baraban, L.; Eng, L.M.; Cuniberti, G. Plasmonic Biosensor Based on Vertical Arrays of Gold Nanoantennas. ACS Sens.
**2018**, 3, 1392–1400. [Google Scholar] [CrossRef] [PubMed] - Schneider, T.; Jahr, N.; Jatschka, J.; Csaki, A.; Stranik, O.; Fritzsche, W. Localized Surface Plasmon Resonance (LSPR) Study of DNA Hybridization at Single Nanoparticle Transducers. J. Nanopart. Res.
**2013**, 15, 1531. [Google Scholar] [CrossRef] - Thamm, S.; Csàki, A.; Fritzsche, W. LSPR Detection of Nucleic Acids on Nanoparticle Monolayers. Methods Mol. Biol.
**2018**, 1811, 163–171. [Google Scholar] - Kaye, S.; Zeng, Z.; Sanders, M.; Chittur, K.; Koelle, P.M.; Lindquist, R.; Manne, U.; Lin, Y.; Wei, J. Label-Free Detection of DNA Hybridization with a Compact LSPR-Based Fiber-Optic Sensor. Analyst
**2017**, 142, 1974–1981. [Google Scholar] [CrossRef] - Ruemmele, J.A.; Hall, W.P.; Ruvuna, L.K.; Van Duyne, R.P. A Localized Surface Plasmon Resonance Imaging Instrument for Multiplexed Biosensing. Anal. Chem.
**2013**, 85, 4560–4566. [Google Scholar] [CrossRef] - Chen, H.; Kou, X.; Yang, Z.; Ni, W.; Wang, J. Shape- and Size-Dependent Refractive Index Sensitivity of Gold Nanoparticles. Langmuir
**2008**, 24, 5233–5237. [Google Scholar] [CrossRef] - Saison-Francioso, O.; Lévêque, G.; Boukherroub, R.; Szunerits, S.; Akjouj, A. Dependence between the Refractive-Index Sensitivity of Metallic Nanoparticles and the Spectral Position of Their Localized Surface Plasmon Band: A Numerical and Analytical Study. J. Phys. Chem. C
**2015**, 119, 28551–28559. [Google Scholar] [CrossRef] - Su, K.-H.; Wei, Q.-H.; Zhang, X.; Mock, J.J.; Smith, D.R.; Schultz, S. Interparticle Coupling Effects on Plasmon Resonances of Nanogold Particles. Nano Lett.
**2003**, 3, 1087–1090. [Google Scholar] [CrossRef] - Jain, P.K.; Huang, W.; El-Sayed, M.A. On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation. Nano Lett.
**2007**, 7, 2080–2088. [Google Scholar] [CrossRef] - Bonyár, A.; Csarnovics, I.; Szántó, G. Simulation and characterization of the bulk refractive index sensitivity of coupled plasmonic nanostructures with the enhancement factor. Photonics Nanostruct. Fundam. Appl.
**2018**, 31, 1–7. [Google Scholar] [CrossRef] - Fu, T.; Du, C.; Chen, Y.; Zhang, R.; Zhu, Y.; Sun, L.; Shi, D. Enhanced RI Sensitivity and SERS Performances of Individual Au Nanobipyramid Dimers. Plasmonics
**2021**, 16, 485–491. [Google Scholar] [CrossRef] - Zhang, R.X.; Sun, L.; Du, C.L.; Fu, T.Y.; Chen, Y.X.; Rong, W.X.; Li, X.; Shi, D.N. Plasmonic properties of individual heterogeneous dimers of Au and In nanospheres. Phys. Lett. A
**2021**, 391, 127131. [Google Scholar] [CrossRef] - Fu, T.Y.; Chen, Y.X.; Du, C.L.; Yang, W.C.; Zhang, R.X.; Sun, L.; Shi, D.N. Numerical investigation of plasmon sensitivity and surface-enhanced Raman scattering enhancement of individual TiN nanosphere multimers. Nanotechnology
**2020**, 31, 135210. [Google Scholar] [CrossRef] [PubMed] - Li, J.; Ye, J.; Chen, C.; Li, Y.; Verellen, N.; Moshchalkov, V.V.; Lagae, L.; Van Dorpe, P. Revisiting the Surface Sensitivity of Nanoplasmonic Biosensors. ACS Photonics
**2015**, 2, 425–431. [Google Scholar] [CrossRef] - Read, T.; Olkhov, R.V.; Shaw, M.A. Measurement of the localised plasmon penetration depth for gold nanoparticles using a non-invasive bio-stacking method. Phys. Chem. Chem. Phys.
**2013**, 15, 6122–6127. [Google Scholar] [CrossRef] - Jatschka, J.; Dathe, A.; Csáki, A.; Fritzsche, W.; Stranik, O. Propagating and localized surface plasmon resonance sensing—A critical comparison based on measurements and theory. Sens. Bio-Sens. Res.
**2016**, 7, 62–70. [Google Scholar] [CrossRef] - Hohenester, U.; Trügler, A. MNPBEM—A Matlab toolbox for the simulation of plasmonic nanoparticles. Comput. Phys. Commun.
**2012**, 183, 370–381. [Google Scholar] [CrossRef] - Trügler, A. Optical Properties of Metallic Nanoparticles: Basic Principles and Simulation; Springer: Berlin/Heidelberg, Germany, 2016. [Google Scholar]
- Waxenegger, J.; Trügler, A.; Hohenester, U. Plasmonics simulations with the MNPBEM toolbox: Consideration of substrates and layer structures. Comput. Phys. Commun.
**2015**, 193, 138–150. [Google Scholar] [CrossRef] - McPeak, K.M.; Jayanti, S.V.; Kress, S.J.P.; Meyer, S.; Iotti, S.; Rossinelli, A.; Norris, D.J. Plasmonic films can easily be better: Rules and recipes. ACS Photonics
**2015**, 2, 326–333. [Google Scholar] [CrossRef] [PubMed] - Maliwal, B.P.; Kusba, J.; Lakowicz, J.R. Fluorescence energy transfer in one dimension: Frequency-domain fluorescence study of DNA−fluorophore complexes. Biopolymers
**1995**, 35, 245–255. [Google Scholar] [CrossRef] - Deng, T.-S.; Parker, J.; Yifat, Y.; Shepherd, N.; Scherer, N.F. Dark Plasmon Modes in Symmetric Gold Nanoparticle Dimers Illuminated by Focused Cylindrical Vector Beams. J. Phys. Chem. C
**2018**, 122, 27662–27672. [Google Scholar] [CrossRef] - Fu, T.Y.; Du, C.L.; Chen, Y.X.; Zhang, R.X.; Sun, L.; Li, X.; Rong, W.X.; Shi, D.N. SERS and RI sensing properties of heterogeneous dimers of Au and Si nanospheres. Mod. Phys. Lett. B
**2021**, 35, 2150378. [Google Scholar] [CrossRef] - Xu, H.; Käll, M. Modeling the Optical Response of Nanoparticle-Based Surface Plasmon Resonance Sensors. Sens. Actuators B
**2002**, 87, 244–249. [Google Scholar] [CrossRef] - Saran, R.; Wang, Y.; Li, I.T.S. Mechanical Flexibility of DNA: A Quintessential Tool for DNA Nanotechnology. Sensors
**2020**, 20, 7019. [Google Scholar] [CrossRef] [PubMed] - Lee, S.; Sim, K.; Moon, S.Y.; Choi, J.; Jeon, Y.; Nam, J.; Park, S. Controlled Assembly of Plasmonic Nanoparticles: From Static to Dynamic Nanostructures. Adv. Mater.
**2021**, 2007668. [Google Scholar] [CrossRef] - Lerch, S.; Reinhard, B.M. Quantum Plasmonics: Optical Monitoring of DNA-Mediated Charge Transfer in Plasmon Rulers. Adv. Mater.
**2016**, 28, 2030–2036. [Google Scholar] [CrossRef] - Kasani, S.; Curtin, K.; Wu, N. A review of 2D and 3D plasmonic nanostructure array patterns: Fabrication, light management and sensing applications. Nanophotonics
**2019**, 8, 2065–2089. [Google Scholar] [CrossRef] - Wei, S.; Zheng, M.; Xiang, Q.; Hu, H.; Duan, H. Optimization of the particle density to maximize the SERS enhancement factor of periodic plasmonic nanostructure array. Opt. Express
**2016**, 24, 20613–20620. [Google Scholar] [CrossRef]

**Figure 1.**Illustration of the different simulation conditions and the definitions of bulk RI sensitivity (RIS) and surface sensitivity. Symbols: D

_{0}—nanosphere diameter, D—interparticle distance (gap), $\Delta {\lambda}_{p}$—extinction peak shift (for single particles, sp, and dimers, dim), t—dielectric layer thickness, n

_{l}—dielectric layer refractive index.

**Figure 2.**Normalized extinction spectra simulated on single-particle and dimer arrangements of gold nanospheres to illustrate the changes in bulk RI sensitivity (

**a**) and surface sensitivity (

**b**) caused by plasmonic coupling between the nanospheres. For the illustration of the different conditions, please see Figure 1.

**Figure 3.**(

**a**) Extinction peak shift of coupled plasmonic dimers ($\Delta {\lambda}_{p,dim}$) and their calculated bulk refractive index sensitivity (RIS) as a function of the dimensionless D/D

_{0}value, where D is the interparticle distance, and D

_{0}is the particle diameter (D

_{0}= 70 nm). (

**b**) Calculated bulk enhancement factor (EF

_{∞}) values compared to single, uncoupled particles with the same size as a function of D/D

_{0}.

**Figure 4.**(

**a**) Extinction peak shift ($\Delta {\lambda}_{p}$) of different single-particle and dimer arrangements as a function of the deposited dielectric layer thickness (n

_{l}= 1.5 in water, medium with n = 1.33). The diameter of the particles was 70 nm, with a 10 nm interparticle gap (D/D

_{0}= 0.14). (

**b**) The relative extinction peak shift as a function of the layer thickness where $\Delta {\lambda}_{p-max}$ was calculated as the peak shift upon changing the RI of the medium from 1.33 to 1.5. (

**c**) Enhancement factor (EF

_{t}) as a function of the layer thickness. (

**d**) Difference between surface and bulk enhancement factors (EF

_{t}− EF

_{∞}) as a function of the layer thickness.

**Figure 5.**(

**a**) An assembled nano-ellipsoid dimer in the MNPBEM toolbox, without layers in dielectric medium (n = 1.33). (

**b**) Sectional perspective of the same nano-ellipsoid dimer with a deposited dielectric layer (n

_{l}= 1.5) of 7 nm. The blue mesh represents the vertices of the gold ellipsoids, while the red mesh represents the surface of the dielectric layer. (

**c**) The distribution of the electric field around the gold nano-ellipsoid dimer is illustrated in (

**a**). The map represents the Z = 0 plane (top view). (

**d**) Electric field distribution for the dimer with dielectric layers illustrated in (

**b**).

**Figure 6.**(

**a**) Extinction peak shift ($\Delta {\lambda}_{p}$) of different dimer arrangements as a function of the dimensionless D/D

_{0}value (D

_{0}= 70 nm) with a dielectric layer of 5 nm (n

_{l}= 1.5 in water medium, with n = 1.33). (

**b**) Relative extinction peak shift as a function of the dimensionless D/D

_{0}value, where $\Delta {\lambda}_{p-max}$ is calculated as the peak shift upon the RI of the medium changing from 1.33 to 1.5. (

**c**) Enhancement factor (EF

_{t=5nm}) as a function of D/D

_{0}. (

**d**) Difference between surface and bulk enhancement factors (EF

_{t=5nm}− EF

_{∞}) as a function of D/D

_{0}.

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**MDPI and ACS Style**

Bonyár, A.
Maximizing the Surface Sensitivity of LSPR Biosensors through Plasmon Coupling—Interparticle Gap Optimization for Dimers Using Computational Simulations. *Biosensors* **2021**, *11*, 527.
https://doi.org/10.3390/bios11120527

**AMA Style**

Bonyár A.
Maximizing the Surface Sensitivity of LSPR Biosensors through Plasmon Coupling—Interparticle Gap Optimization for Dimers Using Computational Simulations. *Biosensors*. 2021; 11(12):527.
https://doi.org/10.3390/bios11120527

**Chicago/Turabian Style**

Bonyár, Attila.
2021. "Maximizing the Surface Sensitivity of LSPR Biosensors through Plasmon Coupling—Interparticle Gap Optimization for Dimers Using Computational Simulations" *Biosensors* 11, no. 12: 527.
https://doi.org/10.3390/bios11120527