Surface Plasmon Resonance on Nanoscale Organic Films

Abstract

Over the past 20 years, surface plasmon resonance (SPR) has evolved into a very versatile detection method, particularly in bioscience applications. Not only the scientific literature has greatly expanded, but also the various commercial vendors of instrumentation, detection chips, and reagents have emerged. In the scientific sphere, the accent lies more and more on fabrication of nanostructures with interesting optical behavior (plasmonics), while in the R&D area, there are many new miniaturization efforts and combination with other detection methods, such as electrochemistry and quartz crystal microbalance (QCM). The present chapter will focus on the latest developments in making functional biochemical coatings for SPR detection as well as will review the basic theory behind the detection techniques.

Appendices

Appendix A

The Jones matrix I _ifor reflection/transmission at an interface between layer i and i + 1 is based on the Fresnell reflection/transmission coefficients r _i and t _i, according to:

$${\rm{I}}_i = \left( {\frac{1}{{t_i }}} \right)\left({\begin{array}{lll}1 & {r_i } \\{r_i } & 1\\\end{array}}\right),$$

where in the case of p-polarized light, the coefficients are:

$$r_i = \frac{{\hat n_{i+ 1} c_i - \hat n_i c_{i+ 1} }}{{\hat n_{i+ 1} c_i+ \hat n_i c_{i+ 1} }} and \,t_i = \frac{{2\hat n_i c_i }}{{\hat n_{i+ 1} c_i+ \hat n_i c_{i+1} }}$$

in the case of s-polarised light, the coefficients are:

$$r_i = \frac{{\hat n_i c_i - \hat n_{i+ 1} c_{i+ 1} }}{{\hat n_i c_i+ \hat n_{i+ 1} c_{i+ 1} }} and\, t_i = \frac{{2\hat n_i c_i }}{{\hat n_i c_i+ \hat n_{i+ 1} c_{i+ 1} }}.$$

The Jones matrix L _i for the light absorption in layer i takes the form, according to the Lambert-Beer law as:

$${{\rm{L}}_i = \left( {\begin{array}{lll}{{\rm{e}}^{ - i\beta _i } } & 0 \\0 &{{\rm{e}}^{i\beta_i}} \\\end{array}} \right)\,\rm with\,\, \beta _i = \frac{{2\pi }}{\lambda }d_i }\it \hskip-3pt n_i \it c_i $$

(when using the convention $\hat n = n+ ik)\,$ $where\, c_i = \cos (\theta _i ) = \sqrt {1 - \frac{{\hat n_1^2 }}{{\hat n_i^2 }}\sin ^2 (\theta _1 )}.$

Appendix B

Reaction Schemes and rate equations for the most frequently used binding systems, from [57] in modified form.

One-to-one reaction

$${\bf{A}}{\rm{ }}+{\rm{ }}{\bf{B}} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over{\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {\bf{AB}}$$

$${\rm{d}}R/{\rm{d}}t = k_{\rm{a}} \cdot \left[ {\rm{A}} \right] \cdot (R_{{\rm{max}}} - R){\rm{ }} - k_{\rm{d}} \cdot R$$

One-to-one reaction with mass transfer

$${\bf{A}}^\ast \mathbin{\bf{A}}{\rm{ }}+ {\rm{ }}{\bf{B}} \mathbin {\bf{AB}}$$

$${\rm{d}}\left[ {\rm{A}} \right]/{\rm{d}}t{\rm{ }} = k_{\rm{t}} \cdot \left( {\left[ {{\rm{A}}^\ast} \right] - \left[ {\rm{A}} \right]} \right){\rm{ }}-k_{\rm{a}} \cdot \left[ {\rm{A}} \right] \cdot \left( {R_{{\rm{max}}} - R} \right){\rm{ }}+ k_{\rm{d}} \cdot R$$

$${\rm{d}}R/{\rm{d}}t = k_{\rm{a}} \cdot \left[ {\rm{A}} \right] \cdot \left( {R_{{\rm{max}}} - R} \right){\rm{ }}-k_{\rm{d}} \cdot R$$

One-to-two reaction (bivalent analyte)

$${\bf{A}}{\rm{ }}+ {\rm{ }}{\bf{B}} \mathbin {\bf{AB}}\,\,\,\,\,\,\,{\rm{ }}{\bf{A}}{\rm{ }}+ {\rm{ }}{\bf{AB}} \mathbin {\bf{A}}_{\bf{2}} {\bf{B}}$$

$${\rm{d}}R_{\rm{1}} /{\rm{d}}t = k_{{\rm{a1}}} \cdot \left[ {\rm{A}} \right] \cdot \left( {R_{{\rm{max}}} - R_{\rm{1}} - R_{\rm{2}} } \right){\rm{ }}-k_{{\rm{d1}}} \cdot R_{\rm{1}} -k_{{\rm{a2}}} \cdot \left[ {\rm{A}} \right] \cdot R_{\rm{1}}+ k_{{\rm{d2}}} \cdot R_{\rm{2}} $$

$${\rm{d}}R_{\rm{2}} /{\rm{d}}t = k_{{\rm{a2}}} \cdot \left[ {\rm{A}} \right] \cdot R_{\rm{1}} -k_{{\rm{d2}}} \cdot R_{\rm{2}}$$

Two-state reaction

$${\bf{A}}{\rm{ }}+{\rm{ }}{\bf{B}} \mathbin {\bf{AB}}\,\,\,\,\,\,{\rm{ }}{\bf{AB}} \mathbin {\bf{AB}},$$

$${\rm{d}}R_{\rm{1}} /{\rm{d}}t = k_{{\rm{a1}}} \cdot \left[ {\rm{A}} \right] \cdot \left( {R_{{\rm{max}}} - R_{\rm{1}} - R_{\rm{2}} } \right){\rm{ }}-k_{{\rm{d1}}} \cdot R_{\rm{1}} -k_{{\rm{a2}}} \cdot R_1 + k_{{\rm{d2}}} \cdot R_{\rm{2}}$$

$${\rm{d}}R_{\rm{2}} /{\rm{d}}t = k_{{\rm{a2}}} \cdot R_{\rm{1}} -k_{{\rm{d2}}} \cdot R_{\rm{2}}$$

Competing analyte

$${\bf{A}}{\rm{ }}+ {\rm{ }}{\bf{B}} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over{\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {\bf{AB}}\,\,\,\,\,\,\,\,{\rm{ }}{\bf{C}}{\rm{ }}+ {\rm{ }}{\bf{B}} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over{\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {\bf{CB}}$$

$${\rm{d}}R_{\rm{1}} /{\rm{d}}t = k_{{\rm{a1}}} \cdot \left[ {\rm{A}} \right] \cdot \left( {R_{{\rm{max}}} - R_{\rm{1}} - p \cdot R_{\rm{2}} } \right){\rm{ }}-k_{{\rm{d1}}} \cdot R_{\rm{1}} $$

$${\rm{d}}R_{\rm{2}} /{\rm{d}}t = k_{{\rm{a2}}} \cdot \left[ {\rm{C}} \right] \cdot \left( {R_{{\rm{max}}} /p - R_{\rm{1}} /p - R_{\rm{2}} } \right){\rm{ }}-k_{{\rm{d2}}} \cdot R_{\rm{2}},$$

where A and C are the analyte species involved in the reaction, with square brackets indicating their concentration at the surface, and A* denoting species A in the bulk of the solution. B is the immobilized species, and AB, CB, AB’, and A₂B are the complexes formed at the surface, with R, R ₁, and R ₂ are the responses of the bound species, and R _max is the maximum response of species B. The parameter p is a correction factor, for example, to account for difference in molecular weight between species A and C. k is the rate constant, with a and d indicating the forward (association) and reverse (dissociation) reaction, and indices 1 and 2 indicating the equation

Surface Plasmon Resonance on Nanoscale Organic Films