Anal. Chem. 2004, 76, 6861-6870
Surface Plasmon Resonance: Theoretical Evolutionary Design Optimization for a Model Analyte Sensitive Absorbing-Layer System James M. Rooney and Elizabeth A. H. Hall*
Institute of Biotechnology, University of Cambridge, Tennis Court Road, Cambridge CB2 1QT, U.K.
Surface plasmon resonance (SPR) has been widely used in a Kretschmann configuration to study optical thickness changes of layers on a Au surface in response to an analyte. The method has been popularized and optimized for protein layers, but has also been used in the same format for other layers without further optimization including those absorbing at the incident wavelength. In this paper, we examine whether SPR remains the “best” attenuated reflectivity format for absorbing overlayers. Experimental data from the SPR response of a copper phthalocyanine film to nitrogen dioxide are used as an input example for a design process using an evolutionary algorithm. The data showed a trend toward thinner gold layer systems (∼25 nm gave an contrast-enhancement of 42.9% compared with ∼50-nm Au) or Au-free solutions including a layer with low refractive index. From the evolutionary design predictions, further modification could be tested based on available materials and “redundant layers” could be eliminated from the final selection. By inclusion of the external optics, a design could be selected to accommodate poor precision ((0.5°) in the incident angle and a possible multilayer solution was shown using Teflon AF 1600, with refractive index ∼1.3. The predicted NO2 response showed an improvement compared with the classical SPR configuration, and the incident angle chosen by the SGA for the interrogation of these layers was close to a stationary point in the absolute response curve, thus offering very good tolerance to automatic position referencing to the reflectivity minimum. Surface plasmon resonance (SPR) is a powerful analytical technique, able to detect minor changes in optical thickness of dielectric layers on a metal film and within the evanescent field.1,2 Using the now classical SPR Kretschmann configuration with ∼53nm Ag, detection of changes in refractive index of ∼5 × 10-7 have been reported.3 Various ingenious methods have also been devised * To whom correspondence should be addressed. E-mail: lisa.hall@ biotech.cam.ac.uk. (1) Peterlinz K.; Georgiadis R. Langmuir 1996, 12, 4731-4740. (2) Jonsson, U.; Fagerstam, L.; Ivarsson, B.; Johnsson, B.; Karlsson, R.; Lundh, K.; Lofas, S.; Persson, B.; Roos, H.; Ronnberg, I.; Sjolander, S.; Stenberg, E.; Stahlberg, R.; Urbaniczky, C.; Ostlin, H.; Malmqvist, M. Biotechniques 1991, 11(5), 620-627. (3) Nelson, S. G.; Johnston, K. S.; Yee, S. S. Sens. Actuators, B 1996, 35, 187191. 10.1021/ac0496751 CCC: $27.50 Published on Web 10/15/2004
© 2004 American Chemical Society
to increase resolution, centered on the use of metal nanoparticles to enhance the SPR,4,5 but as described by Knoll’s group,6 this introduces a more complex model, since both the metal and the overlayer are absorbing and the SPR signal is no longer related to the refractive index in the same way and may not be the best attenuated total reflection (ATR) format. This is more generally the case if the many reagents that react with an analyte with a change in absorbance are considered. For example, Boussaad et al.7 have examined the wavelength-dependent change in the SPR for cytochrome c and a similar response has been seen with π-conjugated polymer film spin-coated onto a gold film and then doped with iodine.8 In these instances, it could be convenient to use simple absorbance measurements, but increasingly, assays are designed in a format to avoid interference from the transparency or scattering character of the sample layer and to use “imobilized” reagents, where the measurement of the analyte-determining reaction is confined within the evanescent field of a film/layer on a substrate that provides suitable reagent immobilization chemistry and may also contribute to the optics of the response. SPR has arguably become the most widely used ATR method for both routine analytical laboratories and research. Most typically, a modified Au film is employed, adopting the SPR configuration initially optimized to probe protein overlayers of refractive index ∼1.4, but it would be convenient to expand this general ATR format for different materials. A greater choice of substrates would allow a much wider choice of surface chemistries to be considered. This can be examined by experimental iteration or by theoretical design processes, such as simulated annealing,9 Tabu search,10 and evolutionary algorithms (EAs),11 as used in other fields.12,13 In EAs, evolution is not implicit but is an emergent property of the algorithm obeying a set of rules due to the application of different operations. The genesis of the algorithm (4) Lyon L. A.; Musick M. D.; Natan M. J. Anal. Chem. 1998, 70, 5177-5183. (5) He, L.l; Musick, M.; Nicewarner, S.; Salinas, F.; Benkovic, S.; Natan, M.; Keating, C J. Am. Chem. Soc. 2000, 122, 9071-9077. (6) Ekgasit, S.; Thammacharoen, C.; Knoll, W. Anal. Chem. 2004, 76, 561568. (7) Boussaad, S.; Pean, J.; Tao, N. J. Anal. Chem. 2000, 72, 222-226. (8) Koh, K.; Kim; J.; Hur Y. Polym. Prepr. 2002, 43, 1401-1402. (9) Hasancebi, O.; Erbatur, F. Adv. Eng. Software 2002, 33, 681-696. (10) The, Y.; Ranagaiah, G. Comput. Chem. Eng. 2003, 27, 1665-1679. (11) Bentley, P. In Evolutionary Design by Computers; Bentley, P., Ed.; Morgan Kaufmann: San Francisco, 1999; pp 1-73. (12) Komarov, V. A.; Weisshaar, T. A. J. Aircraft 2002, 39, 227-233. (13) Negm, H. M.; Maalawi, K. Y. Comput. Struct. 2000, 74, 649-666.
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involves the creation of a population of possible solutions to the given problem, and the efficacy of each solution is then evaluated according to a set of “limitations” defined by the user (e.g., incident angle range, sensitivity, accuracy, reproducibility, material properties etc), which are then used as the driving force for the evolution.14 During the lifetime of a population, members are selected stochastically to create a generation of the “best” solutions, where the population size can be fixed or variable. Selected members of the new generation exchange information (the exact method depending on the type of EA) to give potentially better solutions. Mutation can also be introduced and is important in preventing the algorithm from stagnating at nonglobal optimums, by creating solutions that can be theoretically anywhere in the search space. Evolutionary methods have already been used to aid in the design and optimization of optical systems14 to generate complex shapes (commonly found in SLR cameras) or to optimize multilayer structures (such as antireflection coatings and wavelength rejection filters15). In the work reported herein, we revisit the SPR layer system and examine the use of such design optimization in multilayer reflection, taking the NO2 response involving an 18crown-6 copper phthalocyanine (CuPc) layer as a model for a system where a change of absorbance is involved in the assay. Analogues of phthalocyanine are a common reagent for nitrogen dioxide detection and have been extensively studied in the last 30 years.16,17 Metal phthalocyanines have strong absorbance bands18,19 in the range of 620-855 nm, with variations in the location due to coordinated metal, morphology, or peripheral substitutions.20 Thin absorbing phthalocyanine films spin-coated onto thin gold layers have shown broadening in the SPR curve and an increase in the resonance angle and reflectivity21,22 as predicted from theoretical models.6,7,23 Upon exposure of such films to nitrogen dioxide, the resonance reflectivity was seen to decrease (consistent with the decrease in absorbance at the excitation wavelength), with only a small shift in the resonance angle24 modulated according to metal and by peripheral substitution. MATERIALS AND METHODS Chemicals and Equipment. For the surface plasmon measurements, gold films were evaporated onto glass microscope slides (BDH). These slides were chemically cleaned with 2-propanol (Fisher 99.9%) and then physically by a “plasma glow” process prior to evaporation of gold. All the thin gold films used for SPR experiments were prepared in an Edwards Auto 306 evaporator at a pressure of ∼2 × 10-6 mbar. The thickness of the films was measured during evaporation by a FTM7 crystal (14) Bentley, P.; Wakefield, J., Eng. Des. Autom. 1997, 2(3), 119-131. (15) Martin, S.; Rivory, J.; Schoenauer, M. Appl. Opt. 1995, 34, 2247-2254. (16) Szuber, J.; Grz_dziel, L. Thin Solid Films 2000, 376, 214-219. (17) Newton, M.; Starke, T.; Willis, M.; McHale, G. Sens. Actuators, B 2000, 67, 307-311. (18) Hassan, A.; Ray, A.; Travis, J.; Ghassemlooy, Z.; Cook, M.; Abass, A.; Collins, R Sens. Actuators, B 1998, 49, 235-239. (19) Brunet, J.; Talazac, L.; Battut, V.; Pauly, A.; Blanc, J. P.; Germain, J. P.; Pellier, S.; Soulier, C. Thin Solid Films 2001, 391, 308-313. (20) Hassan, B.; Li, H.; McKeown, N. J. Mater. Chem. 2000, 10, 39-45. (21) Vukusic, P.; Sambles, J.; Wright, J. J. Mater. Chem. 1992, 2, 1105-1106. (22) Wright, J. D.; Cado, A.; Peacock S. J. Sens. Actuators, B 1995, 29, 108114. (23) Kurihara, K.; Suzuki, K. Anal. Chem. 2002, 74, 696-701. (24) Jory, M. J.; Cann, P. S.; Sambles, J. R. J. Phys. D 1994, 27, 169-174.
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monitor. To aid in adhesion of the gold to the microscope slides, a 0.5-nm film of chromium (chromium-plated tungsten rods, Megatech) was initially evaporated, followed by gold (99.9994% purity Alfa Aesar) at a rate of ∼0.1 nm s-1. The copper phthalocyanine with peripheral substitution of four 18-crown-6 rings (18-C-6 CuPc) was synthesized in-house and was a gift from Dr Sohna-Sohna. Films of 18-C-6 CuPc were spin-coated on to gold-coated glass from a 4 mM solution in chloroform giving layers between 30 and 45 nm. A KW-4A spin-coater from Chemat Technology was used at a spin speed of 2000 rpm. The method has been used previously to produce reproducible layers on gold for SPR.25 The UV-visible spectra of the phthalocyanine films were taken with a Perkin-Elmer Lambda 16 spectrometer. The background absorbance due to the gold-coated slide was measured after rinsing with ethanol to remove the phthalocyanine films. All the SPR readings were taken on a custom-built optical bench system. Light from a 632.8-nm He-Ne 4-mW laser, polarized in either the s- or p-polarization, was coupled into the SPR gold film by a hemicylindrical BK7 prism/flow cell unit mounted on a computer-controlled turntable. Compared with the triangular prism, this gives lower angular precision, since the beam inside the prism is not parallel (see also angular robustness test used for genetic algorithm). The reflected light from the SPR layers was collected by a photodiode and amplified, and the data were stored as comma delimited files. The Matlab package (The Mathworks) was used. Unless started otherwise, experimental data are presented as the ratios of the p-polarized to s-polarized reflectivity. This removes any errors from the response due to fluctuations in the input intensity. However, since there is little change in the s-polarization at the experimental detection angle (∼0.24%), the experimental response will be compared directly to theoretical responses based on the reflection of p-polarized light. THEORY Physical Models. The numerous recent theoretical models describing the reflectance from multilayers (stacks of thin films) with different dielectric properties are usually based on Fresnel’s reflection coefficients.6,26-30 Other approaches have started from the “exact” theory and then have diverged to produce approximations to aid in the fitting of reflection data.31,32 However, to move from an analyte-sensitive multilayer to an optical sensor33-36 also requires the external optics that couple the light from the source to the detector via the multilayers, but the optimization of these optics is seldom reported. (25) Hassan, A. K.; Ray, A. K.; Nabok, A. V.; Davis, F. Sens. Actuators, B 2001, 77, 638-641. (26) Connes P. J. Opt. 1986, 17, 5-28. (27) Zacher, T.; Wischeroff, E. Langmuir 2002, 18, 1748-1759. (28) Liao, C. H.; Shyu J. S. Jpn. J. Appl. Phys. 2001, 40, 4109-4113. (29) Monzon, J. J.; Sanchez-Soto, L. L. J. Opt. Soc. Am. A 1999, 16, 2013-2017. (30) Kurihara, K.; Nakamura, K.; Suzuki, K. Sens. Actuators, B 2002, 86, 4957. (31) Roy D. Appl. Spectrosc. 2001, 55, 1046-1052. (32) Palumbo, M.; Pearson, C.; Nagel, J.; Petty M. C. Sens. Actuators, B 2003, 90, 264-270. (33) Toyama, S.; Doumae, N.; Shoji, A.; Ikariyama, Y. Sens. Actuators, B 2000, 65, 32-34. (34) Hur, Y.; Ock, K.; Kim, K.; Jin, S.; Gal, Y.; Kim, J.; Kim, S.; Koh, K. Ana. Chim. Acta 2002, 460, 133-139. (35) Kieser, B.; Pauluth, D.; Gauglitz G. Anal. Chim. Acta 2001, 434, 231-237. (36) Faull, J. D.; Gupta V. K. Langmuir 2001, 17, 1470-1476.
Figure 1. (a) Simplified picture of an optical sensor with light coupled through a prism incident on a series of multilayers. The layers l1 to ln make up the transducer layers that are proposed to augment the change in optical properties of the final sensing layer. These multilayers are described by a chromosome, in relation to the prism and the sensing layer. (b) Diagram showing the rays involved in calculating the refraction and reflection at an interface between two optical materials.
Here we divide the model into two sections with overlapping boundaries: the internal optics (Figure 1), which depend on the optical and physical properties of the prism/coupler, and the multilayer structure, including the analyte sensing layer, based on the Fresnel coefficients. The external optics depend on the optical properties, physical size/shape, and location of the source, detector, and prism. The passage of light through the external optics can be modeled using ray tracing. The reflection coefficient of s- or p-polarized light, reflected from an interface between two materials of differing values of dielectric constant can be calculated using the Fresnel relation. Equation 1 has been used as the basis for predicting the reflection
( ) ( )
m+1 k - kz,m+1 m z,m rm,m+1 ) ) m+1 k + kz,m+1 m z,m
ray tracing technique37,38 with the rays described using the standard vector equation of a line (eq 3).39 The intersections of
ˆd × t R(t) ) Ro + R Ro ) ray origin R ˆ d ) ray direction t ) Distance travelled from ray origin
the rays with the surface are found mathematically by substituting eq 3 into the algebraic description of the surface and solving for the variable t. For the case of a planar surface at a perpendicular distance D from the origin with a surface normal of P ˆ n, the value of t is found using eq 4. At the intersection point, the incident ray
t)
amplitude reflection coefficient, from interface m ) dielectric constant for layer lm kz,m ) k vector for layer lm parallel to the plane
(1)
of p-polarized light from a series of layers as shown in Figure 1, For multilayer systems of n layers, the reflections, transmissions and propagations at each interface produce a reflection coefficient referred to as the Fresnel multilayer equation (eq 2).30
rk,... n )
rm,m+1 + rm+1,... n exp(i2kz,m+1dm+1) 1 + rm,m+1rm+1,... n exp(i2kz,m+1dm+1)
)
amplitude reflection coefficient, from multilayer stack dm ) thickness of layer lm
(2)
To expand this relationship to consider the light entering the prism of known refractive index (Figure 1) at incident angle θ, and with prism angle R, the path of light is modeled using the
(3)
-(P ˆ n‚Ro + D) P ˆ n‚R ˆd
(4)
with direction vector Iˆ is either reflected in the direction R ˆ or it is refracted in the direction Tˆ . Both of these vectors can be found algebraically as shown in eqs 5 and 6, respectively.
R ˆ ) (Iˆ - (P ˆ n‚Iˆ)P ˆ n) Tˆ ) n1 n1 n1 2 Iˆ + (P ˆ n‚Iˆ) - 1 + ((P ˆ n‚Iˆ)2 - 1) n2 n2 n2
() (()
( ()
(5)
)) 0.5
P ˆ n (6)
Multilayer Evolution. The simple genetic algorithm (SGA)40 has been chosen as the evolution method. In this instance, the sensing layer material is fixed as 18-C-6-CuPc and the SGA for (37) Haines, E. Essential Ray Tracing Algorithms: An Introduction to Ray Tracing; Glassener, A., Ed.; Academic Press: London, 1989; pp 33-77. (38) Glassner, A. An Overview of Ray Tracing: An Introduction to Ray Tracing; Glassener, A. Ed.; Academic Press: London, 1989; pp 3-31. (39) Boas, M. Mathematical Methods in the Physical Sciences, 2nd ed.; Wiley & Sons: New York, 1983; pp 107-108 (40) Fanjoy, D. W.; Crossley, W. A. Eng. Optimizations 2002, 34, 1-22.
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the internal optics uses experimentally measured optical properties of this material to define the parameters for the sensing layer (Figure 1). Since reflectivity measurements from multilayers result in information about optical thickness, there can be degenerate solutions of refractive index and thickness that will fulfill the same result. However, these solutions may differ in terms of material properties and availability and in practical realizability. Thus, each layer was described by two “chromosomes”, containing the refractive index and the layer thickness, respectively, to allow material properties to be selected. The goal was to examine the properties of the multilayer system where maximum change in reflectivity of the 18-C-6-CuPc layer occurs in response to NO2. The “fitness values” (based on change in reflectivity) of all the multilayer stacks in the population were then used in the selection process to identify a general population of good solutions. There are a number of procedures available to stochastically select members for the next population.41 In this instance, “roulette wheel” selection was initially used in the algorithm,42 where the probability of selection is directly related to the proportional fitness of a chromosome. This is appropriate for an initial simple evolutionary model but has been largely superseded by other methods where further complexity is introduced in the system description.41,43 After selection, “mating” occurs between randomly chosen pairs by the exchange of identical length substrings. This process occurs in three stages: the chromosome is split at a randomly chosen break point, the substrings are then exchanged in crossover, and the process is completed by recombination of the chromosomes. In most simple examples of genetic algorithms, mutation generally occurs by the flipping of a single bit in the chromosome,44 but in the algorithm demonstrated here, mutation was induced over a whole layer by multiplication with a percentage generated by sampling from a Gaussian distribution (eq 7). Since a Gaussian peak is symmetric, the choice of plus or minus in the equation was random with an equal probability of selection. σ was set to a value of 5 × 10-3, which was found to give diverse, highperformance solutions.
f ) 1 ( x-σ ln(rand) ) mutation factor
(7)
Coevolution with Inclusion of External Optics. The external optics were included by multispecies coevolution of information from separate areas of the design space45 with a second “species” of chromosomes specifically describing the parameters of the external optics. The solutions presented were confined to a triangular prism design to couple light into the multilayer systems, but could be expanded to consider other geometries. Specifically, the critical parameters were the apex half-angle of the triangular prism, R, and the incident angle of the light, θ (Figure 1). (41) Schmitt, L. M. Theor. Comput. Sci. 2001, 259, 1-61. (42) Lindfield, G.; Penny, J. Numerical Methods Using Matlab; Ellis Horwood: New York, 1995; pp 284-295. (43) Strassner, T.; Busold, M.; Herrmann, W. A. J. Comput. Chem. 2001, 23, 282-290. (44) Fishwick, R.; Liu, X.; Begg, D. Comput. Methods Appl. Mech. Eng. 2000, 189 (3), 931-942. (45) Bugajska, M.; Schultz, A., Proceedings of 2002 NASA/DoD Conference on Evolvable Hardware, Washington, DC, 2002.
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In multispecies coevolution, the separate populations created interact by destructive46 or cooperative47 exchange of fitness data. In this instance, cooperative coevolution was used with the second population of external optics parameters solely benefiting from the fitness of the multilayer structures from the first population. Using the two parameters that describe the external optics, the ray tracing equations are used to find the angle at which the beam is incident on the multilayers. The goal was to examine their influence on the response to NO2. Further options for experimental robustness can then be introduced. Depending on the input parameters included in the description of the external optics, laser noise, drift, or angular precision may be included or other issues of robustness can be selected depending on the instrument layout employed. For demonstration in the data presented here, solutions with low precision of incident angle ((0.5°) are tested. This scenario is appropriate where the angle is selected by the instrument automatically from a reference point of similar low angular precision, e.g., a broad reflectivity minimum. It is also appropriate in the generation of low-cost instrumentation using LED light sources without perfect collimation. The fitness of this system was thus obtained from the response at the measurement angle divided by the standard deviation across the (0.5° angular spread. This promotes more robust solutions. This double-SGA was evaluated for 60 separate populations, which were each run for 10 min. RESULTS AND DISCUSSION Establishing Sensing Layer Properties. Development of a chemical sensor is often achieved by methodical adjustment of the experimental conditions to find a parameter that can be improved. Theoretical modeling can aid this process, but it is often used independently to gain understanding of the system mechanism. In contrast, the SGA evolution method requires initial experimental data input to evolve theoretical improvements. As a starting point in this process, it is necessary to know and input the specific information that describes the “analytical signal” requiring evolution. In this instance, the model analyte-sensitive layer was 18-C-6-CuPc and the optical parameters that describe its response to NO2 were of interest. The UV-visible (600-750 nm, Figure 2a) records the NO2 detection step for this layer on a glass slide, as a decrease in the imaginary part of the dielectric constant, consistent with the decrease in the Q-band absorbance associated with the HOMO to LUMO transition of the delocalized π-orbital (Figure 2a).18,20 This is also distinguishable for the 18C-6-CuPc film formed on a gold-coated slide (Figure 2b). In both cases, there is significant decrease in absorbance at 632 nm, the wavelength at which the SPR measurements were taken. The dispersion relationship for the imaginary part of the refractive index obtained from these spectra confirms a large imaginary part of the refractive index. Ekgasit et al.6 pointed out that for SPR in an absorbing medium the evanescent field distribution in the metal film is altered by the absorbing dielectric, which results in a shift and broadening of the resonance, together with an increase in reflectance. A tendency to increased reflectance and broadening of the resonance may decrease the resolution or dynamic range of the SPR (46) Floreano, D.; Nolfi, S. Genetic Programming: Proceedings of the Second Annual Conference, 1997. (47) Yeo, K. K.; Park, K.; Ko, J. Comput. Oper. Res. 2003, 30, 1151-1171.
Figure 2. Change in UV-visible spectrum, with exposure to 16 ppm nitrogen dioxide for 5 min, of phthalocyanine films formed on (a) a blank glass slide and (b) a gold-coated glass slide. (c) Experimental response of phthalocyanine film to nitrogen dioxide. (d) Experimental data for a phthalocyanine film formed on an ultrathin gold layer to simulate the effect of no SPR supporting gold layer and (e) the theoretical reflectivity for the film, assuming a thickness of 50 nm. Experimental and theoretical response to NO2 for these films was ∼0.2 reflectivity unit at angles between 50° and 60°.
measurement of analyte if measured as a shift in resonance angle, particularly if the imaginary part of the refractive index dominates any change in response. Conversely, measurements based on reflectivity at a fixed incident angle are complicated by the shift and attenuation of the resonance. Consistent with the theoretical
predictions, the initial SPR profile of the phthalocyanine film on gold shows an increase in the reflectivity at the resonance minimums and a shift to higher angle compared with uncovered Au. On exposure to nitrogen dioxide, the reflectivity decreases (by ∼0.15 reflectivity units) due to a large decrease in absorbance Analytical Chemistry, Vol. 76, No. 23, December 1, 2004
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Figure 3. Isosurfaces showing the theoretical enhanced response from the phthalocyanine layer using a simple two-layer stack as calculated by the brute force evaluation of the ATR/SPR profiles. The bar on the right shows that low responses are dark and high are brighter. Solutions predicted by the SGA are shown as dots. The population size in an individual SGA was 30 and the algorithm run for 5 min; the algorithm was run 150 times.
Table 1. Optical Properties of a 18-Crown-6 Copper Phthalocyanine Layer Extracted from SPR Data from Layers Formed by Spin-Coating a 4 mM Solution of 18-C-6-CuPc in Chloroform
before 16 ppm NO2 after 16 ppm NO2
thickness (nm)
dielectric constant
48.00 45.83
-2.82 + 1.18i -2.95 + 0.66i
at the SPR exciting wavelength (as confirmed in Figure 2a and b), but the shift in resonance angle is poorly resolved. The optical parameters of the phthalocyanine film on the Au layer could be extracted from these data by fitting the experimental SPR curves (Figure 2c) with the Fresnel multilayer equation (Table 1). The dominant effect was the decrease in the imaginary part of the dielectric constant as predicted also from the change in the UV-visible spectrum. With a very thin Au layer, an ATR profile from the 18-C-6-CuPc layer can also be recorded (Figure 2d). In this instance, the change in the dielectric constant identified in Table 1 causes a decrease in reflectivity from the layer after exposure to 16 ppm NO2 (∼0.2 reflectivity unit), which is confirmed in the theoretical model (Figure 2e) in contrast to SPR where absorbance at the excitation wavelength disrupts the excitation of the surface plasmons and thus increases reflectivity at the resonance angle (Figure 2c). These results thus offer two ways of combining the CuPc layer in an ATR measurement, but the change in reflectivity is of opposite sign, so exploration of other multilayer formats can be expected to reveal members of both populations. Layer Optimization. As an initial evolution from the classical SPR system insertion of an extra layer between the Au layer and 6866
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18-C-6-CuPc capping layer was explored. The evolution was thus constrained to work with layer l1 (Figure 1) defined as the SPR supporting gold film (and hence with defined refractive index, but variable thickness), an outer layer with the properties obtained experimentally from the data above for the 18-C-6-CuPc film and a new intermediate layer, l2, as a nonmetallic dielectric material with variable optical thickness (layer thickness and refractive index). This is a relatively simple system that can be examined by brute force evaluation of the layers over a grid of values, although it is computationally expensive. Figure 3 shows a series of isosurfaces displaying the predicted signal size in response to 16 ppm NO2 for these new layer systems. The image shows that the best responses are at low gold thickness and low refractive index in three main areas, denoted A-C. Optimization algorithms will often converge on a local minimum that fulfills the conditions for that technique (e.g., metal film for SPR) without exploring “better” solutions outside the technique’s design-space. However, the figure shows that by invoking an SGA approach the rest of the design space is potentially visible without needing the brute force global evaluation. By choosing a small population size (30) and a low evolution time (5 min), the algorithm does not reach the global optimum but still highlights the areas of interest, and it can be seen that predictions from the SGA lie in all three critical areas identified above, not just the zone of most optimal response. Layer systems in zone A have the smallest response but are close to the traditional SPR format, retaining an angular response profile reminiscent of SPR (Figure 4a). Nevertheless, the SGA has appraised the results according to the best resolution of the analytical response to NO2, rather than looking for optimization of the SPR coupling itself, and we find that they show a trend
Figure 4. ATR profiles, from parameters suggested by the SGA optimizing a two-layer stack, for the systems described in Table 2 (a) area A, (b) area B, and (c) area C. ATR profiles, from parameters suggested by the SGA optimizing a maximum of 10 layers, for the systems described in Table 3a-c.
toward decreasing Au thickness (∼25 nm optimization for l1). Taken to the extreme, the trend from zone A seen here could be consistent with the results in Figure 2, where the total omission of the Au layer, allowing a straightforward ATR absorbance measurement of the CuPc, without interference of SPR coupling, improves the resolution of the NO2 response. This was also confirmed for the two-layer system without the new l2 layer, which predicts a change in reflectivity of 0.2143 unit at 25-nm Au, significantly greater than the experimentally observed 0.15 obtained with 40-nm Au (Figure 2c) and also slightly greater than the equivalent area A solution with a very thin l2 layer. From the zone A data it might be concluded that the Au layer should be thin or absent to optimize response to NO2. Furthermore, comparison with the theoretical and existing experimental data for a simple CuPc layer structure seems to suggest that inclusion of l2 offers no improvement. However, layer systems in area B include a thicker l2 and produce an SPR-like profile (Figure 4b) that is sharper than the zone A solution and have a generally higher response that those in area A (Table 2). Area C is more complicated being made up of two “tubes” in this parameter space. The core of these tubes contains the best responses with many of the layer systems lying along the center of the tube that runs from lower to higher layer l2 refractive index. Most solutions however, are clustered at low gold thickness and layer l2 refractive index. This is demonstrated by the layer parameters for the best system (Table 2). Figure 4c shows that the NO2 response now causes a decrease in reflectivity, suggesting that any SPR coupling is minimal. Indeed, it can also be seen here that the gold thickness is very small and its removal further increases the response, by a very small amount (0.08%). In these systems, therefore, the presence of the metal layer and SPR coupling acts to reduce the response seen through direct CuPc absorbance. In principle, these are readily achieved designs requiring only a change in the material of the substrate carrying the 18-C-6-CuPc
Table 2. Layer Parameters for Best Layer System, Predicted by the SGA, in Areas A-C of Figure 3 area
layer
thickness (nm)
refractive index
response to 16 ppm NO2
A
l1 gold l2 dielectric l1 gold l2 dielectric l1 gold l2 dielectric
25.21 5.37 29.68 166.70 0.134 216.44
0.115 + 3.47i 1.676 0.115 + 3.47i 1.916 0.115 + 3.47i 1.029
0.2135
B C
0.2183 0.2442
layer (not the instrumentation) and could be easily adopted alongside classical SPR, if the materials would be available. In the case of the area C optimum, this would require a substrate of refractive index 1.029, but such materials are not readily available, so that alternative solutions were sought. In the optics industry, genetic algorithms have been used to optimize multilayers for optical filters, such as antireflection coatings and wavelength rejection filters.15,50 Such multilayers can have hundreds of layers to obtain the desired result.41 It is thus pertinent to consider more complex layer structures, if the materials are easily available and the response contrast enhancement warrants the additional production complexity. In this instance, the SGA can generate systems with between 1 and n layers, with layer characteristics equivalent to gold or a nonmetallic dielectric; the prism layer (Figure 1) is also included (as layer l0) with variable refractive index (the thickness is redundant for this layer) and ln+1 is the 18-C-6-CuPc. Within the 200 n-layer designs (with nmax ) 10), only two systems included a gold layer and in both cases it was thinner (48) http://www.dupont.com/teflon/chemical/pdf/h44587-3.pdf. (49) Pierre, A.; Pajonk, G. Chem. Rev. 2002, 102, 4243-4265. (50) Yang, J.-M.; Kao, C.-Y Lect. Notes Comput. Sci. 1998, 1498, 947-956.
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Table 3. Optical and Physical Properties of Best Layer Systems Predicted by the SGAa
layerb prism multilayers
prism multilayers
prism multilayers prism multilayers prism multilayers prism multilayers
l0 l1 l2 l3 l4 l5 l6 l7 l8 l0 l1 l2 l3 l4 l5 l6 l0 l1 l2 l3 l0 l1 l2 l0 l1 l2 l0 l1
refractive index
thickness (nm)
1.3990 1.8250 1.5681 1.5430 0.1154 + 3.4660i 1.3680 1.1740 1.3570 1.6610 1.5900 1.7630 1.4770 0.1154 + 3.4660i 1.8499 1.3540 1.1760 1.5827 1.1790 1.0696 1.0119 1.5827 1.1790 1.00027 1.5827 1.29 1.00027 1.5827 1.29
n/ac 56.68 31.22 63.08 16.75 45.67 87.35 29.69 33.07 n/a 80.78 31.29 0.87 36.15 76.52 113.51 n/a 107.39 94.32 88.56 n/a 107.39 182.88 n/a 107.39 182.88 n/a 290.27
response to 16 ppm NO2 (δ reflectivity) (a) 0.2232
(b) 0.2318
(c) 0.2440
(d) 0.2452 (e) 0.2418 (f) 0.1914
a These include an Au layer (a) and (b) and without an Au layer (c). Also user variations on the parameters in (c) by (d) combining l2 and l3 into an air gap; (e) then same, but converting l1 into a Teflon layer and combining layers l1, l2, and l3 into (f) a Teflon layer. b For all response a-f, the sensing layer is a phthalocyanine detertion layer and the bulk medium is air. c n/a, not available.
than for the classical SPR (Table 3a and b). Furthermore, complete removal of the Au layer did not influence the response obtained, so the layer had become redundant. In using SGAs, redundant layers may still be present in the design (this can be tested by comparing results with and without the layer), but they are not removed from the population artificially until the design process is completed, since this tampers with the evolutionary process. The properties of the layer could become reactivated at a later time in the evolution by imposing different requirements on the solutions. Interestingly, in the 200-SGA population, 78% of the solutions were within 5% of the maximum response and all solutions were better than the experimentally obtained classical SPR response in Figure 2c giving considerable scope for design selection to be based on criteria such as material availability, ease of fabrication, and potential for simplification that can lead or redirect the design process. However, the scope of each SGA design recommendation needs to be tested. For example, the data appear to indicate that the SGA recommends significant modification to the prism refractive index between the different solutions and is often quite different from the experimental value (1.521) used for the data in Figure 2c. To explore the real effect of this parameter, the solution in Table 3c suggested by the 200 SGAs was examined for prism refractive index values between 1.3 and 1.8. A maximum response was found at a refractive index of 1.52, near the experimental value, 6868 Analytical Chemistry, Vol. 76, No. 23, December 1, 2004
but the variation over the entire range was less than 0.2%, demonstrating a different kind of redundancy. Such an assessment identifies the precision with which the material refractive index must be defined and the complexity/redundancy of a layer as a design parameter. In contrast to the hundreds of layers designed to achieve antireflection coatings and wavelength rejection filters51 and notwithstanding the seven- and nine-layer systems in Table 3 and the residual presence of an Au layer, the SGA evolution does tend toward structures with fewer layers to perform this NO2 detection event. As expected, the most preferred multilayer solution from the 200 populations (Table 3c) did not contain Au. However, consistent with the simpler CuPc ATR system (Figure 4c), a striking general theme is toward dominance of “thick” (>100 nm) layers with low refractive index values close to those usually found for gases and suggesting that, without constraining the choice of materials, the algorithm is evolving toward a design requiring coupling across an air gap. This was tested by combining layers l2 and l3 (Table 3c) in a single layer with refractive index 1.000 27 (air) and thickness 182.88 nm (Table 3d). This solution now converges to a two-layer system with 63.5% higher response than the original experiment. Based on this theme, a directed evolution was sought in alternative choices for materials with low refractive index, e.g., Teflon or aerogel. Aerogels are produced from sol-gel films, which undergo a supercritical drying. The resultant material is highly porous, and this gives it a low bulk refractive index of between 1 and 1.1; specifically in silicon aerogels, the refractive index is proportional to the density of the film.49 Thin, opticalquality films of Teflon can be formed by spin coating a powdered resin dissolved in a perfluorinated solvent; these films have a typical refractive index of ∼1.3.48 In a previous work looking at multilayer structures including metal phthalocyanines,52 we showed that a coploymer of tetrafluoroethylene and 2,2-bistrifluoromethyl4,5-difluoro-1,3-dioxole (refractive index ∼1.29) could be used to spin coat layers below or sandwiching the Pc layer. In this instance, we can test the tolerance of the l1 layer to materials with increased refractive index and find that if the thickness is maintained constant, a reduction of 0.9% (Table 3e) is found in increasing the l1 layer from 1.179 to 1.29. In contrast, if l2 is included with l1 as a single layer with refractive index 1.29, the response drops by 21.56% (Table 3f) unless compensation for thickness is made. Remembering that optical thickness has degenerate solutions for refractive index and thickness, this decrease is intuitive if the original 200-SGA solution was close to an optimum in the design space. Based on these data, therefore, a suitable Teflon-based system would require a thinner layer than that in Table 3f, to compensate for the increase in refractive index of l1 + l2. Inclusion of External Optics. To finalize the design, the external optics need to be included. The goal is to find a design that can be used for an analyte response according to a simple measurement protocol, e.g., reflectivity at a single incident angle, shift in a reflectivity minimum/maximum, etc. The ATR profile for the layer system described in Table 3a has its best response (51) Sullivan, B.; Dobrowolski, J. A.; Clarke, G.; Akiyama, T.; Osborne, N.; Ranger, M.; Howe, L.; Matsumoto, A.; Song, Y.; Kikuchi, K. Vacuum 1998, 51(4), 647-654. (52) Kessler, M.; Hall, E. A. H. Thin Solid Films 1996, 272, 161-169.
Table 4. Parameters Suggested by the Double-SGA for the Design with (a) the Best Response and (b) the Best Tolerance Fitness and c) a Replacement of Layer l1 in (a) with a More Feasible Teflon Layer
a b
Figure 5. Response versus incident angle tolerance. Solid line shows the best design responses from the 60 evaluated double-SGA populations; the dashed line shows the best possible response for the multilayers used in each design.
to NO2 at high angles (Figure 4d). This reflectivity curve is quite different from the classical SPR curve, although the multilayer system still contains Au. In contrast, the ATR profiles for the layer systems described in Table 3b and c still resemble the general shape of the familiar SPR curve (Figure 4e and f, respectively) and are similar to the profile of the two-layer system seen in Figure 4c previously, where the response to NO2 results in an increase in reflectivity with a decrease in CuPc absorbance. This is consistent with the theoretical response for a phthalocyanine film on a glass slide, rather than the experimental SPR response. Basing the measurement on a change in reflectivity minimum is not appropriate for these systems, so how do we choose the incident angle to perform the measurement? In classical SPR with a nonabsorbing overlayer, or in predictions from SPR with an absorbing overlayer,6 a suitable interrogation angle to follow the NO2 response could be chosen close to the reflectivity minimum. To follow this practice (for example, in using an SPR instrument with automatic angle selection), the prism angle could also be fixed in the SGA and the best multilayers extracted that perform well at this angle. However, to find the “formula” for these nonSPR layers, a search was integrated into the selection process in the SGA evolutionary design, by extending the SGA with populations describing the physical parameters of the external optics of the system, defined by an incident angle and the prism angle (see Figure 1). In this case, since the refractive index of the prism was shown to be noncritical in the multilayer evolution, it could be fixed to avoid conflict between the populations. A low-precision guideline for angle selection is more versatile than an exact model specific solution, so Figure 5 compares the response evaluated for the best designs of 60 populations from the double-SGA when a selection pressure requiring high tolerance to incident angle was imposed ((0.5°), with the maximum response that could be achieved at a precise incident angle from the multilayer system in that design. This exercise reveals how, generally, experimental reflectivity data must include quite accurate angular referencing to ensure a reproducible signal. From Figure 5, the properties for the best overall design describes a single layer of low refractive index between the 18-C-6-CuPc and the prism (Table 4a), but as predicted from the data in Table 3df, the layer thickness is smaller. By some compromise of the magnitude of the response, even greater angular tolerance can
c
a
layer
thickness (nm)
refractive ndex
response to 16 ppm NO2 by systema
l1 prism angle incident angle l1 l2 l3 prism angle incident angle l1 prism angle incident angle
62.16 39° 52.36° 65.4340 119.8980 5.1910 41° 61.06° 62.16 39° 52.36°
1.0795
0.2335 (0.2340)
1.6340 1.3750 1.3849
0.2152 (0.2152)
1.29
0.2271 (0.2303)
Maximum theoretical response from multilayer given in parentheses.
Figure 6. Simulated ATR profiles before and after NO2 exposure for the layer parameters in Table 4c, which are a combination of those suggested by the double-SGA and user intervention to produce a more feasible system. Also shown is the absolute response profile for these curves.
be achieved. For example, Table 4b shows a more complex layer structure within 8% of the response for the system described in Table 4a. The tolerance fitness value for this system (calculated as response divided by the standard deviation of the surrounding angles) is, however, much greater: it scored 2030.2 whereas the system in Table 4a obtained from the SGA scored 400.4. This indicates that there could be a tradeoff between response and angle tolerance. The former design is also accompanied by a recommendation for the prism angle being 39° whereas the latter design suggested 41°. In both cases, the angle is close to that for SPR or the simple ATR system (Figure 2), so that the deformation factor (cos θ) in the horizontal direction remains unchanged. The importance of the precision of this angle for the different multilayers was tested by manual modification between 35° and 45° in steps of 0.1° to examine the variation in response. In the latter case (Table 4b), little deviation from the SGA output was produced with an optimal angle of 41.1° (response also 0.2152) and tolerance fitness of 2079.9. However, for the former (Table 4a) improvement on double-SGA 39° design could be achieved with a prism angle close to the same optimum at 41.4°. This predicted a response equal to the best possible response of the system (0.2340) found so far and also had a maximum tolerance fitness value at 2123.7, making this system better than that in Table 4b. These tolerances make Analytical Chemistry, Vol. 76, No. 23, December 1, 2004
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the system highly amenable to automated angular selection from an easily found reflectivity reference point. The predicted ATR profiles for the general design shows that the incident angle chosen for the interrogation lies ∼1° higher than the reflectivity minimum close to a stationary point in the absolute response curve (Figure 6) and does not lie at the reflectivity minimums for any of the curves nor at an angle lower than the reflectivity minimum, as would typically be selected in SPR. CONCLUSIONS SPR has been widely developed to measure response of proteins at surfaces, for which a ∼50-nm gold film has been found an optimum substrate. The same substrate could be conveniently used to look at many other reactions at the surface, but the design has not been optimized for all other applications. One strategy could be the iterative experimental variation of the substrate according to the desired surface chemistry and optimum response. However, these processes can be significantly aided by application of design theory. By using a simple genetic algorithm, layer structures were predicted that could theoretically be used to produce an ATR system with a 18-C-6 CuPc film and would potentially enhance the response to nitrogen dioxide. Several conclusions were drawn from this design process. Importantly, for the 18-C-6 CuPc film, ATR response to NO2 did not require an Au layer. The double-SGA evolutionary design recommendations, which include consideration of the external coupling optics, predict contrast enhancement of the response to NO2 can be obtained, compared with the classical SPR for 18-C-6-CuPc on gold, if the gold is replaced with a layer of low refractive index. This result is also significantly better than for a simple CuPc ATR layer without supporting intermediate layers. A very low refractive index underlayer with thickness of >100 nm was a consistent feature of many of the designs predicted, and an equivalent response could also be obtained even when the refractive index of this layer was increased to that of Teflon, so long as a concomitant decrease in thickness was made (60-100 nm). Furthermore, the “best” design could be selected to accommodate (0.5° differences in the incident angle selection or poor collimation. By keeping the multilayer and external optics parameters in separate populations, the need for multiple fitness values and more
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complex selection methods was avoided and the two-species genetic algorithm including external optics gave an initial exploration of potential instrumental tolerance. The fitness profile was found generally to decrease compared with the stand-alone solution, highlighting the need to evaluate robustness of theoretical solutions in the context of proposed usage. Such factors as manufacturability, tolerance, and cost can also be included into the genetic algorithm to find suitable layer systems. However, in such an algorithm, a multilayer system would have multiple fitness values and more complex methods of selection would be needed. In this instance, the roulette wheel method would not be suitable and the more commonly used “tournament method” might be utilized. In this method, at least two members of the population must compete against each other, with the largest fitness winning.41 The motivation toward such design methods in optimizing experiments involving optical multilayers is evident from the lead away from SPR in this work for an absorbing overlayer and contrast enhancement that is predicted even from this initial study, where relatively simple changes to the substrate are made that support the analyte sensitive layer. The study reveals a scenario where SPR would not be the preferred method, although it has been proposed for Pc layers, and a similar type of response has been seen with π-conjugated polymer films spin-coated onto a gold film and then doped with iodine7 and for many other absorbing layers on Au. While for these examples a simple absorbance measurement (via ATR) might be instinctive, the instinct is less developed for proteins. For example, Boussaad et al.7 have examined the wavelength-dependent change in the SPR for cytochrome c. Will a SGA approach reveal SPR as the best choice in this instance? Contrast enhancement in ATR, by using substrates other than Au does not require any change in instrumentation and so is readily achievable for most systems currently used for SPR measurement.
Received for review March 1, 2004. Accepted September 3, 2004. AC0496751
