SynopsisAssuming that the rate of reaction of an unreacted site in polymer reactions depends upon whether the two immediate neighboring sites on either side (four neighboring sites in all) are reacted or unreacted, differential equations were obtained giving the rate of change of N , with time (where N , is the number of sequences of n consecutive unreacted sites with a reacted site a t both ends) and solved numerically with the help of a computer. N , was obtained as a function of time and also as a function of M , the total number of unreacted sites. Three sets of values of k were tried, one of these relating to autocatalytic reaction, one to autoretarding reaction, and one to the null case in which the reaction rates do not depend upon the neighbors.

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Bimetal clad planar waveguide having polyaniline polymer as a guiding layer is proposed and studied for biosensing applications. The dispersion relation and reflectivity of the proposed sensor is obtained using transfer matrix method. The sensing performance and stability of proposed waveguide-based sensor is optimized using different volume fraction of Ag–Au bimetal. The volume fraction 1 represents pure Ag metal coating waveguide that shows maximum sensing performance in our all considered cases. In this case, maximum obtain sensitivity, detection accuracy and quality parameter is 74.140, 11.199 and 559.970°/RIU respectively, at the cover refractive index 1.410. Since, resonance angle and full width at half maxima of resonance peak decreases with increase of Ag metal percentage in Ag–Au bimetal therefore the presence of Au metal decreases the sensing performance of the sensor. Hence, a small volume fraction of Au metal is recommended for higher sensitivity with stability.