Analytical Expressions of Concentrations of Substrate and Hydroquinone in an Amperometric Glucose Biosensor

Table 1

Summary of analytical expressions of concentrations and currents.

Limiting case	Concentration and current	Eqn. no	Figures	Parameter values
	𝑈(𝑋,𝛼,𝑀)=cosh(𝛼𝑋)+cosh(𝛼)𝑀cosh(𝛼𝑋)(cosh(2𝛼)−3)6cosh^3−(𝛼)𝑀(cosh(2𝛼𝑋)−3)6cosh^2(𝛼)	(see (10))	Figure 2	𝛼=(0.1,…,100); and 𝑀=(0.001,…,1)
	𝑉()=𝛼𝑋,𝛼,𝑀^2𝛼^′2()𝑒𝑀+11−^𝛼′𝑋+𝑒^𝛼′(1−𝑋)𝑒^𝛼′+1	(see (11))	Figure 3	𝛼=(0.1,…,10),𝛼^′=(0.01,…,100), and 𝑀=(0.01,…,100)
All Values of 𝑀	𝜓S(𝛼,𝛼^′𝛼,𝑀)=^2(𝑒^𝛼′−1)𝛼^′(𝑀+1)(𝑒^𝛼′+1)	(see (12))	Figures 4(a) and 4(b)	𝛼=1,10; and 𝑀=(0.01,…,100)
	𝜓P(𝛼,𝛼^′𝛼,𝑀)=^2(𝛼^′𝑒^𝛼′−𝑒^𝛼′+𝛼^′+1)𝛼^′3(𝑀+1)(𝑒^𝛼′−𝛼+1)^2(𝑒^𝛼′−1)𝛼^′3(𝑀+1)(𝑒^𝛼′+1)	(see (13))	Figures 4(c) and 4(d)	𝛼=1,10; and 𝑀=(0.01,…,100)
	𝜓T=𝜓S+𝜓P	(see (14))	Figures 5(a) and 5(b)	𝛼=1,10; and 𝑀=(0.01,…,100)
	𝑈(𝛼,𝑋)=cosh(𝛼𝑋)cosh(𝛼)	(see (16))
	𝑉(𝑋,𝛼,𝛼^′𝛼)=^2(𝛼^2−𝛼^′2)𝑒^𝛼′𝑋−cosh(𝛼)cosh(𝛼𝑋)−cosh(𝛼)sinh(𝛼^′𝑋)sinh(𝛼^′)𝑒^𝛼′cosh(𝛼)−1	(see (17))
First-order catalytic	𝜓S(𝛼,𝛼^′𝛼)=^′𝛼^2(𝛼^2−𝛼^′2)1−1cosh(𝛼)sinh(𝛼^′)𝑒^𝛼′cosh(𝛼)−1	(see (18))	Figure 6(a)	𝛼=10,50,100
Kinetics 𝑀𝑈<1	𝜓P(𝛼,𝛼^′𝛼)=^2(𝛼^2−𝛼^′2)1−1cosh(𝛼)2sinh(𝛼^′)𝑒^𝛼′1cosh(𝛼)−1𝛼^′(𝑒^𝛼′−1)+(𝑒^−𝛼′−1)2𝛼′sinh(𝛼^′)𝑒^𝛼′−cosh(𝛼)−1sinh(𝛼)𝛼^2cosh(𝛼)	(see (19))	Figure 6(b)	𝛼=0.5,…,100
	𝜓T=𝜓S+𝜓P	(see (20))	Figure 6(c)	𝛼=0.5,…,100
	𝛼𝑈(𝑋,𝛼,𝑀)=1−^22𝑀1+𝑋^2	(see (22))
	𝑉(𝑋,𝛼,𝛼^′𝛼,𝑀)=^2𝑀𝛼^′21−𝑀𝑒^𝛼′𝑋+𝑒^𝛼′(1−𝑋)𝑀(𝑒^𝛼′+1)	(see (23))
Zero-order catalytic	𝜓S(𝛼,𝛼^′𝛼,𝑀)=^2𝑀𝛼^′2(𝑒^𝛼′𝑒+1)(𝑒^𝛼′+^𝛼′1)−𝛼^′	(see (24))	Figure 7(a)	𝑀=0.01,…,100 and 𝛼=1
Kinetics 𝑀𝑈>1	𝜓P(𝛼,𝛼^′,𝑀)=2𝛼^2(1−𝑒^𝛼′)𝑀𝛼^′3(1+𝑒^𝛼′)	(see (25))	Figure 7(b)	𝑀=0.01,…,100 and 𝛼=1
	𝜓𝑇=𝜓𝑆+𝜓P	(see (26))	Figure 7(c)	𝑀=0.01,…,100 and 𝛼=1