lecture notes-enzyme-diffusional limitation in immobilized enzyme system-web

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Diffusional Limitation in Immobilized Enzyme System Immobilized enzyme system normally includes - insoluble immobilized enzyme - soluble substrate, or product They are heterogeneous systems

Substrate

HIGH

Immobilized EnzymeLow S concentration

SbDIFFUSION DRIVING FORCE

HIGH

Immobilized EnzymeREACTION

SbDIFFUSION DRIVING FORCE

PRODUCT

HIGH

Immobilized Enzyme

SbDIFFUSION DRIVING FORCE

HIGH

Immobilized EnzymeREACTION

SbPRODUCT

Diffusional Limitation in Immobilized Enzyme SystemsIn immobilized enzyme systems, the overall production rate is determined by- liquid film mass transfer (external diffusion) substrate, product - intraparticle mass transfer (internal diffusion) substrate, product in porous supports - enzyme catalysis reaction

Diffusional Limitation in Immobilized Enzyme SystemDiffusion Effects in Surface-bound Enzymes on Nonporous Support MaterialsSs

E+S

k2 ES p P E

Sb

Assume the enzyme catalyzed reaction rate follows Michaelis-Menten type kinetics.

Enzyme Liquid Film Thickness, L

Ss: substrate concentration at the surface; Sb: substrate concentration in bulk solution.

Diffusion Effects in Surface-bound Enzymes on Nonporous Support MaterialsAssume: -Enzyme are evenly distributed on the surface of a nonporous support material. -All enzyme molecules are equally active.Enzyme Ss Sb

-Substrate diffuses through a thin liquid film surrounding the support surface to reach the reactive surface.

Liquid Film Thickness, L No intraparticle diffusion

-The process of immobilization has not altered the enzyme structure and the intrinsic parameters (Vm, Km) are unaltered.

Diffusion Effects in Surface-bound Enzymes on Nonporous Support MaterialsTo determine the significant effect of external diffusion resistance on the rate of enzyme catalytic reaction rate: Damkhler numbers (Da)

Vm ' maximum rate of reaction Da ! ! maximum rate of diffusion k L [ Sb ]Vm 'is the maximum reaction rate per unit of external surface area (e.g. g/cm2-s) is the liquid mass transfer coefficient (cm/s) Is the substrate concentration in bulk solution (g/cm3)

kL[ Sb ]

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Vm ' maximum rate of reaction Da ! ! maximum rate of external diffusion k L [ Sb ]

When Da >> 1, the external diffusion rate is limiting; Da >1

The system behaves as pseudo first order. The rate is a linear function of bulk substrate concentration.

Diffusion Effects in Surface-bound Enzymes on Nonporous Support MaterialsTo increase the overall reaction rate with external diffusion limitation

Vm ' maximum rate of reaction Da ! ! maximum rate of diffusion k L [ Sb ]-Increase -Increase ..

The liquid film mass transfer coefficient kL: D2 / 3 1/ 2 AB U k L } 0.6 v v 1/ 6 R d p1 / 2 (H. Fogler, Elements of Chemical Reaction Engineering 1999, p705)

DAB is mass diffusivity of the substrate in the liquid phase, a function of temperature and pressure (m2/s) is the kinematic viscosity (m2/s), a function of temperature. U is the free-system liquid velocity (velocity of the fluid flowing past the particle) (m/s). dp is the size of immobilized enzyme particle (m). At specific T and P, increasing U and decreasing dp increase the liquid film mass transfer coefficient and the external diffusion rate.

Diffusion Effects in Surface-bound Enzymes on Nonporous Support MaterialsWhen the system is strongly reaction limited, [Sb] [Ss] the overall reaction rate is equal to the rate:

Vm '[ Sb ] v! K m, app [ Sb ]where

Da

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