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

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Page 1: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Diffusional Limitation in Immobilized Enzyme System

• Immobilized enzyme system normally includes

- insoluble immobilized enzyme- soluble substrate, or product

• They are heterogeneous systems

Page 2: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

CONCENTRATION DIFFERENCE

FILM

TRANSFER

DRIVING FORCEDIFFUSION

HIGH

Immobilized Enzyme

Sb

ELECTRIC ATTRACTION

Low S concentration

Substrate

Page 3: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

CONCENTRATION DIFFERENCE

FILM

TRANSFER

DRIVING FORCEDIFFUSION

HIGH

Immobilized Enzyme

Sb

ELECTRIC ATTRACTION

REACTION

PRODUCT

Page 4: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

FILM

TRANSFER

DRIVING FORCEDIFFUSION

HIGH

Immobilized Enzyme

Sb

INTRA-PARTICLE

TRANSFER

Page 5: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

FILM

TRANSFER

PRODUCT

HIGH

Immobilized Enzyme

Sb

INTRA-PARTICLE

TRANSFER

REACTION

Page 6: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Diffusional Limitation in Immobilized Enzyme Systems

In 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

Page 7: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Diffusional Limitation in Immobilized Enzyme System

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

Enzyme

SsSb

Liquid Film Thickness, L

EPkES 2E+S

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Assume the enzyme catalyzed reaction rate follows Michaelis-Mententype kinetics.

Page 8: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Enzyme

SsSb

Liquid Film Thickness, L No intraparticle diffusion

Assume:

-Enzyme are evenly distributed on the surface of a nonporous support material.

-All enzyme molecules are equally active.

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

-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 Materials

Page 9: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

is the maximum reaction rate per unit of external surface area (e.g. g/cm2-s)

To determine the significant effect of external diffusion resistance on the rate of enzyme catalytic reaction rate: Damköhler numbers (Da)

]['

diffusion of rate maximumreaction of rate maximum

bSLkmVDa

'mV

Lk][ bS

is the liquid mass transfer coefficient (cm/s)

Is the substrate concentration in bulk solution (g/cm3)

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Page 10: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

When Da >> 1, the external diffusion rate is limiting; Da << 1, the reaction rate is limiting; Da ≈ 1, the external diffusion and reaction

resistances are comparable.

]['

diffusion external of rate maximumreaction of rate maximum

bSLkmVDa

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Page 11: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

][][''

sm

sm

SKSVv

If the product formation rate is :

])[]([ sSbSLksJ The external diffusion rate (g/cm2-s):sJ

'mV the maximum reaction rate per unit surface area.(g/cm2-s)

Lk is the liquid mass transfer coefficient (cm/s).

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Page 12: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

][]['

])[]([sSmKsSmV

sSbSLksJ

At steady state, the reaction rate is equal to the external diffusion rate:

With the equation and known Sb, KL, Vm’ or Km, to determine numerically or graphically:- The substrate concentration at the surface.- The reaction rate.

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

EPkES 2E+S

Page 13: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Graphical solution for reaction rate per unit of surface area for enzyme immobilized on a non-porous support

])[]([ sSbSLksJ

Page 14: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

][ bSLkv

When the system is strongly external diffusion (liquid film mass-transfer) limited, [Ss]≈0,the overall reaction rate is equal to the rate:

The system behaves as pseudo first order.

The rate is a linear function of bulk substrate concentration.

Da>>1

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Page 15: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

To increase the overall reaction rate with external diffusion limitation

-Increase .

-Increase .

]['

diffusion of rate maximumreaction of rate maximum

bSLkmVDa

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Page 16: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

The liquid film mass transfer coefficient kL:

(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)

ν 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.

2/1

2/1

6/1

3/26.0

pd

UABDLk

Page 17: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

When the system is strongly reaction limited,[Sb] ≈ [Ss]

the overall reaction rate is equal to the rate:

][,

]['

bSappmKbSmVv

Da << 1

)]([1

'

,mbL

mmappm KSk

VKK

Km,app is increased. It is a function of mixing speed and Sb.

where

Page 18: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Diffusion Effects in Enzymes Immobilized in a Porous Matrix

- Substrate diffuses through the tortuous pathway within the porous support to reach the enzyme.

- Substrate reacts with enzyme on the pore surface.

Ex. Spherical support particles

Sr

Page 19: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Diffusion Effects in Enzymes Immobilized in a Porous Matrix

Assume:- Enzyme is uniformly distributed in a spherical support particle.- The reaction kinetics follows Michaelis-Menten kinetics.- There is no external diffusion limitation.

Page 20: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

is .

11

the rate is .

the rate is .

.limitationdiffusion without ratereaction limitationdiffusion cleintraparti with ratereaction

][]["

sm

sms SK

SVr

Under internal diffusion limitations, the rate per unit volume is expressed in terms of the effectiveness factor as follows:

"mV is the maximum velocity per volume of the support.

mK is the M-M constant.][ sS is the substrate concentration on the surface of the support.

Page 21: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

Relationship of effectiveness factor with the size of immobilized enzyme particle and enzyme loading

Page 22: Lecture notes-enzyme-Diffusional Limitation in Immobilized Enzyme System-web

At specific conditions (T, P) for a fixed system,

To increase the intra-particle mass transfer rate:

- the size of immobilized enzyme particle

- the porosity or specific surface area of the particle