Chapter -3Immobilization of Enzymes

Motivation• Consider two different modes of a continuous process involving

enzymatic reactions as shown below

S,E

S,E,P S,P

S

(a) (b)

Immobilized Enzyme

Definitions• Enzyme Immobilization • Enzyme immobilization may be defined as a process of confining the

enzyme molecules to a solid support over which a substrate is passed and converted to products.

• Immobilized Enzyme• An immobilized enzyme is one whose movement in space has been restricted

either completely or to a small limited region.

Ideal Characteristics of Supports• Inert.

• Physically strong and stable.

• Cost effective.

• Possibility to regenerate.

• Reduction in product inhibition.

Immobilization Techniques

Immobilization Techniques

Physical methodsAdsorption

Entrapment

Encapsulation

Chemical methodsSupport

Copolymerization

Cross Linking

Entrapment EncapsulationAdsorption

Copolymerization Cross LinkingSupport

Rapid Reaction on the surface

Effect of Mass-Transfer Resistance• Due to the large particle size of immobilized enzyme or due to

inclusion of enzyme in polymeric matrix.

External Mass Transfer Resistance• Enzymes are immobilized on surface of uncharged, nonporous flat

plate.• Entire surface is uniformly accessible to substrate in adjacent fluid.• At steady state product and substrate do not accumulate at the

surface and rate of mass transfer equals rate of reaction

𝑵 𝒔=𝒌𝒔𝒂 (𝑪𝒔𝒃−𝑪 𝒔)=𝒓 𝑷=𝒓𝒎𝒂𝒙𝑪 𝒔

𝑲𝑴+𝑪𝒔

Dimensionless form𝟏− 𝒙𝒔

𝑵𝑫𝒂=

𝜷 𝒙𝒔

𝟏+𝜷 𝒙𝒔

• Damklher number : Ratio of the maximum reaction rate over maximum mass transfer rate.• Reaction limited• Mass transfer limited• Mass transfer and reaction rates are comparable

Concentration profiles

𝑪𝑺𝒃

Distance from the surface

Conc

entr

ation 𝑪𝑺𝒃

Distance from the surface

Conc

entr

ation

Reaction Limited Mass Transfer Limited

Rate of Reaction Vs Concentration

Concentration

rate

of r

eacti

on

rate

of r

eacti

on 𝒓𝒎𝒂𝒙

Reaction LimitedMass Transfer Limited

r =

Concentration

r =

Effectiveness Factor

=

Example• Given

• Find reaction rate and effectiveness factor.

Internal Mass Transfer Resistance• Enzymes are immobilized to a porous support having large internal

surface areas.

Internal Mass Transfer ResistanceIn : Out : Accumulation : 0 Generation :

rdr

In – Out = Accumulation – Generation 𝑱 𝒓=−𝑫𝒆𝒇𝒇𝒅𝑪𝒔

𝒅𝒓

Boundary Conditions

1. = 0 (or) = 0

First-order Kinetics

Non-Dimensional Variables1. = Zero-order Kinetics

𝑥𝑠=sinh (3𝜙�̇� )�̇� sinh (3𝜙)

Concentration Profiles

Effectiveness Factor

• First-order Kinetics

• Zero-order Kinetics

Effectiveness FactorNo resistance to

pore diffusionStrong pore

diffusion effects

• The following data are available for a first order reaction in a porous catalyst.: 2 : 5.1 × R: 100 mk: 125 /min

1) Find at R = 50 m 2) Find

Effective Diffusion Coefficient

porosity of the support = Tortuousness H = Hindrance Factor (pores having small diameter (same scale as size of molecules) hinders diffusion)

[E. M. Renkin, J. Gen. Physiol. 38 (1954) 225-243]

Effective Diffusivities in Biological gels • The gel structure increases the path length for diffusion, and as

a result decreases the diffusion rate.• One of the most reliable techniques is the thin-disk method • A diffusion cell with two compartments divided by a thin gel. • Each compartment contains a well-stirred solution with different solute

concentrations.

• Effective diffusivity can be calculated from the mass flux verses timemeasurement

Simultaneous External & Internal Mass Transfer Resistance• is not equal to • Biot Number (Bi) = • If Bi > 100 then external resistance is negligible

P.3.3