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
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