According to the question, I would like to place my point of view regarding it:
The immobilized enzyme activity generally depends upon the type of support (immobilization medium) it has. When an enzyme is immobilized, then its microenvironment conditions gets changed in terms of conformational change in enzyme structure. Consequently, there will be change in its denaturation activation energy (Ead), I.e. Ead will be increased which makes enzyme more resistant to different thermal conditions. If we analyze it in a subtle way, As enzymes has different forms, some are dimer or polymeric as well in respective to their subunits. (There must be immobilization of enzyme properly in accordance to its subunits, otherwise it may fluctuate the optimum stability condition). The immobilized enzyme subunits acts as monomers (doesn't dissociates), nevertheless shows good stability with the immobilizer. Similarly, pH conditions works. Example, FTase (fructosyltransferase) enzyme shows good stability under pH 6 from its general stability level (pH 4.5). Similar kinds of points have been evaluated to justify the stability and working mechanisms according to the methodology and some calculations.
I hope this will help you to clear some of your doubts.
Immobilization involves the addition of enzyme with stabilizing agents which change the natural environment of the enzymes and these are mostly responsible for differences in optimum pH and temperature stability.
Immobilization of enzymes enhances the stability to protein to broad pH / temperature/ the specific activity of the enzyme to the media variations is less significant. . The repeated use enzymes without much loss of enzyme activity though sometimes the rate of reaction will be slow.
Immobilized enzymes have better pH and temperature stability because of covalent bond formation between carries matrics and enzyme by cheating agent (glutaraldehyde or any other chemical) which make confirmational change in the enzyme structure.
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An alternative is that the enzyme "only" appears to be more stable. If the carrier material is overloaded with enzyme substrate diffusion will limit the reaction rate. Substrate will only reach the outher enzyme layer(s) before it is converted. Once enzyme lose activity the substrate will (have to) diffuse further into the enzyme layers/carrier material before it is converted. You will not see much change in activity/reaction rate, so the enzyme appears to be more stable...
Immobilized enzyme get the microenvironment that protect the enzyme from other environmental parameters such as pH, temperature, pressure etc that's why immobilized enzymes have better pH and temperature resistance.