Impact Factors of Biocatalysts on Reactive Distillation

Based on the overview on the characteristics of biocatalysts, several impact factors on the application in reactive distillation columns can be identified in addition to the aspects discussed in section 2.1:

• Additional decisive parameter = enantioselectivity: Provision of enantioselective transformations in biocatalysts offers the possibility to synthesize chiral molecules instead of bulk chemicals, which may lead to numerous additional applications of reactive distillation technology.

For effective synthesis of chiral molecules via biocatalysts, the competition for binding at the active site between two enantiomers (A, B) can be expressed via the ratio of their reaction rates (ν^A, ν^B [mol∙s^-1]) by the dimensionless enantioselectivity (E [-]) also alled e a tio e i atio (Eq. 4) [93]:

= Eq. 4

The corresponding reaction to the products P as well as Q is presented in Figure 2.4, A. Both competing enantiomers form a complex consisting of the biocatalyst and the enantiomeric starting material ([BiocatA], [BiocatB]), which exhibit different Gibbs free energies (∆G [J]) in their transition-states (Figure 2.4, B). Generally, the system always has the tendency to preferentially convert the enantiomeric starting material with the lowest ∆G (here: A) due to less effort for

overcoming the activation energy Ea. Hence, a faster reaction rate ν^A compared to ν^B is present in the given example. The difference between the values of Gibbs free energies in the transition-states (∆∆G [J]) as well as the reaction rates can be referred to the present enantioselectivity of the reaction. Assuming thermodynamic equilibrium conditions, the relation between ∆∆G and the reaction rates (ν^A, ν^B [mol∙s^-1]) is defined by the ideal gas constant (R [J∙mol^-1∙K^-1]) and the temperature (T [K]) as follows (Eq. 5):

ΔΔ = − ∙ ∙ ( ) Eq. 5

For the application in reactive distillation, the enantioselectivity should be as high as possible to achieve the synthesis of optical pure chiral molecules. A detailed discussion on the influence of E on biocatalytic reaction performance in asymmetric synthesis is given in section 2.2.4.

Figure 2.4: Principle of enantiomeric differentiation in a biocatalytic reaction. A: Reaction of either enantiomer A or B with the biocatalyst (Biocat) to P or Q with different reaction rates νA and νB. B: Energy diagram (transition state [BiocatA] is preferred due to less ∆G)

• Narrowed operating window: With respect to the feasible operating window in classical reactive distillation (Figure 2.3), thermal sensitivity of biocatalysts causes a narrowed temperature constrain for biocatalytic reactive distillation. Basically, the applied temperature is not only influencing the operating window, but determines the accessible catalytic activity according to the principle of Arrhenius [94]. In fact, the Arrhenius-equation describes the dependency of the reaction rate (k) on the operating temperature (T [K]) involving a pre-exponential factor (k0), the activation energy (Ea [J∙mol^-1]) and the ideal gas constant (R [J∙mol^-1∙K^-1]). While k0 represents a reaction-related constant for the frequency of collision between the applied starting materials, Ea

is defined as the minimum energy, which is necessary for reaction performance (Eq. 6):

[BiocatA] Biocat + P

= ∙ ^{− ∙𝑎} Eq. 6 With increasing temperature, rising reaction rates k are achieved and simultaneously higher catalytic activity is detected (and vice versa). As a rule of thumb going back to va ’t-Hoff (RGT-rule), nearly doubled reaction rates are obtained at a temperature increase of T = 10 K for numerous chemical reactions. However, the RGT-rule does not hold in the case of many biocatalytic reactions [95]. Moreover, the value of the activation energy (Ea) influences the effect on the reaction rate, while typical activation energies range from Ea = 20 – 150 kJ∙mol^-1 [96]. At low activation energies (Ea < 20 kJ∙mol^-1) an increase in the operating temperature has a lower impact on the reaction rate, whereas higher values for Ea result in an increased effect on the reaction rate. Beside rising reaction rates at increased temperatures, oppositional deactivation with respect to increased temperature reduces the catalytic activity especially for biocatalysts [36] [32]. The effect on the biocatalytic reaction rate (ν) can be described by an exponential deactivation term kd [s^-1] within the reaction kinetics, which reduces the initial biocatalytic reaction rate (ν0) in dependency of time (t [s]) (Eq. 7):

= ∙ ^{− 𝑑∙} Eq. 7

One specific case in the deactivation kinetic becomes even more important to compare the behavior of a biocatalyst under changed temperature conditions. The parameter of interest is the half-life time (τ^0.5 [s]), describing the time point at which 50 % of initial activity (boundary condition: v = 0.5∙v0) is present in consequence of activity losses (Eq. 8):

𝜏 _.5=ln⁡ Eq. 8

It has to be mentioned, that the deactivation term (kd [s^-1]) is not only affected by temperature but involves the sum of multiple impact factors such as the applied solvent material and inhibition phenomena. Independent from the applied biocatalyst, long-term stability represented by increased half-life times should be realized to compete with well-established chemical catalysts.

Within biocatalytic reactive distillation, temperature is expected to be the most important influencing factor on kd. Hence, a tradeoff between reduced catalytic activity in consequence of thermal sensitivity and increased reaction rates at rising temperatures should be focused for biocatalytic reactive distillation approaches.

• Prevent inhibition phenomena and overcome equilibrium limitations: Similar to chemical reactions in reactive distillation, shifting the equilibrium to the desired side of reaction needs to be performed in all equilibrium limited reactions to increase the final target compound molar fraction and in this respect the overall yield. Thermodynamically, the equilibrium for an exemplified

equilibrium limited reaction involving the starting materials A and B as well as the formed products C and D with the stochiometric factors (νi [-]) (Eq. 9)

| | + | | ⇌ | | + | | Eq. 9

is expressed by the equilibrium constant Keq [-] (Eq. 10). It is composed of the thermodynamic activities (ai) to the power of the stochiometric factors of the products and the starting materials ( i), while the products are placed in the numerator and the starting materials in the denominator.

𝐾 = ∏ 𝑎 ^𝑖=𝑎^{| |}∙ 𝑎^{| |}

𝑎^{| |}∙ 𝑎^{| |} Eq. 10

Therefore, an equilibrium limitation is present at values of Keq < 1, while Keq > 1 refers to less equilibrium limited reactions. In real solutions, thermodynamic activity ai is connected to the molar fraction (xi [mol∙mol^-1]) via the following relation (Eq. 11).

𝑎 = 𝛾 ∙ Eq. 11

For ideal solutions, intermolecular interactions described by the activity coefficient can be neglected (𝛾 → ) and ai becomes similar to xi. The corresponding equilibrium conversion Xeq [-]

for a stochiometric reaction of the type presented in Eq. 9 can be calculated with the equilibrium constant Keq according to Eq. 12:

= √ 𝐾

+ 𝐾 Eq. 12

As long as an equilibrium limitation in the desired direction of the reaction is defined, it should be modified to allow a successful operation. Useful strategies date back to the principle of Le Chatelier (1884), in which changed pressure, temperature or moles of the reactants mainly influence the equilibrium of the reaction [97]. The possibility to address all those parameters in reactive distillation makes it a powerful approach in handling equilibrium limited reaction systems.

Additionally, in situ separation of reactants from the position of the catalyst leads to the reduction of inhibition phenomena, which proves biocatalytic reactive distillation to be an interesting alternative concept for chiral synthesis.