**2. Influence of mass transfer in various PTC assisted organic reactions**

#### **2.1 O-Alkylation**

Previously, we reported a simplified model [53] to predict the dynamic behavior of the allylation for 2, 4, 6-tribromophenol catalyzed by tetra-*n*-butylammonium bromide. The intermediate product viz., of tetra-*n*-butylammonium 2,4,6-tribromophenoxide ((C6H2)- Br3OBu4N) was successfully identified [54]. Kinetic run was started by dissolving a known quantity of potassium hydroxide and 2,4,6-tribromophenol in water. The solution was then introduced into the reactor, which was thermostated at the desired temperature. A measured quantity of allyl bromide and diphenyl ether (internal standard), were dissolved in the chlorobenzene solvent and then added to the reactor. To start the reaction, tetra-*n*butylammonium bromide (TBAB) was then added to the reactor. Aliquot samples (0.8 mL) were collected from the reactor at regular intervals of time. After the separation of organic phase from aqueous phase, 0.1 mL of the organic-phase sample was immediately diluted with 4.5 mL of methanol and the sample was analyzed by HPLC analysis. A general schematic diagram of phase-transfer catalysis for the allylation of 2, 4, 6-tribromophenol is presented in Scheme 1.

Scheme 1. O-Alkylation of 2,4,6-tribromophenol under PTC Conditions

where the parameters, Kaq, Korg, KArOQ and KQBr are given in the Nomenclature section.

crown ethers and cryptands have all been immobilized on various kinds of supports, including polymers (most commonly (methylstyrene-costyrene) resin crosslinked with divinylbenzene), alumina, silica gel, clays, and zeolites [40–51]. Kinetics of triphase phasetransfer-catalyzed reactions [52] are influenced by (i) mass transfer of reactant from bulk liquid to catalyst surface; (ii) diffusion of reactant through polymer matrix to active site; (iii) intrinsic reaction rate at active site; (iv) diffusion of product through polymer matrix and mass transfer of product to external solution; (v) rate of ion exchange at active site. In heterogeneous conditions, for a proper mass transfer to occur, both the liquid phases should be in contact with catalyst. Thus, mass transfer of reactant from bulk solution to catalyst surface and mass transfer of the product to the bulk solution are the significant steps involved. The reaction mechanism of these PTC's system is often complicated and several factors affect the conversion of reactants. With all these antecedents, in this chapter, a kinetic and mathematical model of phase-transfer catalysis concerning mass transfer with various organic reactions will be presented. An extensive detail has been made on the effects of mass transfer in the PTC reaction systems. Further, it is proposed to present the diffusion resistance of an active phase-transfer catalyst in the organic phase and mass-transfer

resistance between the droplet and the bulk aqueous phase.

K+ Q+Br- ArO-

KQBr

Kaq

Korg

+ +

Scheme 1. O-Alkylation of 2,4,6-tribromophenol under PTC Conditions

**2.1 O-Alkylation** 

presented in Scheme 1.

+

ArO-

**2. Influence of mass transfer in various PTC assisted organic reactions** 

Previously, we reported a simplified model [53] to predict the dynamic behavior of the allylation for 2, 4, 6-tribromophenol catalyzed by tetra-*n*-butylammonium bromide. The intermediate product viz., of tetra-*n*-butylammonium 2,4,6-tribromophenoxide ((C6H2)- Br3OBu4N) was successfully identified [54]. Kinetic run was started by dissolving a known quantity of potassium hydroxide and 2,4,6-tribromophenol in water. The solution was then introduced into the reactor, which was thermostated at the desired temperature. A measured quantity of allyl bromide and diphenyl ether (internal standard), were dissolved in the chlorobenzene solvent and then added to the reactor. To start the reaction, tetra-*n*butylammonium bromide (TBAB) was then added to the reactor. Aliquot samples (0.8 mL) were collected from the reactor at regular intervals of time. After the separation of organic phase from aqueous phase, 0.1 mL of the organic-phase sample was immediately diluted with 4.5 mL of methanol and the sample was analyzed by HPLC analysis. A general schematic diagram of phase-transfer catalysis for the allylation of 2, 4, 6-tribromophenol is

ArOR QBr ArOQ RBr Organic Phase

where the parameters, Kaq, Korg, KArOQ and KQBr are given in the Nomenclature section.

KArOQ

+

Q+ K+Br- Aqueous Phase

In order to formulate a mathematical model to describe the dynamic behavior of the twophase reaction shown above, a two-film theory is employed to consider the mass transfer of the catalysts between two phases. Hence, those equations which model the two-phase reaction are presented below. The rate of change for ArOQ in the organic phase is the difference of mass-transfer rate and organic-phase reaction rate.

$$\frac{d\mathbf{C}\_{ArOQ}^{org}}{dt} = K\_{ArOQ}A \left( \mathbf{C}\_{ArOQ}^{aq} - \frac{\mathbf{C}\_{ArOQ}^{org}}{m\_{ArOQ}} \right) - K\_{org}\mathbf{C}\_{RBr}^{org}\mathbf{C}\_{ArOQ}^{org} \tag{1}$$

The rate of change for ArOQ in the aqueous phase is the difference of aqueous-phase reaction rate and mass transfer rate.

$$\frac{d\mathbf{C}\_{ArOQ}^{aq}}{dt} = \mathbf{K}\_{org}\mathbf{C}\_{ArOK}^{aq}\mathbf{C}\_{QBr}^{aq} - \mathbf{K}\_{ArOQ}A\mathbf{f}\left(\mathbf{C}\_{ArOQ}^{aq} - \frac{\mathbf{C}\_{ArOQ}^{org}}{m\_{ArOQ}}\right) \tag{2}$$

Similarly, the rate of change for QBr either in the organic phase or in the aqueous phase is obtained as shown in (3) and (4).

$$\frac{d\mathbf{C}\_{QBr}^{org}}{dt} = \mathbf{K}\_{org}\mathbf{C}\_{ArOQ}^{org}\mathbf{C}\_{RBr}^{org} - \mathbf{K}\_{QBr}A\left(\mathbf{C}\_{QBr}^{org} - m\_{QBr}\mathbf{C}\_{QBr}^{aq}\right) \tag{3}$$

$$\frac{d\mathbf{C}\_{QBr}^{aq}}{dt} = \mathbf{K}\_{QBr} A f \left( \mathbf{C}\_{QBr}^{org} - m\_{QBr} \mathbf{C}\_{QBr}^{aq} \right) - \mathbf{K}\_{aq} \mathbf{C}\_{ArOK}^{aq} \mathbf{C}\_{QBr}^{aq} \tag{4}$$

The reaction rate of ArOK in the aqueous phase is

$$\frac{d\mathbf{C}\_{ArOK}^{aq}}{dt} = -\mathbf{K}\_{aq}\mathbf{C}\_{ArOK}^{aq}\mathbf{C}\_{QBr}^{aq} \tag{5}$$

The reaction rate of RBr in the organic phase is

$$\frac{d\mathbb{C}\_{RBr}^{org}}{dt} = -K\_{org}\mathbb{C}\_{ArOQ}^{org}\mathbb{C}\_{RBr}^{org} \tag{6}$$

In the above equations, "f" is defined as the ratio of the volume of organic phase (V0) to the volume of aqueous phase (Va), *i.e.*

$$f = \frac{V\_o}{V\_a} \tag{7}$$

The distribution coefficients of catalysts mArOQ and mQBr are defined as

$$\mathfrak{I}m\_{ArOQ} = \frac{\mathfrak{C}\_{ArOQ}^{org(s)}}{\mathfrak{C}\_{ArOQ}^{aq(s)}}\tag{8}$$

$$m\_{QBr} = \frac{\mathbf{C}\_{QBr}^{org(s)}}{\mathbf{C}\_{QBr}^{aq(s)}} \tag{9}$$

Role of Mass Transfer in Phase Transfer Catalytic Heterogeneous Reaction Systems 689

*aq aq aq ArOQ*

*org aq org RBr org QBr aq ArOQ aq ArOK*

⎛ ⎞ <sup>=</sup> ⎜ ⎟ <sup>−</sup>

0

*K A K C*

⎡ ⎤

*org org*

( ) ,0 1

<sup>−</sup> = = (28)

*K A* <sup>=</sup> (29)

(30)

*aq ArOK QBr ArOQ ArOQ*

*fK C C C*

*org aq QBr QBr dC dC*

*org org org org ArOQ RBr aq QBr QBr QBr QBr*

*org org org* 1 *QBr QBr org ArOQ RBr aq QBr aq ArOK m f C KC C*

*org org RBr aq ArOK org RBr <sup>o</sup> ArOQ QBr aq <sup>o</sup> ArOQ ArOQ QBr aq ArOK Q K C kC K C*

*V fm fK A K A K C* <sup>−</sup> <sup>⎧</sup> ⎛ ⎞ <sup>⎫</sup> <sup>⎪</sup> <sup>⎪</sup> = + + ++ + <sup>⎨</sup> ⎜ ⎟ <sup>⎬</sup>

> *ArOQ ArOQ K C K XC*

> > *K C*

The concentration of ArOK in the aqueous phase can be obtained from the material balance of 2,4,6-tribromophenol, which is shown in (12). As shown in (28) and (29), the Damkohler number indicates the ratio of the chemical reaction rate to the mass-transfer rate of the catalyst. An effective fraction of catalyst, η, which is defined as the ratio of the observed two-phase reaction rate to the organic-phase reaction rate with catalyst completely used, is given as

*QBr*

*Da*

*KA KA*

⎩ ⎭ ⎪ ⎝ ⎠ ⎪

*org org org RBr org RBr*

> *aq aq ArOK*

> > *QBr*

0 0

*K C V C <sup>Q</sup> <sup>Q</sup> K C*

*org RBr o*

*V*

<sup>=</sup> <sup>=</sup> ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

*org org app RBr o ArOQ org*

<sup>1</sup> 1 1

Applying the Damkohler numbers of ArOQ and QBr, respectively, as

*C fm*

*rOQ*

η

*A*

*Da*

<sup>=</sup> <sup>⎢</sup> <sup>+</sup> <sup>⎥</sup> <sup>⎢</sup> <sup>⎥</sup> <sup>⎣</sup> <sup>⎦</sup>

*KC C C m C*

*K C C K Af C*

Eliminating CaqArOK from (21) and (22), we obtain

From (3), (4), and (23), we have

Combining (11),( 21), (23), and (26), we have

Substituting (23) into (25)

In a similar way, the following equation is held for QBr:

*org*

*C*

*m*

⎝ ⎠

*ArOQ*

*K C* <sup>=</sup> (23)

*dt dt* <sup>=</sup> <sup>=</sup> (24)

*K A* <sup>=</sup> <sup>+</sup> (25)

(22)

(26)

1

(27)

where the superscript "s" denotes the characteristics of the species at the interphase. The conversion of allyl bromide (RBr) is defined as X,

$$X = 1 - \frac{\mathbf{C}\_{RRr}^{org}}{\mathbf{C}\_{RRr,0}^{org}} \tag{10}$$

where the subscript "0" denotes the initial concentration of allyl bromide. The total number of moles of catalyst (Qo) and the total number of moles of 2,4,6-tribromophenol (Eo) initially are

$$Q\_0 = V\_o \left( \mathbf{C}\_{ArOQ}^{org} + \mathbf{C}\_{QBr}^{org} \right) + V\_a \left( \mathbf{C}\_{ArOQ}^{aq} + \mathbf{C}\_{QBr}^{aq} \right) \tag{11}$$

$$E\_0 = V\_o \left( \mathbf{C}\_{ArOQ}^{org} + \left[ \mathbf{C}\_{RBr,0}^{org} - \mathbf{C}\_{RBr}^{org} \right] \right) + V\_a \left( \mathbf{C}\_{ArOK}^{aq} + \mathbf{C}\_{ArOQ}^{aq} \right) \tag{12}$$

The initial conditions of the above equations are

$$\begin{aligned} \mathbf{C}^{\alpha \text{gr}}\_{QBr} &= \mathbf{0}, \; \mathbf{C}^{\alpha \text{g}}\_{QBr} = \mathbf{C}^{\alpha \text{g}}\_{QBr, 0}, \; \mathbf{C}^{\alpha \text{g}}\_{RBr} = \mathbf{C}^{\alpha \text{g}}\_{RBr, 0}; \; t = 0\\ \mathbf{C}^{\alpha \text{g}}\_{ArOO} &= \mathbf{0}, \; \mathbf{C}^{\alpha \text{g}}\_{ArO} = \mathbf{0}, \; \mathbf{C}^{\alpha \text{g}}\_{ArOK} = \mathbf{C}^{\alpha \text{g}}\_{ArOK, 0}; \; t = 0 \end{aligned} \tag{13}$$

,0

The parameters mQBr, mArOQ, KQBrA, KArOQA, Kaq and Korg for the allylation of 2,4,6 tribromophenol in a two phase catalyzed reaction [54] are as follows:

*ArOQ ArOQ ArOK ArOK*

$$m\_{QBr} = 7.1 \times 10^{-2} - 0.56 \mathcal{C}\_{QBr}^{aq} \tag{14}$$

$$m\_{ArOQ} = (8.02 + 0.05T) + (78.35T - 1165)C\_{ArOQ}^{aq} \tag{15}$$

$$K\_{Q\mathbb{B}r}A = \text{2.69} \qquad \text{min}^{-1} \tag{16}$$

$$K\_{ArOQ}A = 3.84 + 0.06T \qquad \text{min}^{-1} \tag{17}$$

$$K\_{aq} = 3.2 \times 10^7 \exp\left[\frac{-4840}{T + 273.16}\right] \qquad M^{-1} \text{min}^{-1} \tag{18}$$

$$K\_{\rm org} = 3.3 \times 10^9 \exp\left[\frac{-7016}{T + 273.16}\right] \qquad M^{-1} \text{ min}^{-1} \tag{19}$$

After a small induction period, the concentration of ArOQ is kept at a constant value and hence, the pseudo-steady-state hypothesis (PSSH) can be made in the system under investigation, i.e.,

$$\frac{d\mathbf{C}\_{ArOQ}^{org}}{dt} = \frac{d\mathbf{C}\_{ArOQ}^{aq}}{dt} = \mathbf{0} \tag{20}$$

Thus, (1) and (2) become

$$\mathbf{C}\_{ArOQ}^{aq} = \left(\frac{\mathbf{1}}{m\_{ArOQ}} + \frac{K\_{org}\mathbf{C}\_{RBr}^{org}}{K\_{ArOQ}A}\right)\mathbf{C}\_{ArOQ}^{org} \tag{21}$$

$$\mathbf{K}\_{\mathrm{aq}}\mathbf{C}\_{ArOK}^{\mathrm{aq}}\mathbf{C}\_{QBr}^{\mathrm{aq}} = \mathbf{K}\_{ArOQ}A\mathbf{f}\left(\mathbf{C}\_{ArOQ}^{\mathrm{aq}} - \frac{\mathbf{C}\_{ArOQ}^{\mathrm{org}}}{m\_{ArOQ}}\right) \tag{22}$$

Eliminating CaqArOK from (21) and (22), we obtain

$$\mathbf{C}\_{QBr}^{aq} = \frac{f \mathbf{K}\_{org} \mathbf{C}\_{RBr}^{org}}{\mathbf{K}\_{aq} \mathbf{C}\_{ArOK}^{aq}} \mathbf{C}\_{ArOQ}^{org} \tag{23}$$

In a similar way, the following equation is held for QBr:

$$\frac{d\mathbf{C}\_{QBr}^{org}}{dt} = \frac{d\mathbf{C}\_{QBr}^{aq}}{dt} = \mathbf{0} \tag{24}$$

From (3), (4), and (23), we have

$$\mathbf{C}\_{QBr}^{org} = \frac{\mathbf{K}\_{org}\mathbf{C}\_{ArOQ}^{org}\mathbf{C}\_{RBr}^{org}}{\mathbf{K}\_{QBr}A} + m\_{QBr}\mathbf{C}\_{QBr}^{aq} \tag{25}$$

Substituting (23) into (25)

688 Mass Transfer - Advanced Aspects

,0

,0 ,0

0, , ; 0 0, 0, ; 0

= = = = = = = =

The parameters mQBr, mArOQ, KQBrA, KArOQA, Kaq and Korg for the allylation of 2,4,6-

<sup>2</sup> 7.1 10 0.56 *aq m C QBr QBr*

7 1 <sup>4840</sup> <sup>1</sup> 3.2 10 exp min 273.16

9 1 <sup>7016</sup> <sup>1</sup> 3.3 10 exp min 273.16

0

*dt dt* <sup>=</sup> <sup>=</sup> (20)

⎡ ⎤ <sup>−</sup> <sup>−</sup> <sup>−</sup> = × ⎢ ⎥ ⎣ + ⎦

<sup>1</sup> *org aq org RBr org ArOQ ArOQ ArOQ ArOQ*

*K C*

After a small induction period, the concentration of ArOQ is kept at a constant value and hence, the pseudo-steady-state hypothesis (PSSH) can be made in the system under

> *org aq ArOQ ArOQ dC dC*

*C C m KA* ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠

⎡ ⎤ <sup>−</sup> <sup>−</sup> <sup>−</sup> = × ⎢ ⎥ ⎣ + ⎦

*K M aq <sup>T</sup>*

*K M org <sup>T</sup>*

<sup>0</sup> ( ) ( ) *org org aq aq Q VC C VC C o a ArOQ QBr ArOQ QBr* = ++ + (11)

,0

(8.02 0.05 ) (78.33 1165) *aq m T TC ArOQ ArOQ* =+ + − (15)

⎣ ⎦ (12)

<sup>−</sup> =× − (14)

<sup>1</sup> *K A QBr* 2.69 min<sup>−</sup> <sup>=</sup> (16)

<sup>1</sup> *KA T ArOQ* 3.84 0.06 min<sup>−</sup> = + (17)

(13)

(18)

(19)

(21)

*<sup>C</sup>* = − (10)

*org RBr org RBr*

where the superscript "s" denotes the characteristics of the species at the interphase.

1

where the subscript "0" denotes the initial concentration of allyl bromide. The total number of moles of catalyst (Qo) and the total number of moles of 2,4,6-tribromophenol (Eo) initially

<sup>0</sup> ( ,0 ) ( ) *org org org aq aq E VC C C VC C o a ArOQ RBr RBr ArOK ArOQ* = + −+ + ⎡ ⎤

*org aq aq org org QBr QBr QBr RBr RBr org aq aq aq ArOQ ArOQ ArOK ArOK*

tribromophenol in a two phase catalyzed reaction [54] are as follows:

*C CC CC t C C CC t*

*<sup>C</sup> <sup>X</sup>*

The conversion of allyl bromide (RBr) is defined as X,

The initial conditions of the above equations are

are

investigation, i.e.,

Thus, (1) and (2) become

$$\mathbf{C}\_{QBr}^{org} = \mathbf{K}\_{org}\mathbf{C}\_{ArOQ}^{org}\mathbf{C}\_{RBr}^{org} \left[ \frac{1}{\mathbf{K}\_{QBr}A} + \frac{m\_{QBr}f}{\mathbf{K}\_{aq}\mathbf{C}\_{ArOK}^{aq}} \right] \tag{26}$$

Combining (11),( 21), (23), and (26), we have

$$\mathbf{C}\_{ArOQ}^{org} = \frac{\mathbf{Q}\_o}{V\_o} \left\{ 1 + \frac{1}{f m\_{ArOQ}} + \frac{\mathbf{K}\_{org} \mathbf{C}\_{RBr}^{org}}{f \mathbf{K}\_{ArOQ} A} + \left( 1 + f m\_{QBr} + \frac{k\_{aq} \mathbf{C}\_{ArOK}}{\mathbf{K}\_{QBr} A} \right) \frac{\mathbf{K}\_{org} \mathbf{C}\_{RBr}^{org}}{\mathbf{K}\_{aq} \mathbf{C}\_{ArOK}^{aq}} \right\}^{-1} \tag{27}$$

Applying the Damkohler numbers of ArOQ and QBr, respectively, as

$$Da\_{A\_{rOQ}} = \frac{K\_{org}C\_{RBr}^{org}}{K\_{ArOQ}A} = \frac{K\_{org}(1-X)C\_{RBr,0}^{org}}{K\_{ArOQ}A} \tag{28}$$

$$
\Delta D a\_{QBr} = \frac{K\_{aq} C\_{ArOK}^{aq}}{K\_{QBr} A} \tag{29}
$$

The concentration of ArOK in the aqueous phase can be obtained from the material balance of 2,4,6-tribromophenol, which is shown in (12). As shown in (28) and (29), the Damkohler number indicates the ratio of the chemical reaction rate to the mass-transfer rate of the catalyst. An effective fraction of catalyst, η, which is defined as the ratio of the observed two-phase reaction rate to the organic-phase reaction rate with catalyst completely used, is given as

$$\eta = \frac{K\_{app}C\_{RBr}^{org}}{K\_{org} \left(\frac{Q\_0}{V\_o}\right)C\_{RBr}^{org}} = \frac{V\_o C\_{ArOQ}^{org}}{Q\_0} \tag{30}$$

Role of Mass Transfer in Phase Transfer Catalytic Heterogeneous Reaction Systems 691

(Figure 1). Thus, the reaction rate of the organic-phase reaction is much lower than the masstransfer rate of ArOQ. Hence, the mass-transfer resistance of ArOQ from the aqueous phase to the organic phase is negligible when compared with the reaction rate in the organic phase. In addition, the Damkohler number of ArOQ increases with the increase of temperature for a certain value of conversion. This is attributed to the increase in the organic phase reaction rate at a higher temperature while the resistance of mass transfer of ArOQ is

Temperature (°C)

60

Conversion. X 0.0 0.2 0.4 0.6 0.8 1.0

Fig. 1. Dependence of the ratio of the reaction to the mass transfer rate for ArOQ (DaArOQ) on conversion (X) at different temperatures: 0.7 g of allyl bromide, 3.0 g of 2,4,6-tribromophenol, 0.2 g of TBAB catalyst, 1.0 g of KOH, 50 mL of H2O, 50 mL of chlorobenzene. (Adapted from

The order of magnitude of the Damkohler number of QBr (DaBr) for the whole range of conversion is about unity (Figure 2). These results reflect the fact that the mass-transfer rate of QBr from the organic phase to the aqueous phase is slightly larger than the reaction rate in the aqueous phase. A plot of R value, which denotes the relative reactivity of the organic phase to the aqueous phase *vs.* conversion, is given in Figure 3. The R value is less than unity. In combining the results from Figures 1-3, the step of the organic-phase reaction is confirmed as the rate-determining step of the whole reaction quantitatively rather than

From the plot of η *vs.* X, it was found that about 75-90% of the catalyst exists in the form of ArOQ remaining in the organic phase. Further, we found that the concentration of ArOQ in the organic phase increases when the initial amount of catalyst added to the reactor

i. The reaction system was simulated by the proposed model in conjunction with the system parameters, such as mass-transfer coefficients of catalysts, distribution coefficients of catalysts and the intrinsic reaction rate constants either in the organic

ii. The Damkohler numbers, which directly reflect the relative rate of chemical reaction to

50

40

30

qualitatively by other investigators in the published documents.

increases. Some of the salient features of the study are:

the mass transfer of the catalysts, are defined.

phase or in the aqueous phase.

very small.

35

28

21

14

DaArOQ

Ref. [53], by permission)

×103

7

0

where

$$K\_{app} = K\_{org} \mathcal{C}\_{ArOQ}^{org} \tag{31}$$

Thus, η can be expressed as

$$\eta = \frac{1}{1 + \frac{\alpha}{f} + (1 + \beta)R} \tag{32}$$

where

$$\alpha = \frac{1}{m\_{\text{ArOQ}}} + D a\_{\text{ArOQ}} \tag{33}$$

$$
\beta = f m\_{QBr} + D a\_{QBr} \tag{34}
$$

$$R = \frac{K\_{org}C\_{RRr}^{org}}{K\_{aq}C\_{ArOK}^{aq}}\tag{35}$$

The parameters "α" and "β" reflect the effects of the equilibrium distribution of catalysts between two phases and the mass transfer of catalysts across the interphase. "R" is a ratio of the reaction velocity in the organic phase to that of velocity in the aqueous phase. Thus, the concentrations of ArOQ and QBr either in the organic phase or in the aqueous phase can be represented by the following equations:

$$C\_{AroQ}^{org} = \frac{\frac{Q\_0}{V\_o}}{1 + \frac{\alpha}{f} + (1 + \beta)R} \tag{36}$$

$$\mathbf{C}\_{ArOQ}^{aq} = \left(\frac{Q\_0}{V\_o}\right) \eta \alpha \tag{37}$$

$$\mathbf{C}\_{Q^Br}^{or\chi} = \left(\frac{Q\_0}{V\_o}\right) \eta \rho \mathbf{R} \tag{38}$$

$$\mathbf{C}\_{QBr}^{aq} = \left(\frac{Q\_0}{V\_o}\right) \eta f \mathbf{\mathcal{R}} \tag{39}$$

By solving the nonlinear algebraic equations of (11), (12), (32), (36), (37), (38), and (39) with the specified parameters or the operating conditions, the simulation results for f = 1 are given in Figures 1-3.

As given in (28) and (29), the Damkohler number (Da) is defined as the ratio of the reaction rate to the mass transfer rate. From the plot of Da *vs.* the conversion of allyl bromide, it is obvious that the Damkohler number of ArOQ, which also depends on the initial concentration of allyl bromide, is much less than unity for the whole range of conversion

( )

*Da*

*QBr QBr*

*K C*

*K C*

The parameters "α" and "β" reflect the effects of the equilibrium distribution of catalysts between two phases and the mass transfer of catalysts across the interphase. "R" is a ratio of the reaction velocity in the organic phase to that of velocity in the aqueous phase. Thus, the concentrations of ArOQ and QBr either in the organic phase or in the aqueous phase can be

*org org RBr aq aq ArOK*

( )

ηα

ηβ ⎛ ⎞ <sup>=</sup> ⎜ ⎟ ⎝ ⎠

β

*R*

0

*Q*

1 1

+++

*o*

*V*

*o <sup>Q</sup> C R V*

*o <sup>Q</sup> <sup>C</sup> fR V* η

⎛ ⎞ <sup>=</sup> ⎜ ⎟ ⎝ ⎠

By solving the nonlinear algebraic equations of (11), (12), (32), (36), (37), (38), and (39) with the specified parameters or the operating conditions, the simulation results for f = 1 are

As given in (28) and (29), the Damkohler number (Da) is defined as the ratio of the reaction rate to the mass transfer rate. From the plot of Da *vs.* the conversion of allyl bromide, it is obvious that the Damkohler number of ArOQ, which also depends on the initial concentration of allyl bromide, is much less than unity for the whole range of conversion

⎛ ⎞ <sup>=</sup> ⎜ ⎟ ⎝ ⎠

*f* α

*aq* 0 *ArOQ*

*<sup>Q</sup> <sup>C</sup>*

*org* 0 *QBr*

*aq* 0 *QBr*

*org <sup>o</sup> ArOQ*

*<sup>V</sup> <sup>C</sup>*

=

β

*ArOQ*

1 1 1 *R f*

α

1

*m* α

β

*R*

*ArOQ*

+++

η =

*org K KC app org ArOQ* <sup>=</sup> (31)

= + (33)

= *fm Da* + (34)

= (35)

(32)

(36)

(37)

(38)

(39)

where

where

Thus, η can be expressed as

represented by the following equations:

given in Figures 1-3.

(Figure 1). Thus, the reaction rate of the organic-phase reaction is much lower than the masstransfer rate of ArOQ. Hence, the mass-transfer resistance of ArOQ from the aqueous phase to the organic phase is negligible when compared with the reaction rate in the organic phase. In addition, the Damkohler number of ArOQ increases with the increase of temperature for a certain value of conversion. This is attributed to the increase in the organic phase reaction rate at a higher temperature while the resistance of mass transfer of ArOQ is very small.

Fig. 1. Dependence of the ratio of the reaction to the mass transfer rate for ArOQ (DaArOQ) on conversion (X) at different temperatures: 0.7 g of allyl bromide, 3.0 g of 2,4,6-tribromophenol, 0.2 g of TBAB catalyst, 1.0 g of KOH, 50 mL of H2O, 50 mL of chlorobenzene. (Adapted from Ref. [53], by permission)

The order of magnitude of the Damkohler number of QBr (DaBr) for the whole range of conversion is about unity (Figure 2). These results reflect the fact that the mass-transfer rate of QBr from the organic phase to the aqueous phase is slightly larger than the reaction rate in the aqueous phase. A plot of R value, which denotes the relative reactivity of the organic phase to the aqueous phase *vs.* conversion, is given in Figure 3. The R value is less than unity. In combining the results from Figures 1-3, the step of the organic-phase reaction is confirmed as the rate-determining step of the whole reaction quantitatively rather than qualitatively by other investigators in the published documents.

From the plot of η *vs.* X, it was found that about 75-90% of the catalyst exists in the form of ArOQ remaining in the organic phase. Further, we found that the concentration of ArOQ in the organic phase increases when the initial amount of catalyst added to the reactor increases. Some of the salient features of the study are:


Role of Mass Transfer in Phase Transfer Catalytic Heterogeneous Reaction Systems 693

Later, we investigated the reaction of 2,4,6-tribromophenol with allyl bromide catalyzed by triphase catalyst (polymer supported tributylamine chloride) in an organic/alkaline solution [55]. The apparent reaction rates were observed to obey the pseudo-first-order kinetics with respect to the organic reactant when excess 2,4,6-tribromophenol was used. Also, a kinetic model in terms of the intrinsic reactivity and intra-particle diffusion limitations for a spherical catalyst is proposed to describe the triphase catalytic reaction system. The pseudosteady-state approach to the mass balance equation was employed to get the solution. The effective diffusivity of the reactants within the catalyst was obtained from this model and used to predict the observed reaction rate. The apparent reaction rate constants were measured at various agitation speeds using 40-80 mesh of catalyst. Kinetic results indicate that the mass-transfer resistance outside the catalyst can be neglected for agitation speeds

> 0 200 400 600 800 1000 Agitation Speed (rpm)

Fig. 4. Effects of the agitation speed on the apparent reaction rate constant: 9.06 x 10-3 mol of 2,4,6-tribromophenol; 50 mL of water; 1.567 mole ratio of allyl bromide to 2,4,6-tribromophenol; 1.97, mole ratio of KOH to 2,4,6-tribromophenol; 0.488 g of catalyst pellet (40-80 mesh); 50 mL

**2.2 Substitution reaction between hexachlorocyclotriphosphazene and sodium 2,2,2-**

Effects of mass transfer and extraction of quaternary ammonium salts on the conversion of hexachlorocyclotriphosphazene were investigated in detail [56]. Initially, a known quantity of sodium hydroxide, trifluoroethanol, and tetra-*n*-butylammonium bromide were introduced into the reactor which was thermostated at the desired temperature. Measured quantities of phosphazene reactant, (NPCl2)3 and *n*-pentadecane (internal standard) were dissolved in chlorobenzene solvent at the desired temperature. Then, the organic mixture was added into the reactor to start a kinetic run. An aliquot sample was withdrawn from the reaction solution at the chosen time. The sample (0.5 mL) was immediately added to 3 mL of

of chlorobenzene; 50 °C. (Adapted from Ref. [55], by permission)

higher than 600 rpm (Figure 4)

6

5

4

3

2

Kapp × 103

**trifluoro-ethoxide** 

(min ) -1

1

0

iii. The mass-transfer resistance of catalysts from the aqueous phase to the organic phase is negligible.

Fig. 2. Dependence of the ratio of the reaction to the mass transfer rate for QBr (DaQBr) on conversion (X) at different temperatures: 0.7 g of allyl bromide, 3.0 g of 2,4,6-tribromophenol, 0.2 g of TBAB catalyst, 1.0 g of KOH, 50 mL of H20, 50 mL of chlorobenzene. (Adapted from Ref. [53], by permission)

Fig. 3. Dependence of the ratio of the organic-phase reaction to the aqueous-phase reaction rate (R value) on conversion (X) at different temperatures: 0.7 g of allyl bromide, 3.0 g of 2,4,6-tribromophenol, 0.2 g of TBAB catalyst, 1.0 g of KOH, 50 mL of H20,50 mL of chlorobenzene. (Adapted from Ref. [53], by permission)

iii. The mass-transfer resistance of catalysts from the aqueous phase to the organic phase is

50

Conversion. X 0.0 0.2 0.4 0.6 0.8 1.0

40

Fig. 2. Dependence of the ratio of the reaction to the mass transfer rate for QBr (DaQBr) on conversion (X) at different temperatures: 0.7 g of allyl bromide, 3.0 g of 2,4,6-tribromophenol, 0.2 g of TBAB catalyst, 1.0 g of KOH, 50 mL of H20, 50 mL of chlorobenzene. (Adapted from

> Temperature (°C) 60

Conversion. X 0.0 0.2 0.4 0.6 0.8 1.0

Fig. 3. Dependence of the ratio of the organic-phase reaction to the aqueous-phase reaction rate (R value) on conversion (X) at different temperatures: 0.7 g of allyl bromide, 3.0 g of 2,4,6-tribromophenol, 0.2 g of TBAB catalyst, 1.0 g of KOH, 50 mL of H20,50 mL of

50

40

30

30

Temperature (°C) 60

negligible.

DaQBr

Ref. [53], by permission)

1.0

0.8

0.6

0.4

0.2

0.0

0.10

0.08

0.06

0.04

R Value

0.02

0.00

chlorobenzene. (Adapted from Ref. [53], by permission)

Later, we investigated the reaction of 2,4,6-tribromophenol with allyl bromide catalyzed by triphase catalyst (polymer supported tributylamine chloride) in an organic/alkaline solution [55]. The apparent reaction rates were observed to obey the pseudo-first-order kinetics with respect to the organic reactant when excess 2,4,6-tribromophenol was used. Also, a kinetic model in terms of the intrinsic reactivity and intra-particle diffusion limitations for a spherical catalyst is proposed to describe the triphase catalytic reaction system. The pseudosteady-state approach to the mass balance equation was employed to get the solution. The effective diffusivity of the reactants within the catalyst was obtained from this model and used to predict the observed reaction rate. The apparent reaction rate constants were measured at various agitation speeds using 40-80 mesh of catalyst. Kinetic results indicate that the mass-transfer resistance outside the catalyst can be neglected for agitation speeds higher than 600 rpm (Figure 4)

Fig. 4. Effects of the agitation speed on the apparent reaction rate constant: 9.06 x 10-3 mol of 2,4,6-tribromophenol; 50 mL of water; 1.567 mole ratio of allyl bromide to 2,4,6-tribromophenol; 1.97, mole ratio of KOH to 2,4,6-tribromophenol; 0.488 g of catalyst pellet (40-80 mesh); 50 mL of chlorobenzene; 50 °C. (Adapted from Ref. [55], by permission)

#### **2.2 Substitution reaction between hexachlorocyclotriphosphazene and sodium 2,2,2 trifluoro-ethoxide**

Effects of mass transfer and extraction of quaternary ammonium salts on the conversion of hexachlorocyclotriphosphazene were investigated in detail [56]. Initially, a known quantity of sodium hydroxide, trifluoroethanol, and tetra-*n*-butylammonium bromide were introduced into the reactor which was thermostated at the desired temperature. Measured quantities of phosphazene reactant, (NPCl2)3 and *n*-pentadecane (internal standard) were dissolved in chlorobenzene solvent at the desired temperature. Then, the organic mixture was added into the reactor to start a kinetic run. An aliquot sample was withdrawn from the reaction solution at the chosen time. The sample (0.5 mL) was immediately added to 3 mL of

Role of Mass Transfer in Phase Transfer Catalytic Heterogeneous Reaction Systems 695

6 5 5 0 0 \* *dy y <sup>k</sup>*

2 3 0 0 2 3

*o o*

*o*

*o*

*o*

*o*

*o*

*o*

0 123456 *y yyyyyy* = 1, = = = = = = 0 (54)

; 0,1,2,3,4

(55)

[( ) ] [( ) ]

33 5 2 3 1 0

3 3 4 2 32

[ ( )] [( ) ]

[ ( )] [( ) ]

*NPCl OCH CF*

*N P Cl OCH CF*

[ ( )] [( ) ]

*N P Cl OCH CF*

*<sup>y</sup> NPCl* <sup>=</sup>

*<sup>y</sup> NPCl* <sup>=</sup>

*<sup>y</sup> NPCl* <sup>=</sup>

*<sup>y</sup> NPCl* <sup>=</sup>

*<sup>y</sup> NPCl* <sup>=</sup>

*<sup>y</sup> NPCl* <sup>=</sup>

In general, eq. 48-53 can be solved with the following initial conditions of yi.

and

phase and *ko\** = 1.

The solutions are

2 0

3 0

4 0

5 0

6 0

2 3

2 3

3 2 33

2 3

2 3

2 3

2 3

33 2 2 34

3 3 2 35

[ ( )] [( ) ]

[( ( ) ) ] [( ) ]

*NP OCH CF*

\*\*\*\*\* 1 2 3 5 4 12345

where [(NPC12)3]O0 represents the initial concentration of reactant (NPC12)3 in the organic

\* \* 1 0 0 <sup>1</sup> <sup>1</sup> \* \* 0

*<sup>l</sup> <sup>n</sup> <sup>k</sup>*

*k y y n k k*

( )

= = −

*i l*

( )

*n i*

∏

*i i l*

= ≠

*<sup>i</sup> <sup>n</sup> <sup>n</sup> l o*

<sup>+</sup> <sup>=</sup> <sup>+</sup> <sup>+</sup> <sup>=</sup>

∑ ∏

,,,, *k k k k <sup>k</sup> kkkkk kkkkk* <sup>=</sup> <sup>=</sup> <sup>=</sup> <sup>=</sup> <sup>=</sup>

00000

*N P Cl OCH CF*

[ ( )] [( ) ]

*N P Cl OCH CF*

*o*

*o*

*o*

*o*

*o*

2 323

*o*

*NPCl <sup>y</sup> NPCl* <sup>=</sup>

where the dimensionless variables and parameters are defined as

*dy y* <sup>=</sup> (53)

hydrochloric acid to quench the reaction and then the organic-phase contents are analyzed quantitatively by GC using the method of internal standard.

In organic reactions which are driven by SN2 mechanism under phase transfer catalysis conditions, the substrate and the nucleophile react directly *via* a transittion state to product. The system can be explained by first order reaction by plotting ln [(NPCl2)3] *vs.* time, which results in a straight line. Thus, the system can be expressed as:

$$-\frac{d[(NPCl\_2)\_3]\_o}{dt} = k\_{o,app}[(NPCl\_2)\_3]\_o \tag{40}$$

where,

$$k\_{o,app} = k[QOCH\_2CF\_3]\_o \tag{41}$$

The fixed value of *k0,,app* is called the pseudo-steady-state first-order reaction rate constant. The series reaction of the organic phase was explained by the SN2 mechanism [57, 58]. The reaction expressions can be written as:

$$\text{(NPCl}\_2\text{)}\_3 + \text{QOCH}\_2\text{CF}\_3 \xrightarrow{k\_r} \text{N}\_3\text{P}\_3\text{Cl}\_5\text{(OCH}\_2\text{CF}\_3\text{)} + \text{QCl} \tag{42}$$

$$\mathrm{N}\_3\mathrm{P}\_3\mathrm{Cl}\_5\mathrm{(OCH}\_2\mathrm{CF}\_3\mathrm{)} + \mathrm{QOCH}\_2\mathrm{CF}\_3 \xrightarrow{k\_1} \mathrm{N}\_3\mathrm{P}\_3\mathrm{Cl}\_4\mathrm{(OCH}\_2\mathrm{CF}\_3\mathrm{)}\_2 + \mathrm{QCl} \tag{43}$$

$$\mathrm{N\_3P\_3Cl\_4(OCH\_2CF\_3)\_2} + \mathrm{QOCH\_2CF\_3} \xrightarrow{k\_2} \mathrm{N\_3P\_3Cl\_3(OCH\_2CF\_3)\_3} + \mathrm{QCl} \tag{44}$$

$$N\_3P\_3Cl\_3(OCH\_2CF\_3)\_3 + QOCH\_2CF\_3 \xrightarrow{k\_3} N\_3P\_3Cl\_2(OCH\_2CF\_3)\_4 + QCl \tag{45}$$

$$\mathrm{N\_3P\_3Cl\_2(OCH\_2CF\_3)\_4} + \mathrm{QOCH\_2CF\_3} \xrightarrow{k\_4} \mathrm{N\_3P\_3Cl} \text{ (OCH\_2CF\_3)\_5} + \mathrm{QCl} \tag{46}$$

$$\text{N}\_3\text{P}\_3\text{Cl} \text{ (OCH}\_2\text{CF}\_3\text{)}\_5 + \text{QOCH}\_2\text{CF}\_3 \xrightarrow{k\_5} \text{(NP (OCH}\_2\text{CF}\_3\text{)}\_2\text{)}\_3 + \text{QCl} \tag{47}$$

Thus, the reaction rate can be expressed as,

$$\frac{dy\_1}{dy\_0} = -1 + k\_1 \ast \frac{y\_1}{y\_0} \tag{48}$$

$$\frac{dy\_2}{dy\_0} = k\_1 \ \* \frac{y\_1}{y\_0} - k\_2 \ \* \frac{y\_2}{y\_0} \tag{49}$$

$$\frac{dy\_3}{dy\_0} = k\_2 \ast \frac{y\_2}{y\_0} - k\_3 \ast \frac{y\_3}{y\_0} \tag{50}$$

$$\frac{dy\_4}{dy\_0} = k\_3 \ \* \frac{y\_3}{y\_0} - k\_4 \ \* \frac{y\_4}{y\_0} \tag{51}$$

$$\frac{d\underline{y\_5}}{dy\_0} = k\_4 \ast \frac{\underline{y\_4}}{\underline{y\_0}} - k\_5 \ast \frac{\underline{y\_5}}{\underline{y\_0}} \tag{52}$$

$$\frac{dy\_6}{dy\_0} = k\_5 \ast \frac{y\_5}{y\_0} \tag{53}$$

where the dimensionless variables and parameters are defined as

$$\begin{aligned} y\_0 &= \frac{[(NPCl\_2)\_3]\_{\text{lo}}}{[(NPCl\_2)\_3]\_{\text{lo}}^0} \\\\ y\_1 &= \frac{[N\_3P\_3 \, \_{Cl}]\_{\text{t}} (OCH\_2CF\_3)]\_{\text{lo}}}{[(NPCl\_2)\_3]\_{\text{lo}}^0} \\\\ y\_2 &= \frac{[N\_3P\_3 \, \_{Cl}]\_{\text{t}} (OCH\_2CF\_3)\_2}{[(NPCl\_2)\_3]\_{\text{lo}}^0} \\\\ y\_3 &= \frac{[NPCl\_3 (OCH\_2CF\_3)\_3]\_{\text{lo}}}{[(NPCl\_2)\_3]\_{\text{lo}}^0} \\\\ y\_4 &= \frac{[N\_3P\_3 \, \_{Cl}]\_{\text{t}} (OCH\_2CF\_3)\_4}{[(NPCl\_2)\_3]\_{\text{lo}}^0} \\\\ y\_5 &= \frac{[N\_3P\_3 \, \_{Cl}]\_{\text{t}} (OCH\_2CF\_3)\_5}{[(NPCl\_2)\_3]\_{\text{o}}^0} \\\\ y\_6 &= \frac{[(NP(OCH\_2CF\_3)\_2)\_{\text{lo}}]\_{\text{o}}}{[(NPCl\_2)\_3]\_{\text{o}}^0} \end{aligned}$$

and

694 Mass Transfer - Advanced Aspects

hydrochloric acid to quench the reaction and then the organic-phase contents are analyzed

In organic reactions which are driven by SN2 mechanism under phase transfer catalysis conditions, the substrate and the nucleophile react directly *via* a transittion state to product. The system can be explained by first order reaction by plotting ln [(NPCl2)3] *vs.* time, which

> [( ) ] [( ) ] *<sup>o</sup> o app <sup>o</sup> d NPCl k NPCl*

The fixed value of *k0,,app* is called the pseudo-steady-state first-order reaction rate constant. The series reaction of the organic phase was explained by the SN2 mechanism [57, 58]. The

> 1 33 5 2 3 2 3 3 3 4 2 32 ( ) ( ) *<sup>k</sup> N P Cl OCH CF QOCH CF N P Cl OCH CF QCl* <sup>+</sup> ⎯⎯→ + (43)

> 2 3 3 4 2 32 2 3 3 3 3 2 33 ( ) ( ) *<sup>k</sup> N P Cl OCH CF QOCH CF N P Cl OCH CF QCl* <sup>+</sup> ⎯⎯→ + (44)

> 3 3 3 3 2 33 2 3 33 2 2 34 ( ) ( ) *<sup>k</sup> N P Cl OCH CF QOCH CF N P Cl OCH CF QCl* <sup>+</sup> ⎯⎯→ + (45)

> 4 33 2 2 34 2 3 3 3 2 35 ( ) ( ) *<sup>k</sup> N P Cl OCH CF QOCH CF N P Cl OCH CF QCl* <sup>+</sup> ⎯⎯→ + (46)

5 3 3 2 35 2 3 2 323 ( ) ( ( )) *<sup>k</sup> N P Cl OCH CF QOCH CF NP OCH CF QCl* <sup>+</sup> ⎯⎯→ + (47)

> 1 1 1 0 0 1 \* *dy y <sup>k</sup> dy y*

212 1 2 000 \* \* *dy y y k k*

323 2 3 0 00 \* \* *dy y y k k*

434 3 4 000 \* \* *dy y y k k*

5 45 4 5 0 00 \* \* *dy y y k k*

, 2 3

2 3 2 3 33 5 2 3 ( ) ( ) *<sup>o</sup> <sup>k</sup> NPCl QOCH CF N P Cl OCH CF QCl* + ⎯⎯→ + (42)

*dt* − = (40)

, 2 <sup>3</sup> [ ] *o app <sup>o</sup> k k QOCH CF* = (41)

=− + (48)

*dy y y* = − (49)

*dy y y* = − (50)

*dy y y* = − (51)

*dy y y* = − (52)

2 3

quantitatively by GC using the method of internal standard.

results in a straight line. Thus, the system can be expressed as:

reaction expressions can be written as:

Thus, the reaction rate can be expressed as,

where,

$$k\_1 \stackrel{\*}{=} \frac{k\_1}{k\_0} \, \prime \qquad k\_2 \stackrel{\*}{=} \frac{k\_2}{k\_0} \, \prime \qquad k\_3 \stackrel{\*}{=} \frac{k\_3}{k\_0} \, \prime \qquad k\_4 \stackrel{\*}{=} \frac{k\_4}{k\_0} \, \prime \qquad k\_5 \stackrel{\*}{=} \frac{k\_5}{k\_0} \, \prime$$

where [(NPC12)3]O0 represents the initial concentration of reactant (NPC12)3 in the organic phase and *ko\** = 1.

In general, eq. 48-53 can be solved with the following initial conditions of yi.

$$y\_0 = 1, \qquad y\_1 = y\_2 = y\_3 = y\_4 = y\_5 = y\_6 = 0 \tag{54}$$

The solutions are

$$y\_{n+1} = \sum\_{l=0}^{n+1} \frac{\left(\prod\_{i=0}^{n} k\_i^\*\right) y\_0}{\prod\_{i=1 \atop i \neq l}^{n+1} (k\_i^\* - k\_l^\*)}; \qquad n = 0, 1, 2, 3, 4 \tag{55}$$

Role of Mass Transfer in Phase Transfer Catalytic Heterogeneous Reaction Systems 697

Relative Reactivity

PTC 0.5 1.0 1.5 2.0 *k0.5/2 ROH,b % ROH,c %* ROH, Eappd TEAC 0.022 0.022 0.033 0.022 1.00 Trace 0 0 BTMAC 0.039 0.038 0.034 0.033 1.18 4.67 0 0 CTMAB 0.26 0.19 0.17 0.14 1.86 100 4.1 3.7 Aliq.336 0.32 0.25 0.19 0.14 2.3 100 100 ∞ BTEAC 0.28 0.23 0.19 0.16 1.75 19.20 0 0 TBAB 0.36 0.27 0.21 0.17 2.10 100 18 18 BTBAB 0.39 0.29 0.22 0.18 2.16 100 31 51 (a0.0059 mol of (NPCl2)3, 7 g of HOCH2CF3, 3 g of NaOH, 9.6 x 10-5 mol of PTC, 50 mL of chlorobenzene, 20 mL of water, 20 °C; b7 g of HOCH2CF3,3 g of NaOH, 9.6 x 10-5 mol of PTC, 50 mL of chlorobenene, 20 mL of water, 20 °C; c3 g of NaOH, 9.6 x 10-5 mol of PTC, 50 mL of chlorobenene, 20 mL of water, 20 °C. dEapp= [QY]o/[Q+]/[Y-

Table 2. Effects of Catalysts on the Relative Reactivitiesa. (Adapted from Ref. [56], by

Rel. Reactivity

1,2-Dichloroethane 0.82 0.59 0.45 0.30 2.73 5 + 10.36(25) 6.1 Chlorobenzene 0.36 0.27 0.21 0.17 2.10 8 - 5.6(25) <0.1 Dichloromethane 0.36 0.26 0.19 0.14 2.57 5 + 9.08(20) 35 Benzene 0.11 0.09 0.08 0.071 1.55 2 + 2.28(20) <0.001 Toluene 0.14 0.11 0.095 0.07 2.00 4 + 2.37(25) <0.001 Hexane 0.046 0.046 0.041 0.04 1.10 0 + 1.89(20) <0.001 Chloroform 0.059 0.059 0.047 0.043 1.53 2 + 4.8(20) 47

Table 3. Effects of Solvents on the Relative Reactivitiesa. (Adapted from Ref. [56], by

We measured the percentage of quaternary ions in the organic phase of the chlorobenzene/NaOH aqueous system with or without adding HOCH2CF3 (Table 3). From the reaction mechanism it is clear that either the catalyst QOR or QX may stay within the organic phase or the aqueous phase. We attribute the competition of QOR with QX to stay within the organic phase is due to the addition of HOCH2CF3. It is obvious that the addition of the organophilic substance will make the quaternary cation move into the organic phase.

No PTC reaction

]a. Reaction conditions: HOCH2CF3 = 7 g, T BAB = 9.6 x 10-5 mol, solvent = 50

H 0 C H 2 C F3 extracted in solvent

Dielectric constant (temp, °C)

% *+/- <sup>ε</sup>* ETBAB

App. extraction const.

Q+ in chlorobenzene with adding

Q+ in chlorobenzene with out adding

Apparent extraction constants with out addding

*k0,app,* min-1 (NPCl2)3, g

]a )

*k0,app,* min-1 (NPCl2)3, g

PTC 0.5 1.0 1.5 2.0 *k0.5/2* (NPCl2)3

permission)

a ETBAB= [ QBr]o/[Q+]a[Br-

permission)

mL, H2O = 20 mL, NaOH = 3 g, temp = 20 °C

$$y\_6 = \sum\_{l=0}^5 \frac{k\_5^\* \prod\_{i=0}^4 k\_i^\* \left( y\_o^{k\_i^\*} - 1 \right)}{k\_l^\* \prod\_{\substack{i=0 \\ i \neq l}}^5 (k\_i^\* - k\_l^\*)} \tag{56}$$

From eqs 55 and 56, the concentrations of the distributed products, N3P3C16-y(OCH2CF3)y, y = 1-6, including the intermediate and final products, are thus determined. In order to follow the kinetics of phase-transfer catalyzed reactions, it is necessary to sort out the rate effects due to equilibria and anion-transfer mechanism for transfer of anions from the aqueous to the organic phase *i.e.,* the concentration of QOCH2CF3 would remain constant if Q+ concentration in the organic phase remained constant throughout the entire course of a kinetic run and the equilibrium constant *K* is very small.

$$\text{\textbullet QOCH}\_2\text{CF}\_3\text{\textdegree\text{\textbullet Cl}^\cdot\text{\textbullet d}^\cdot\text{\textbullet CCl}^\cdot\text{\textbullet g}^\cdot} \text{\textbullet Cl}^\cdot\text{\textbullet CCl}\_2\text{CF}\_3\text{\textbullet\tag{57}}$$

Many experimental runs were carried out to examine the Q+ values and K values. More than 99.5% of Q+ stay in the organic phase and K value was calculated to be less than 1x10-2. Therefore, the concentration of QOCH2CF3 in the organic phase remains constant. Based on this experimental evidence, those factors affecting the reaction are discussed in the following sections.

In PTC systems, it is recognized that the rate-determining step is controlled by the chemical reaction in the organic phase. In systems involving fast mass-transfer rate of catalyst between two phases, the influence of mass transfer on the reaction can be neglected. However, on varying the concentration of (NPCl2)3, the apparent reaction rate constant values also changes (Table 1). Further, the value of *k0.5/ 2*, defined as the ratio of the *ko,app* value using 0.5 g of (NPCl2)3 to the *ko,app* value using 2 g of (NPCl2)3, is increased for increasing reaction temperature. This phenomenon indicates that the present reaction system is both controlled by chemical kinetics and mass transfer.

Organic reactions, which are controlled by purely chemical reaction kinetics, will be independent of the mass of the reactant on the conversion. The effect of the mass of (NPCl2)3 in presence of different phase transfer catalysts, on the conversion is shown in Table 2. Only in the presence of TEAC the reaction is controlled purely by chemical reaction kinetics. On the other hand other reactions, with different kinds of catalysts, are both controlled by chemical reaction kinetics and mass transfer. A higher influence of mass transfer on the reaction rate is confirmed by higher value of *k0.5/2* .


aReaction conditions: 7 g of HOCH2CF3, 0.0059 mol of (NPCl2)3, 3 g of NaOH, 20 mL of water, 9.6 x 10-5 mol of TBAB, 50 mL of chlorobenzene.

Table 1. Effects of Mass Transfer on the Reaction System*<sup>a</sup>* . (Adapted from Ref. [56] by permission)

0

= ≠

From eqs 55 and 56, the concentrations of the distributed products, N3P3C16-y(OCH2CF3)y,

In order to follow the kinetics of phase-transfer catalyzed reactions, it is necessary to sort out the rate effects due to equilibria and anion-transfer mechanism for transfer of anions from the aqueous to the organic phase *i.e.,* the concentration of QOCH2CF3 would remain constant if Q+ concentration in the organic phase remained constant throughout the entire

Many experimental runs were carried out to examine the Q+ values and K values. More than 99.5% of Q+ stay in the organic phase and K value was calculated to be less than 1x10-2. Therefore, the concentration of QOCH2CF3 in the organic phase remains constant. Based on this experimental evidence, those factors affecting the reaction are discussed in the

In PTC systems, it is recognized that the rate-determining step is controlled by the chemical reaction in the organic phase. In systems involving fast mass-transfer rate of catalyst between two phases, the influence of mass transfer on the reaction can be neglected. However, on varying the concentration of (NPCl2)3, the apparent reaction rate constant values also changes (Table 1). Further, the value of *k0.5/ 2*, defined as the ratio of the *ko,app* value using 0.5 g of (NPCl2)3 to the *ko,app* value using 2 g of (NPCl2)3, is increased for increasing reaction temperature. This phenomenon indicates that the present reaction

Organic reactions, which are controlled by purely chemical reaction kinetics, will be independent of the mass of the reactant on the conversion. The effect of the mass of (NPCl2)3 in presence of different phase transfer catalysts, on the conversion is shown in Table 2. Only in the presence of TEAC the reaction is controlled purely by chemical reaction kinetics. On the other hand other reactions, with different kinds of catalysts, are both controlled by chemical reaction kinetics and mass transfer. A higher influence of mass transfer on the

**mass of reactant, (NPCl2)3, g**

. (Adapted from Ref. [56] by

**Temp.** °**C 0.5 1.0 1.5 2.0** *k1.5/2 k1/2 k0.5/2* 20 0.36 0.27 0.21 0.17 1.24 1.59 2.11 30 0.58 0.40 0.31 0.24 1.29 1.67 2.42 40 0.87 0.75 0.52 0.31 1.67 2.42 2.81

aReaction conditions: 7 g of HOCH2CF3, 0.0059 mol of (NPCl2)3, 3 g of NaOH, 20 mL of water, 9.6 x 10-5

∏

*k ky*

*i*

=

∏

0 \* \*\* 0

*l il i i l*

*k kk*

5 5

6 5

*l*

y = 1-6, including the intermediate and final products, are thus determined.

=

=

∑

*y*

course of a kinetic run and the equilibrium constant *K* is very small.

system is both controlled by chemical kinetics and mass transfer.

*k0,app,* **min-1** 

reaction rate is confirmed by higher value of *k0.5/2* .

Table 1. Effects of Mass Transfer on the Reaction System*<sup>a</sup>*

mol of TBAB, 50 mL of chlorobenzene.

permission)

following sections.

\* <sup>4</sup> \* \*

( )( 1)

*l k i o*

−


(56)

( )

−


(a0.0059 mol of (NPCl2)3, 7 g of HOCH2CF3, 3 g of NaOH, 9.6 x 10-5 mol of PTC, 50 mL of chlorobenzene, 20 mL of water, 20 °C; b7 g of HOCH2CF3,3 g of NaOH, 9.6 x 10-5 mol of PTC, 50 mL of chlorobenene, 20 mL of water, 20 °C; c3 g of NaOH, 9.6 x 10-5 mol of PTC, 50 mL of chlorobenene, 20 mL of water, 20 °C. dEapp= [QY]o/[Q+]/[Y- ]a )

Table 2. Effects of Catalysts on the Relative Reactivitiesa. (Adapted from Ref. [56], by permission)


a ETBAB= [ QBr]o/[Q+]a[Br- ]a. Reaction conditions: HOCH2CF3 = 7 g, T BAB = 9.6 x 10-5 mol, solvent = 50 mL, H2O = 20 mL, NaOH = 3 g, temp = 20 °C

Table 3. Effects of Solvents on the Relative Reactivitiesa. (Adapted from Ref. [56], by permission)

We measured the percentage of quaternary ions in the organic phase of the chlorobenzene/NaOH aqueous system with or without adding HOCH2CF3 (Table 3). From the reaction mechanism it is clear that either the catalyst QOR or QX may stay within the organic phase or the aqueous phase. We attribute the competition of QOR with QX to stay within the organic phase is due to the addition of HOCH2CF3. It is obvious that the addition of the organophilic substance will make the quaternary cation move into the organic phase.

Role of Mass Transfer in Phase Transfer Catalytic Heterogeneous Reaction Systems 699

(2) surface or intrinsic reaction of reactants with active sites, and (3) diffusion of reactants to the interior of the catalyst pellet (active sites) through pores. It was found that the diffusional limitation involves both ion diffusion and organic reactant diffusion within the catalyst pellet. The mass transfer limitation influences the triphase reaction rate. The displacement reaction rate of (NPCl2)3 in the organic phase was limited by the particle diffusion and the intrinsic reactivity together. The film diffusion of the aqueous phase in the ion-exchange step is the main rate limiting factor. The mass transport of the ion-exchange step in the aqueous phase was not improved by increasing the concentration of NaOCH2CF3. The effect of the agitation speed on the conversion of hexachlorocyclotriphosphazene is shown in Figure 5. The reaction follows a pseudofirstfirst-order rate law. Rate constants increased with the agitation rate up to 750 rpm and

The essential condition for a reaction to occur is the effective collision of reactant molecules, even in the phase transfer catalysis system. Recently, Vivekanand and Blakrishnan [29] investigated the effect of varying stirring speed on the rate of the reaction of C-alkylation of dimedone by dibromoethane in the range 200–800 rpm under PTC conditions (Scheme 2). The experimental results show that the rate constants increase with the increase of stirring speed from 200 to 600 rpm. Further increase in the speed of agitation had practically no effect on the rate of reaction (Fig. 6). This is because the interfacial area per unit volume of dispersion increased linearly with increasing the stirring speed till 600 rpm is reached and there after there is no significant increase in the interfacial area per unit volume of dispersion with the corresponding increases in the speed. Consequently, increasing the stirring speed changes the particle size in the dispersed phase. At stirring speeds of 700 and 800 rpm, nearly constant rate constant values were observed. This is not because the process is necessarily reaction rate-limited, but because the mass transfer has reached a constant value. Thus, Fig. 6 is indicative of an interfacial mechanism rather than Starks' extraction mechanism. Chiellini et al. [60] observed a continuous increase in the rate of ethylation of PAN, even up to stirring speeds of 1950 rpm, for which an interfacial mechanism was proposed. Similar observations were made under various phase transfer catalytic reactions

Br 10% NaOH / 0.1mol% MPTC

600 rpm, 50oC Br

The synthesis of 1-(3-phenylpropyl)-pyrrolidine-2,5-dione was successfully carried out [23] from the reaction of succinimide with 1-bromo-3-phenylpropane in a small amount of KOH and organic solvent solid–liquid phase medium under phase-transfer catalysis (PTC)

O

O

Br

increased only slightly up to 1200 rpm.

and an interfacial mechanism was proposed [41,61–64].

Scheme 2. C-Alkylation of dmedone under PTC conditions

**2.3 C-Alkylation** 

O

**2.4 N-Alkylation** 

O

+

As a consequence, the preferential extraction of –OCH2CF3 into the organic phase by the quaternary cation catalyst is responsible for the efficiency of the reaction. The apparent extraction constant, *Eapp,,* is thus an index for reflecting the mass transfer effect. Thus, a larger value of *Eapp* implies that the two-phase reaction is dominated by the effects of mass transfer.

Influence of solvents on the rate of the reaction was examined by employing seven different solvents under PTC conditions (Table 3). The order of relative activities of the solvents is dichloroethane > chlorobenzene > dichloromethane > benzene > toluene > chloroform > hexane. Higher values of *k0.5/2* imply a significant influence of the mass transfer on the reaction rate.

From the Arrhenius plot of *k0,app* of *vs.* 1/T for different initial concentration ratios of NaOH and HOCH2CF3, the activation energy, *Ea*, was obtained and presented in Table 4. Thus, the effects of mass transfer and chemical reaction kinetics on the conversion depend highly on the reactant concentrations of NaOH and HOCH2CF3.



Fig. 5. Dependence of the apparent reaction rate constants *kr,app* and *kf,app* on the agitated rate; 7 g of HOCH2CF3,0.0059 mol of (NPCl2)3, 3 g of NaOH, 20 mL of H20, 0.175 mequiv of catalyst, 50 mL of chlorobenzene, 20 °C. (Adapted from Ref. [59], by permission)

Further, the kinetics and the mass transfer behaviors of synthesizing polytrifluoroethoxycyclotriphosphazene from the reaction of 2,2,2-trifluoroethanol with hexachlorocyclotriphosphazene by triphase catalysis in an organic solvent / alkaline solution were studied [59]. In general, the reaction mechanism of the triphase catalysis is: (1) mass transfer of reactants from the bulk solution to the surface of the catalyst pellet, (2) surface or intrinsic reaction of reactants with active sites, and (3) diffusion of reactants to the interior of the catalyst pellet (active sites) through pores. It was found that the diffusional limitation involves both ion diffusion and organic reactant diffusion within the catalyst pellet. The mass transfer limitation influences the triphase reaction rate. The displacement reaction rate of (NPCl2)3 in the organic phase was limited by the particle diffusion and the intrinsic reactivity together. The film diffusion of the aqueous phase in the ion-exchange step is the main rate limiting factor. The mass transport of the ion-exchange step in the aqueous phase was not improved by increasing the concentration of NaOCH2CF3. The effect of the agitation speed on the conversion of hexachlorocyclotriphosphazene is shown in Figure 5. The reaction follows a pseudofirstfirst-order rate law. Rate constants increased with the agitation rate up to 750 rpm and increased only slightly up to 1200 rpm.
