Division of Organic Chemistry

 

Complex Autocatalytic Reaction Mechanisms in the Dehydration of Alcohols in HMPT.

 

              James C. Ullrey
            

         California State University at Hayward

                                                                                           

 

COMPLEX AUTOCATALYTIC REACTION MECHANISMS IN THE DEHYDRATION OF ALCOHOLS IN HMPT. James C. Ullrey,

The first report of the dehydration reaction of alcohols in HMPT was that of Monson (8) who observed that primary and secondary alcohols are converted without added catalysts to unrearranged olefins at temperatures of 220- 240 C.

 

In order to delineate the mechanistic details of the elimination reaction the observed exclusive conversion of 1,2-diphenylethanol in HMPT to trans-stilbene was chosen as a model system for further study.

 

The reaction kinetics at 169.23 C was followed by observing the appearance of the characteristic ultraviolet absorption of trans-stilbene.


The kinetic experiment produced not the expected rate profile of a pseudo first order reaction, but a sigmoid rate profile.

 

The following mechanism, presented in schemes 1, 2, 3A, 3B, 3C, 3D, 3E, 3F, 3G, 3H, 3J and 3K is postulated to account for the observed behavior. It is a chain reaction, and thus necessarily complicated.

 

        The reaction mechanism has been represented as a QuickTime movie: Complex Autocatalytic Reaction Mechanism

[  SHOW SCHEME 1  AND SCHEME 2 HERE  ]

 

The following theoretical rate law was derived from this mechanism:

 

 dP / dt =  (k1 +  k2 P)(P  -  P)                                              (1)

 

where P represents the product of the reaction, trans- stilbene, and the quantity (P - P) represents the reactant.

 

 The form of the rate law was used to classify the reaction type as complex autocatalytic.  The theoretical rate law was expressed as an analytical function by solving the differential equation.. The experimental data was fitted to this analytical function using two algorithms, one that involved a direct search method and another using Bremmerman's optimizer (x).

 

Kawanisi, et al. (19) reported the isolation of the tetramethyl phosphorodiamidate ester of adamantanol which supports the assumption of Monson (9) that an ester of that sort played some role in the alcohol dehydration mechanism.  This report also supports the phosphate ester postulated as an intermediate in the above mechanism

 

Monson also observed (8) that small amounts of the N,N-dimethylamine were formed along with the olefins. The formation of the N,N-dimethylamine by the breakdown of the protonated HMPT molecule in the above mechanism is supported by this observation.

 

 

In order to clearly present this idea it is necessary  to present it in several levels of organization. The first two levels involve displaying the individual reactions 1 through 5 as components of a system of reactions. The first level is displayed in schemes 1 and 2. The second level of organization is depicted in scheme 3A, where the component reactions are organized to show the reaction flow. Schemes 3B, 3C, 3D, 3E, 3F, 3G, 3H, 3J and 3K are duplicates of scheme 3A with the individual reactions listed in schemes 1 and 2  highlighted by shading the boxes containing the compounds participating in the reaction. The third level of organization consists of a discussion of the reactions in schemes 1 and 2 with reference to facts that support those reactions. The fourth level of organization is a discussion of the interaction of the various reactions and the dynamics of their complex interaction. This fourth level discussion follows schemes 3A, 3B, 3C, 3D, 3E, 3F, 3G, 3H, 3J and 3K.

 

Please refer  now  to  schemes 1 and 2.  The first  level of organization is displayed in  schemes 1 and 2  and the second level of organization is displayed in schemes 3A through 3K. The third level of organization commences here. Schemes 1 and 2 show the elementary reactions 1, 2, 3, 4 and 5. In scheme 1, the presence of tetramethylphosphorodiamidic chloride (TMPDA-Cl), designated B, a participant in reaction 1, is postulated and supported by the fact that the species is an intermediate in the manufacture of HMPT (26). Also, there is an article published that gives a procedure for the removal of this chemical from HMPT (25). The reaction of diphenylethanol with TMPDA-Cl is postulated to be a slow step and thus has k1 associated with it. A product of this reaction is the protonated HMPT. Other products of the reaction are  postulated to be the phosphate ester, designated CS, and the chloride ion. The fate of these products will be discussed below but first is a discussion of the fate of the protonated HMPT. The reaction of HMPT with protic acids has been reported by Normant (26) and is shown in scheme 4.

 

According to Normant, when  a protic acid, for example hydrochloric acid, is added to HMPT, HMPT is protonated. This is shown as reaction 6.  The protonated HMPT rearranges so that the proton resides on one of the amide nitrogens. This is shown as reaction 7. The protonated HMPT decomposes to produce the tetramethylphosphorodiamidic phosphocation, designated C+, and  dimethylamine. This is shown as reaction 8. C+ combines with the conjugate base of the acid. This is shown as reaction 9. The scheme of

 

                                                             

                                  O                                       O-H +         

                                  ||                                        ||                             

H + A-    + [Me2N]2PNMe2   --->   [Me2N]2PNMe2   +    A-                         6

                

 

 

                O-H +                              O H +

                ||                                       ||   |

[Me2N]2PNMe2   --->   [Me2N]2P-NMe2                                          7

 

 

                O H +                                O

                ||  |                                     ||                          

[Me2N]2P-NMe2   --->   [Me2N]2P +    + NHMe2                                          8

 

 

                O                                         O

                ||                                          || 

[Me2N]2P +  +  A-   --->   [Me2N]2P-A                                                9

 

SCHEME 4

 

 

 

Normant can be found twice in scheme 1 by threading through the four reactions in that scheme.  In reaction 1 the molecule B corresponds to the product in Normant's scheme of HMPT and HCl. When B interacts with the alcohol the alcohol hydroxylic proton is lost and is picked up by the solvent to form the protonated HMPT which corresponds to the product of Normant's reaction 6 in scheme 4. In reaction 1 the source of the proton is the alcoholic hydroxyl proton. The interaction of the molecule B with the alcohol group results in a bond between the oxygen atom and the phosphorus atom, giving  a complex in which the molecule has a phosphate ester linkage with a proton residing on the oxygen atom of the linkage. This is just a formal description and does not imply any order of bond forming and stretching in the transition state. I consider this formal complex to act as a Bronsted acid. The conjugate base of this acid becomes the chloride ion.

 

The thread passes on to include reaction 3. Reaction 3 is the combination of reactions 7 and 8 in Scheme 4. In reaction 3 the protonated HMPT fragments to produce C+ and dimethylamine. Normant's scheme explains the observed evolution of dimethylamine from reactions of refluxing HMPT with alcohols (21). Reaction 4 completes the first scheme of Normant with the recombination of C+ with the chloride ion to reform B. With this assumption the concentration of B may be considered to be constant, modified only by the short resident time in which the molecular fragments that are part of B are part of the complex with the alcohol. This assumption allows the concentration of B to be unchanged and thus constant, and thus it can be absorbed into the rate constant k1.

 

 

 

The second thread in scheme 1 is started when the ester, CS, eliminates with a loss of a proton. One species, CS, fragments to become three species. The product molecule, trans-stilbene, is the first. The phosphate fragment, F -,  is the second. It assumes the role of the conjugate base, with the third fragment being the proton. The proton is picked up by the solvent to participate in reaction 3. Whether the elimination reaction is initiated by carbon oxygen bond cleavage or whether the elimination is initiated by abstraction of the proton by the solvent is kinetically invisible  and cannot be distinguished in this experiment. The protonated HMPT fragments in reaction 3 to form the C+ ion. The only difference between the products of this version of reaction 3 is that instead of the chloride ion we have the tetramethyldiamidic phosphate anion, F -, as the anionic fragment.   One fate of the C+  and  F -  ions thus formed is for them  to combine to form octamethylpyrophosphorotetraamidate, designated OMPA. This idea is supported by the findings of Leov and Massengale (27) who reported the formation of the pyrophosphate linkage in connection with the thermal decomposition of alkyl tetraethylphosphorodiamidates. Monson and Priest also found evidence for the pyrophosphate linkage in connection with the conversion of benzyl alcohols into benzyldimethylamines in HMPT (21). OMPA is postulated to be unreactive and so thus its formation is a chain termination step.

 

I assume long chains and thus exclude its contribution to the scheme when deriving the equations. The factors considered in assigning to OMPA an unreactive posture is that that compound can be refluxed with strong base (hydroxide) for long times at high temperature with negligible hydrolysis (28). Also the rate of hydrolysis of OMPA in an EtOH-pH 6.0 buffer solution (20:80) at 70 C was investigated (29) and it was found that there was negligible hydrolysis after 96 hours. In scheme 1 reactions 1 and 2, a proton is lost from the substrate in each, and picked up by the solvent. Reaction 3 shows the fate of these protons, and since there are two protons and I am counting protons, reaction 3 is listed twice.

 

In scheme 2 reaction 5 is a major fate of the species C+. This step is postulated to be a slow step and has associated with it the rate constant k2. This reaction is very similar to the reaction of B with the alcohol. In scheme 2 reactions 5 and 2, a proton is lost from the substrate in each, and picked up by the solvent. Reaction 3 shows the fate of these protons and as before, reaction 3 is listed twice. The product of reaction 3, C+, is the major character in this overall reaction scheme and thus rates being accounted for.

 

 

In scheme 2, reaction 5 is the elementary reaction of major significance in the overall reaction mechanism. In scheme 2, again reaction 2 is included and reaction 3, twice included, are noted. Scheme 3A is the overall outlook which includes all the elementary reactions that are included in schemes 1 and 2 and shows how all the elementary reactions interact for the total picture. In scheme 3B reaction 1 from scheme 1 is highlighted by shading in the boxes. In scheme 3C reaction 2 is highlighted.  Scheme 3D highlights reaction 3 where the source of the proton is the hydroxylic proton. Scheme 3E highlights reaction 3 where the source of the proton is the proton from the carbon bond skeleton. Scheme 3F highlights reaction 4, the recombination of the chloride ion with C+. Scheme 3G highlights reaction 5, the combination of a C+ ion with another alcohol molecule. Scheme 3H highlights reaction 2 where the phosphate ester is formed in a chain propagating step, reaction 5, rather than when reaction 2 results from a phosphate ester formed in a chain initiation step as in reaction 1. Scheme 3J highlights reaction 3 where the source of the proton is a hydroxylic proton from the chain propagating step reaction 5. Scheme 3K highlights reaction 3 where the source of the proton is from the carbon skeleton in the chain propagation step in reaction 2.  The net equation for reactions 1, 2, 3, 3 and 4 are shown in scheme 5. The net equation for reactions 5, 2, 3 and 3 are shown in scheme 6. In the net equations the chemical symbols are used but subsequently they will be referred to by alphabetical symbols. The relationship between the alphabetical symbols and the chemical symbols are explicitly listed below.

 

 

 

 

                   OH

                   |

A =        -CH-CH2-

 

                             O

                             ||

B =       [Me2N]2PCl

 

                              O

                              ||

C+ =      [Me2N]2P+

 

 

                              

D =       NHMe2 

 

 

                         O          

                         ||

                   O-P[NMe2]2

                    |

CS =       -CH-CH-

 

 

 

P =          -CH=CH-

 

 

                                    O  O

                                    ||   ||

OMPA  =    [Me2N]2POP[NMe2]2

 

 

Using these symbols and the net equations it is possible to write a set of differential equations to represent the change in concentrations of the various species with respect to time.

 

- dA / dt  =  k1 A  +  k2 A C +                                                   (2)

 

 

 

 

The differential equation (2) is formed from consideration of the net chemical equations 1, 2, 3, 3 & 4 and the net chemical equations 5, 2, 3 & 3. Equation 3 is listed twice in each set  because two protons are lost  for each conversion of reactant to product and I am counting protons. B is absorbed into k1 in  the differential equation (2). I consider the rate limiting step to be the collision of the alcohol with B, but if the reaction were to be considered a three body reaction then the overall order before the absorption of B into the constant is third plus third order. HMPT is the solvent for this reaction and its concentration change over the course of the reaction is negligible. Thus I can eliminate the concentration of HMPT from the differential equation and then the overall reaction order is pseudo second order plus pseudo second order. After the absorption of the concentration of B into the rate constant k1 the overall reaction order is pseudo first plus pseudo second order. The rate expression can be expressed as the sum of two orders because the reaction, as described by the model, is biphasic. The observables are the induction period, where a period of time elapses before any noticable change in the measured concentration of the product. The initiation step is postulated to be a random event of low probability. Once the initiation step occurs the propagation  phase takes over where the rate is limited by the availability of

the C+ species in the early stages. The early stage lasts until half of the reactant is consumed. Once half of the reactant is consumed the late stage commences and the limiting factor becomes the availability of reactant.

 

d C+ / dt  =  k1 A +  k2 A C +                                                    (3)

 

d P / dt  =   k1 A  +  k2 A C +                                                                  (4)

 

d P / dt  =  d C + / dt                                                                                 (5)

 

Integrating equation (5) gives

 

P  =  C +   constant of integration                                                       (6)

 

The argument which follows is intended to convince the reader that the constant of integration is sufficiently close to zero that it may be ignored. It is clear that, according to the postulated mechanism, that for every molecule of product that is produced, a molecule of the phosphocation is produced. Assuming long chains, i.e. that the phosphoanion does not combine with the phosphocation to form OMPA, the difference between the concentration of the product and the concentration of the phosphocation differs by the amount of the phosphocation that has reacted with the alcohol. The reaction of the cation and the alcohol is the slow step. Once formed, the phosphate ester, according to the hypothesis, quickly eliminates to form the product and the protonated HMPT. The HMPT reaction is also considered to be fast, and thus the phosphocation is quickly returned to the pool.    

 

It becomes convenient to make the following approximation:

 

Ao =   P                                                                                                 (7)

 

From the law of mass balance

 

Ao  =  A +  P                                                                                             (8)

 

Substituting eqn. 7 into eqn. 8 and rearranging

 

P    -  P  =  A                                                                                          (9)

 

Substituting eqn. 6 and eqn. 9 into eqn. 4

 

d P / dt  =  k1 (P - P)  +  k2 (P - P) P                                             (10)

 

 

 

Factoring

 

d P / dt  =  (k1  +  k2 P) (P   -  P)                                                        (11)

 

This equation is identical in form to that shown by Zawidzki (30) for complex autocatalysis. This equation is also identical to the observed rate law, eqn. 1.

 

Equation 11 may be rearranged to give

 

d P / (k1 / k2  +  P) (P   -  P)  =  k2 dt                                                 (12)

 

thus separating the variables. The exact solution to this equation is known (31) and has the form

 

 

            1                         (P  +  k1/k2)P

-------------------------  ln  -------------------------      =    k2 t         (13)

  (k1/k2  +   P )          (P  -  P) k1/k2

 

where the boundry conditions are:

P = P  at  t = t,   P = 0  at  t = 0.

 

 

 

Equation 13  may be solved for P to give

 

 

 

                            ( k1 +  k2 P )t

                   k1 e                             -  k1

P  =  P   ---------------------------------------------     (14)

                             ( k1 +  k2 P )t

                   k1 e                                 + k2 P

 

 

 

 

 

To test the hypothesis that tetramethylphosphorodiamidic chloride (TMPDA-Cl, B) is a participant in this scheme, a catalytic amount of this substance (32) was added to the reaction mixture of run #13. The result was a decrease in the time required to achieve 50% reaction to approximately 5 hours ( typical half times for previous runs were 10, 14, 8.25 and 7.75 hours). The result is shown in the extreme left in Figure 25. The experimental data from Figure 22 is included for comparison. Figure 26  shows the trajectory calculated as before  for run 13. The other calculated trajectories are included from Figure 23 for comparison. Figure 27 shows all the trajectories with the experimental data from run 13.

 

 

At the very least I may conclude that the reaction is catalyzed by a proton equivalent, i.e. TMPDA-Cl. At the other extreme I may conclude that indeed the presence of this species as an impurity in the solvent in trace quantities has a dramatic effect in the course of the reaction. In conlusion, more work is needed in this area, namely, the solvent should be treated according to the procedure of Fomicheva (25) and experiments made to determine if the reaction can be initiated in pure solvent. A series of reactions should be run with varying amounts of TMPDA-Cl, which would allow the determination of a rate constant for the component of the rate law where the first term is k1AB. An experiment should be conducted with a catalytic amount of OMPA to test the hypothesis that that species is unreactive.