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Effect of solvent proton affinity on the kinetics of Michael addition polymerization of N,N'-bismaleimide-4,4'-diphenylmethane with barbituric acid.

INTRODUCTION

Polymerization of N,N'-bismaleimide-4,4'-diphenylmethane (BMI) with barbituric acid (BTA) results in materials that possess excellent mechanical properties, chemical resistance, thermal stability and attractive performance/ cost ratio. Pan et al. (1) investigated the polymerizations of BMI with BTA and characterized the resultant hyper-branched polymers. The presence of free radicals during polymerization was confirmed by the electron spin resonance spectra of BTA at different temperatures (363-443 K). Thus, free radicals originating from BTA were capable of initiating the polymerization of BMI containing the reactive bismaleimide groups (i.e., two terminal -C=C- groups). Nevertheless, the potential Michael addition reactions cannot be ruled out because each BTA molecule contains two >NH groups and one >[CH.sub.2] group and the active hydrogen atoms of these functional groups may lake part in the polymerization of BMI with BTA via the Michael addition reaction mechanism. In our previous work (2), (3), hydroquinone (HQ), an extremely effective inhibitor in capturing free radicals, was used as a molecular probe to study the reaction mechanisms and kinetics involved in the polymerizations of BMI wilh BTA. It was concluded that the polymerization of BMI/ BTA was primarily controlled by both the free radical and Michael addition polymerization mechanisms. It was shown that the apparent overall heat of reaction obtained from the nonisothermal polymerizations of BMI with BTA with different molar ratios of BTA/BMI first decreased rapidly and then leveled off as the HQ concentration was increased. In addition, the extent of reduction in the apparent overall heal of reaction decreased with increasing molar ratio of BTA/BMI. These results indicated that free radical polymerization contributed significantly to the polymerizations of BMI with BTA and it became more important as the mole fraction of BTA initially present in the reaction system was decreased. [[.sup.1]H]-NMR and [[.sup.13]C]-NMR characterization of the linear polymer prepared by the polymerization of the model compound N-phenylmaleimide with BTA further supported the coexistence of the Michael addition reaction and free radical polymerization mechanisms.

In our previous work (4), the effects of solvent basicity on the polymerizations of BMI with BTA were studied. The results illustrated the greatly enhanced formation of the three-dimensional crosslinked network structure during polymerization by the nitrogen-containing cyclic solvents such as N-methyl-2-pyrrolidone (NMP). By contrast. the polymerization of BMI with BTA in a cyclic solvent in the absence of nitrogen atoms such as [gamma]-butyrolactone eventually resulted in nil gel content. It was concluded that the higher the solvent basicity, the larger the amount of insoluble polymer species formed. Recently, we have developed a mechanistic model that adequately predicted the Michael addition polymerization of BMI with BTA in the temperature range 383-423 K with the aid of adding sufficient HQ to completely suppress the free radical polymerization (5), This approach is capable of decoupling the rather complicated competitive Michael addition reaction and free radical polymerization mechanisms, thereby leading to the true key kinetic parameters such as the reaction rate constants and activation energy for the Michael addition reaction polymerization. The objective of this work was to focus on the kinetics of Michael addition polymerization of BMI/BTA (2/1 (mol/mol)) carried out in solvents with differ proton affinity at different temperatures. The solvents of choice included NMP, N,N'-dimethylacetamide (DMAC) and N,N'-dimethylfor-mamide (DMF). The values of proton affinity are 923.4, 908.0, and 887.5 kJ [mol.sup.-1]for NMP, DMAC, and DMF, respectively (6). The solvent [gamma]-butyrolactone was not chosen for study simply because the Michael addition polymerization rate was too slow to give satisfactory differential scanning calorimeter (DSC) data for computer simulation. The ratio of BTA/HQ was kept constant at 1/1 (w/w) to eliminate the contribution of the free radical polymerization (5). The dependence of the activation energy for the Michael addition polymerization of BMI/ BTA ([E.sub.a]) on the solvent proton affinity will be presented in this work.

EXPERIMENTAL

Materials

The reagents used in this work include BMI (Beil, 95%), BTA (Merk. 99+%). NMP (Sigma. 99%). DMAC (Acros, 99.5%), DMF (Acros, 99.8%), dimethyl sulfoxide-d6, (DMSO-d6, Aldrich, 99.96%), and HQ (Acros, 99%). All chemicals were used as received.

Polymerization Kinetics and Characterization

The isothermal polymerization of BMI with BTA was carried out in a Tzero hermetic pan in the DSC (TA Instruments Q20). The nitrogen flow rate was set at 50 mL [min.sup.-1]. The molar ratio of BMI/BTA was kepi constant at 2/1, and the total solids content of the resultant BMI/BTA polymer in solution (7 [+ or -] 1 mg in the Tzero hermetic pan) was kept constant at 20.46% without taking into consideration HQ throughout this work. Because of the slightly different solvent density, both the initial concentrations of the -C=C- associated with BMI ([[M].sub.[omicron]]) and the active hydrogen atoms of the two >NH groups and one >[CH.sub.2] group associated wiih BTA ([[[B.sub.H].sub.0]]) were kept constant at 1.04. 0.96. and 0.94 M for NMP. DMAC and DMF. respectively (note that BMI/BTA =2/1 (mol/ mol) and one BMI molecule contains two reactive terminal -C=C- groups, whereas one BTA molecule possesses four reactive hydrogen atoms).

The fractional conversion ([X.sub.M]) was defined as

[X.sub.M]= [[DELTA][H.sub.1] - [DELTA][H.sub.BTA/HQ,t]([[[B.sub.H]].sub.0]]/ [[[B.sub.H]].sub.BTA/HQ,t]])]/[DELTA]H (1)

where [DELTA][H.sub.1] is the integral area under the heat flow versus time (t) curve for the polymerization of BMI/BTA in the presence of HQ at the reaction temperature T from t = 0 to t (Fig. 1a). The term [DELTA][H.sub.BTA/HQ.t] ([[[B.sub.H]].sub.0]/[[[B.sub.H]].sub.BTA/HQ,0]) is the integral area under the heat flow versus time (t) curve for the independent experiment involving the reaction between BTA and HQ at T from t=0 to t (Fig. 1b), which is attributed to the scenario that the addition of sufficient HQ to completely quench the free radical polymerization consumes some active hydrogen atoms of the two >NH groups and one >CH2 group associated with BTA during polymerization. In these independent experiments, the weight ratio of BTA/HQ was kept constant at 1/1 and the values of [[[B.sub.H]].sub.BTA/HQ.0] were 1.20, 1.10, and 1.10 M for the runs with NMP. DMAC and DMF. respectively. The ratio of ([[[B.sub.H]].sub.0]/[[[B.sub.H]].sub.BTA/HQ,0]) represents the concentration correction factor, It should be noted that the value of[DELTA][H.sub.BTA/HQ.t] ([[[B.sub.H]].sub.0]/[[[B.sub.H]].sub.BTA/HQ,0]) used the computer simulation of the kinetics of the polymerization of BMI/ BTA in the presence of HQ may be overestimated (i.e., the conversion of the -C=c- associated with BMI may be underestimated) because of the competitive reaction of BMI with BTA via the Michael addition polymerization mechanism. The parameter AH (= 63.33 [+ or -] 5.73 J [g.sup.1]) in the denominator represents the apparent overall heat of reaction obtained from the isothermal polymerization of BMI with BTA in the absence of HQ at 423 K (the highest reaction temperature used in this work that is lower than the boiling point (477 K.) of NMP to avoid the contamination of the sample cell) over a period of 1 h that is long enough to achieve a satisfactory base line. Thus, this method may well overestimate the conversion of the -c=c- associated with BMI provided that the polymerization was incomplete. The [X.sub.M] versus t profiles thus obtained from the Michael addition polymerizations of BMI/BTA in the presence of HQ in different solvents carried out at different temperatures are shown in Fig. 2. The reproducibility of the experiments in duplicate (see the open and closed data points in Fig. 2) is satisfactory.

To quantitatively determine this side reaction effect, 20 mL of a BTA in NMP solution containing a prescribed amount of HQ [[[[B.sub.H]].sub.0]]= 2 M, BTA/HQ = 1/1 (w/w)| was charged into a 100-mL three-neck flask in a thermostatic oil bath at T, reacted wilh magnetic mixing for 1 h and then cooled to room temperature. It should be noted that the heat-treated sample was precipitated by an excess of toluene in our previous work (5). The resultant product was then filtered and dried in a vacuum oven at 333 K for 24 h. However, we found later on that toluene was incapable of precipitating HQ at room temperature to any appreciable extent. By contrast, approximate 70% of the initial BTA was recovered by using toluene as the precipitant. In this manner, the level of active hydrogen atoms of the two >NH groups and one >[CH.sub.2] group of BTA consumed by HQ was underestimated significantly during the Michael addition polymerization of BMI/BTA in the presence of HQ, as reflected in the quite high value of [theta] (= [[[B.sub.H]].sub.0]/[[M].sub.0] = 0.95) reported in Ref. 5. To resolve this problem, after the reaction of BTA with HQ at T (BTA/ HQ = I/l (w/w): [[[B.sub.H]].sub.BTA/HQ.0]= 1.20. 1.10 M, for NMP. DMAC. and DMF, respectively), the sample of the BTA/HQ solution was placed in an aluminum pan to form a thin film. This was followed by drying the sample in a vacuum oven at 333 K for 24 h. The molecular structure of the resultant powder was characterized by [[.sup.1]H]-NMR (Bruker Avance, 500 MHz). The [[.sup.1]H]-NMR characterization work was described in detail elsewhere (5). In brief, DMSO-d6 was used as the solvent, and tetramethylsilane used as the internal standard in [[.sup.1]H]-NMR measurements. The characteristic peaks of BTA at [delta] = 3.46 and 11.09 ppm corresponding to the >CH2 group and the >NH group, respectively, (7) were used to establish the calibration curve [integral area = 273.12 [times] (BTA/ DMSO-D6). coefficient of determination ([R.sup.2]) = 0.99751 by plotting the integral area of the characteristic peak of >NH at [delta] = 11.09 ppm (or that of >CH2 at [delta] = 3.46 ppm) versus the concentration of BTA in the absence of the HQ treatment.

SCHEME 1. (a) The reaction mechanism involved in the Michael addition of the -C=C- group of BMI with the active hydrogen atom of the >[CH.SUB.2] group of BTA and (b) the reaction mechanism involved in tile aza-Michael addition of the -C=C- group of BMI with the active hydrogen atom of the >NH grimp of BTA (8). The parameters [K.sub.1] and [K.sub.2] are the reaction rate constants, [K.sub.eq] the equilibrium constant, and B: and [H-S.sup.[direct sum]] the base (or solvent) and the protonated base (or solvent), respectively.

RESULTS AND DISCUSSION

Michael Addition Polymerization Kinetics ModeI

Based on the proposed mechanisms involved in the Michael addition reaction of the -C=C- group of BMI with the active hydrogen atom of the >[CH.sub2.] or >NH group of BTA. as illustrated in Scheme 1. a kinetic model for the Michael addition polymerization of BMI/BTA in the presence of sufficient HQ (HQ/BTA = 1/1 (w/w)) to completely quench the free radical polymerization was developed, and the major governing equations (Eqs. 2 and 3) are summarized as follows (5):

[R.sub.M] = ([K.sub.M,CH][[B.sub.CH]] + [K.sub.M,NH][[B.sub.NH]][M] (2)

where [R.sub.M] is the total Michael addition polymerization rate, and the first and the second terms on the right hand are the Michael addition polymerization rates corresponding to the polymerizations of the -C=C- group of BMI with the >[CH.sub.2] group and the >NH group of BTA. respectively. The kinetic parameters [K.sub.M,CH] and [K.sub.M,NH] represent the reaction rate constants, and [[B.sub.CH]].[[B.sub.NH]] and [M] are the molar concentrations of the active hydrogen atom of >[CH.sub.2], the active hydrogen atom of >NH and the -C=C- of BMI, respectively. With an additional assumption that both the active hydrogen atoms of the >[CH.sub.2] and >NH groups of BTA exhibit exactly the same reactivity toward the -C=C- of BMI (i.e.. [k.sub.M,CH] = [k.sub.M,NH]=[K.sub.M]) Eq. 2 can be simplified as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [[B.sub.H]] = [[B.sub.CH]] + [[B.sub.NH].Eq.3 is subject to the initial conditions: [[B.sub.H]] = [[[B.sub.H]].sub.0] and [M] =[[M].sub.0], where[[[B.sub.H].sub.0]] is the initial concentration of the active hydrogen atoms of the >[CH.sub.2] and >NH groups of BTA and [[M].sub.0] is the initial concentration of the -C=C- of BMI. Equation 3 was then taken as the starling point of the following model development work.

In an attempt to take into account the side reaction of BTA with HQ during the Michael addition polymerization of BMI with BTA in the presence of HQ, the following rate expression for the consumption of the active hydrogen atoms of the >[CH.sub.2] and >NH groups of BTA ([R.sub.BH]) was proposed in this study.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[X.sub.M] = 1 - ([M]/[[M].sub.0]) (5)

where [K.sub.BTA/HQ] is the reaction rate constant for the reaction between BTA and HQ during the Michael addition polymerization of BMI/BTA in the presence of HQ at T, [HQ] is the concentration of HQ. and m and n are the reaction orders with respect to [[B.sub.H]] and [HQ] respectively. The rate of consumption of the active hydrogen atoms of the >CH: and >NH groups of BTA by HQ during the Michael addition polymerization of BMI/BTA in the presence of HQ (expressed in the reaction order model fonti of [K.sub.BTA/HQ] [[[B.sub.H]].sup.m] [[HQ].sup.n]) was approximated as the product of [eta],[[BH].sub.0]and the first derivative of the empirical function f(t) ([f.sup.t](t)) determined experimentally, as will be discussed below. [X.sub.M] is the fractional conversion of the -C=C- of BMI at t.

The empirical function f(t) was obtained from [[.sup.1]H]-NMR in combination with DSC for the independent experiment involving the reaction between BTA and HQ in the solvent (NMP, DMAC, or DMF) at T over a period of 1 h.

f(t) = f(0) - ([DELTA][H.sub.BTA/HQ,t]/[DELTA][H.sub.BTA/HQ])[f(0) - f(t)] (6)

where f(t) (= [[B.sub.H]].sub.BTA/HQ/[[B.sub.H].sub.BTA/HQ,0) is the fraction of the active hydrogen atoms of the >[CH.sub.2] and >NH groups of BTA remaining at t, [[B.sub.H].sub.BTA/HQ] are the concentrations of [B.sub.H] at t and the initial concentration of [B.sub.H]. respectively, f(0) (= 1) and f([t.sub.f]) are the initial and final fractions of the active hydrogen atoms of the >[CH.sub.2] and >NH groups of BTA, respectively, [DELTA][H.sub.BTA/HQ,t], is the integral area under the heat flow versus t curve for the polymerization of BMI/BTA in the presence of HQ at the reaction temperature T from t = 0 to t (Fig. 1b), and [DELTA][H.sub.BTA/HQ,t] is the apparent overall heat of reaction obtained from the isothermal reaction between BTA and HQ at T (Fig. 1b). The value of f([t.sub.f]) ([t.sub.f] = 1 h in this work) was determined by [[.sup.1]H]-NMR measurements in duplicate in combination with the calibration curve shown in the EXPERIMENTAL section and the values of f(t) were calculated according to Eq. 6. Representative f(t) data for the reaction between BTA and HQ in NMP at 383 K are illustrated in Fig. 3a. The reproducibility of the

two sets of f(t) data is reasonably good. The least-squares best-fit technique was then used to express the experimental data of f(t) in a polynomial form (Fig. 3a and Table 1 ). Furthermore, the f([t.sub.f]) data as a function of T for the reaction between BTA and HQ in differeni solvents are shown in Fig. 4. It is shown that the effect of solvent on the extent of the reaction between BTA and HQ in decreasing order is: NMP > DMAC > DMF. The data of f(t) thus obtained are summarized in Tables 1-3. Note that the term [eta](t) in Eq. 4 represents the rate of consumption of the active hydrogen atoms of the >CH2 and >NH groups of BTA during the Michael addition polymerization of BMI/BTA in the presence of HQ. as briefly illustrated below:

TABLE 1. The least-squares best-fit results of f(t) and /[nta](t) for
the reaction of BTA with HQ (HQ/BTA = 1/1 (w/w)) in NMP at
differeni temperatures.

T(K)             f(t).[eta](t)

383   [f.sub.I](t)= 6.194 [times] [10.sup.-4]
      [t.sup.2] - 3.884 [times] [10.sup.-2]t + 1
      [f.sub.II](t)= 3.352 [times] [10.sup.-6] [t.sup.2]
       - 4.045 [times] [10.sup.-4]t +6.08 X[10.sup.-1]
      [[eta].sub.I](t)=-4.192 [times] [10.sup.-4] [t.sup.2]
       + 7.949 [times] [10.sup.-2]t+ 1.579 [times] [10.sup.-1]
      [[eta].sub.II](t)= 5.220 [times] [10.sup.-3] [t.sup.3]
       - 1.922 [times] 1[10.sup.-1] [t.sup.2] +2.184 t -
       7.072  19.05, 16.51 0.9971
      [[eta].sub.III](t)= - 3.168 [times] [10.sup.-4] t
      + 3.996 [times] [10.sup.-2]

393   [f.sub.I](t)= 6.850 [times] [10.sup.-3] [t.sup.2]
       - 1.146 [times] [10.sup.-1]t+1
      [f.sub.II](t)= 9.808 [times] [10.sup.-6] [t.sup.2]
     - 9.867 [times] [10.sup.-4] t+ 5.267 [times] [10.sup.-1] 19
        .02. 58.85]0.9999
      [[eta].sub.I](t)= -4.379 [times] [10.sup.-2] [t.sup.2]
       + 3.074 [times] `[10.sup.-1] t + 3.202 [times] [10.sup.
       -1] (0, 2.65] 0.9640
      [[eta].sub.II](t)= 2.853 [times] [10.sup.-2] [t.sup.2]
      - 4.842 x[10.sup.-1] t+ 2.025 [2.67. 7.08
       1 0.9803
      [[eta].sub.III](t)= -1.017 [times] [10.sup.-3]
       t + 6.878 [times] [10.sup.-2]   [7.1, 58.851 0.9728

403   [f.sub.I](t)= 1.407 [times] [10.sup.-2] [t.sup.2]
     - 1.527 [times] [10.sup.-1] t + 1   [0, 4.13] 0.9996
      [f.sub.II](t)=3.182 [times] [10.sup.-5] [t.sup.2]-
       3.140 X[10.sup.-3] t + 6.288 [times] [10.sup.-2]
       14 .15. 58.95] 0.9999
      [[eta].sub.I](t)= -3.703 [times] [10.sup.-2]
       r + 1.078 / +4.658 [times] 10 '2 [0, 1.78] 0.9821
      [[eta].sub.II](t)= 9.167 [times] [10.sup.-2] [t.sup.2]-
       9.021 [times] [10.sup.-1] t + 2.288   [1.8. 4.92] 0.9931
      [[eta].sub.III](t)= 1.050 x[10.sup.-3] t +
      7.283 [times] [10.sup.-2]    [4.93. 58.95] 0.9905
413   [f.sub.I](t)= 4.785 [times] [10.sup.-2] [t.sup.2]
       - 2.537 x[10.sup.-1] t +1   I + 1 OD. 31. 0.9997
      [f.sub.II](t)= 5.504 [times] [10.sup.-5] [t.sup.2]
      - 5.220 [times] [10.sup.-3] t + 6.627 [times] [10.sup.-1]
      [[eta].sub.I](t)= -1.677 [t.sup.2] + 1.800 t
     + 0.4.409 [times] [10.sup.-1] [0.77. 4,05] 0.9885
      [[eta].sub.II](t)= -5.030 [times] [10.sup.-2] [t.sup.3]
      +5.218 [times] [10.sup.-1] [t.sup.2] - 1.794 t + 2.125
      14.07. 59.03] 0.9876[[eta].sub.III](t)= 2.867 x
     [10.sup.-3] t + 7.776 [times] [10.sup.-2]

423   [f.sub.I](t)= 5.033 [times] [10.sup.-2] [t.sup.2]
      - 1.777 [times] [10.sup.-1] + 1  [0, 2] 0,9999
      [f.sub.II](t)= 7.907 [times] [10.sup.-5] [t.sup.2]
      - [10.sup.-3] t + 8.396 [times] [10.sup.-1]
      [[eta].sub.I](t)= -41.040 [t.sup.2] +
      8.993 t +4.494 [times] [10.sup.-4]   [0. 0.17] 0,9880
      [[eta].sub.II](t)= 4.1095 [times] [10.sup.-1] [t.sup.2]
      - 1.369 t + 1.250   [0.18, 1.93] 0.9814
      [[eta].sub.III](t)= 4.671 [times] [10.sup.-7] [t.sup.4]
      - 6.681 [times] [10.sup.-5] [t.sup.3]+ 2.956 [times] [10.sup.-3]
      [t.sup.2] [1.95, 59.07] 0.9984- 2.931 [times] [10.sup.-2] t
      + 1.980 [times] [10.sup.-1]


T(K)      [t.sub.1],[t.sub.2]  [R.sup.2]
383       [0-4]                0.9997

          [14.02,58.53]        0.9999

          [0,9.03]             0.9935

          [9.05,16.5]          0.9975


          [16.52, 58.53]       0.9577


393       [0,9]                0.9995

          [9.02, 58.85]        0.9999


          [0, 2.65]            0.9640


          [2.67, 7.08]         0.9803


          [7. 1, 58.85]        0.9728


403       [0. 4 13]            0.9996

          [4,15 58.95]         0.9999


          [0, 1.78]            0.9821

          [1.8, 4.92           0.9931

          [4.93, 58.95]        0.9905
          [0. 3]               0.9997
413       [3.02, 59.03]        0.9999

          [0, 0.75]            0.9895
          [0. 0.75]            0.9895
          [0.77, 4.05]         0.9885

          [4.07, 59.03]        0.9876




423       [0, 2]              0.9999

          [2.02, 59.07]       0.9999

          [0, 0.17]           0.9880

          [0.18, 1.93]       0.9814

          [1.95, 59.07]      0.9984


[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

As aforementioned, [[[B.sub.H]].sub.BTA/HQ,0]and ][[[B.sub.H]].sub.BTA/HQ], represent the concentrations of the active hydrogen atoms of the >[CH.SUB.2] and >NH groups of BTA at t equal to 0 and t respectively, in the independent experiment involving the side reaction of BTA with HQ. The parameter [eta](t) (0 < [eta] < 1 ) takes in to account the competition between the Michael addition polymerization of BMI with BTA and the side reaction of BTA with HQ. For example, with [eta] equal to one (i.e., the competitive Michael addition polymerization of BMI with BTA appears invisible to the side reaction of BTA wiih HQ), one apparently overestimates the rate of consumption of the active hydrogen atoms of the >[CH.sub.2] and >NH groups of BTA via the side reaction of BTA with HQ. Conversely, the side reaction of BTA with HQ does not contribute to the kinetics of the Michael addition polymerization of BMI/BTA in the presence of HQ to an appreciable extent when [eta] equal to zero. The value of [eta](t) was estimated as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where g(t) and h(t) represem the heat flow versus t curve for the polymerization of BMI/BTA in the presence of HQ (Fig. 1a) and the heat flow versus t curve for the independent experiment involving the side reaction between BTA and HQ (Fig. 1b) at T. respectively, and 0 [less than or equal to] t [less than or equal to] [t.sub.f]-[DELTA]t. Representative [eta](t) data based on the average g(t) and h(t) data obtained from duplicate experiments with NMP as the solvent at 383 K are illustrated in Fig. 3b. The least-squares best-fit technique was then used to express the experimental data of [eta](t) in a polynomial form (Fig. 3b). Some general features of [eta](t) are (i) the effect of [eta](t) on the Michael addition polymerizations of BMI with BTA in a particular solvent decreases rapidly with decreasing temperature and (ii) the influence of [eta](t) on the polymerizations in different solvents in increasing order is: DMF < DMAC [much less than] NMP. which correlates quite well with the solvent proton affinity (the solvent proton affinity in increasing order is: DMF < DMAC < NMP). In fact, the effect of the competitive side react ion of BTA wilh HQ (as reflected in the magnitude of [eta](t)) on the polymerizations carried out in DMAC or DMF is negligible (data not shown here). The experimental data of [eta](t) in a polynomial form obtained from the least-squares best-fit technique for the reactions of BTA with HQ in NMP in the temperature range 383-423 K also can be found in Table 1. For conciseness, the [eta](t) data for the reactions of BTA with HQ in DMAC or DMF were not included in Tables 2 and 3 since the side reactions essentially showed insignificant effect in the kinetic studies.

TABLE 2. The least-squares best-fit resale of f(t) for the reaction of
BTA with HQ (HQ/BTA = 1/1 (w/w)) in DMAC at different temperatures.

T(K)        f(t).[eta](t)                         [t1,t2]    [r.sub.2]

383         f(t)= 4.319 [times] [10.sup.-5]       [0.58.53]  0.9953
            [t.sup.2] - 4.100 [times]
            [10.sub.-3]t + 1

393         f(t)= 1.151 [times] [10.sup.-4]       [0,57,62]  0.9733
            [t.sup.2] - 9.750 [times]
            [10.sup.-3] t +1

403         [f.sub.I](t)= 4.110 [times]           [0,20]     0.9999
            [10.sup.-4] [t.sup.2]-1.834 [times]
            [10.sup.-]t+1

            [f.sub.II](t)= 6.222 [times]          [20,02,    0.9999
            [10.sup.-6][t.sup.2]- 8.939 [times]   57,62]
            [10.sup.-4]t+ 7.918 [times]
            [10.sup.-1])

413         [f.sub.I](t)= 7.248 [times]           [0. 15]    0.9999
            [10.sup.-4] [t.sup.2] - 2.405
            [times] [10.sup.-2] t + 1

            [f.sub.II](t) = 8.365 [times]         [15,.02.,  0.9999
            [10.sup.-6] [t.sup.2] - 2.150         57.,2]
            [times] [10.sup.-3]t + 7.954
             [times] [10.sup.-1]

423         [f.sub.I](t) = 8.951 [times]          [0,10]     0.9999
            [10.sup.-4] [t.sup.2] -1.995 [times]
            [10.sup.-2] t + 1
            [f.sub.II](t)= 1.046 [times]
            [10.sup.-5]
            [t.sup.2] -2.491 [times]
            [10.sup.-3]t+ 8.85 [times]            [10.02.    0.9999
            [10.sup.-1]                           57.03]
TABLE 3. The least-squares best-fit results f(t) for the reaction of BTA
 with HQ (HQ/BTA = 1/1 (w/w) in DMF at different temperatures.

   T(K)                         f(t).n(t)

   383        [f.sub.t](t)= 6.376 [times] [10.suo.-7]
                   [t.sup.4]-3.485 [times] [10.sup.-5] [t.sup.3]
                    + 7.260 [times] [10.sup.-4] [t.sup.2]
              -7.883 [times] [10.sup,-3] t + 9.9870 [times] [10.sup.-1]
              [f.subu](t)  = -2.093 [times] [10.sup.-6] t +
                    9.541 [times] [10.sup.-1]
   393        [f.sub.t](t) = - 1.289 [times] [10.sup.-4]
                  [t.sup.3] + 2.577 [times] [10.sup.-3] [t.sup.2]
                  -1.774 [times] [10.sup.-2] t + 1
              [f.sub.t](t) = -3.568 [times] [10.sup.-6] t
                  + 9.589 [times] [10.sup.-1]
   403        [f.sub.t](t) = -2.014 [times] [10.sup.-3] [t.sup.3]
                  + 2.393 [times] [10.sup.-2] [.sup.2]
                  - 9.865 [times] [10.sup.-2] t + 1.011
              [f.sub.u](t) = -6.481 [times] [10.sup.-5] t
                 + 8.676 [times] [10.sup.t]
   413        f(t) = 1

T(K)   [[t.sub.1].[t.sub.2]]            [R.sup.2]

383    [0,22,38]                        0.9950

    [22.40,57.87]                    0.9999


393    [0, 9]                           0.9963

       [9.02. 57.82]                    1.0000

403    [0, 4.95]                        0.9999

       [4.97.58.97]                     0.9999

413    [0, 58.97]                       1.0000


In this manner, Eqs. 4-7 with one adjustable parameter, [k.sub.M](T), can be solved simultaneously with the aid of the software MATLAB to give the [X.sub.M] versus t profile for the Michael addition polymerization of BMI with BTA in the presence of HQ at T. Finally, the activation energy ([E.sub.a]) can be determined by the Arrhenius equation:

In [K.sub.M] = INA-[E.sub.a]/(RT) (8)

where A is the frequency factor, R the gas constant (8.314 J [mol.sup.1]), and T the absolute temperature.

Effect of Solvent Proton Affinity on Michael Addition Polymerization Kinetics

The general feature of the kinetic data obtained from the Michael addition polymerizations of BMI/BTA in the presence of HQ in NMP at different temperatures was described in detail elsewhere (5) and it will not he reproduced herein. In brief, the fractional conversion ([X.sub.M]) first increases rapidly and then levels off wilh the progress of polymerization (Fig. 2). In addition, the Michael addition polymerization rate ([R.sub.M]), as reflected in the slope of the [X.sub.M] versus t data during the early stage of polymerization, increases significantly with increasing temperature. The following will focus on the effect of solvents with different proton affinity (NMP (923.4 kJ [mol.sup.-1]), DMAC (908.0) and DMF (887.5) (6)) on the Michael addition polymerization kinetics.

Figure 5a shows a representative computer modeling result of the Michael addition polymerization of BMI/ BTA in the presence of HQ in NMP at 403 K. It is shown that the proposed model with [K.sub.M] equal to 3.9 [times] [10.sub.-2] L/ (mol min) predicts the kinetic data reasonable well before a limiting fractional conversion of ca. 0.41 is achieved. During the latter stage of polymerization, the highly crosslinked polymer reaction system with an extremely high viscosity greally retards the mobility of the residual -C=C- of BMI and the >NH and >[CH.sub.2] groups of BTA attached to the gigantic polymer network structure. As a consequence, the reaction rate constant [K.sub.M] is greatly reduced during the latter stage of polymerization, thereby leading to a significant reduction in the polymerization rate (i.e.. the ultimate fractional conversion). In our previous work (5), a diffusion-controlled reaction model was developed to adequately describe the limiting conversion behavior observed during the latter stage of the Michael addition polymerization of BMI/BTA in the presence of HQ in NMP at different temperatures. Thus, only the major pari of the experimental data collected in the chemical reaction-controlled region (e.g.. 0 [leqq] [X.sub.M] < 0.41 for the runs in duplicate at 403 K) were used to determine the kinetic parameter [K.sub.M] (T) in this study. It is also interesting to note that the side reaction of BTA with HQ plays an important role only during the early stage of polymerization ([X.sub.M] < 0.12). as illustrated by the rales of consumption of the active hydrogen atoms of BTA via the competitive Michael addition reaction (corresponding to the term [K.sub.M] [B.sub.H] [M] in Eq. 4) and the side reaction involving HQ (corresponding to the term -[eta](t) [[B.sub.H].sub.BTA/HQ/0 [f.sup.t](t) in Eq. 4) (Fig. 5b). Similar theoretical results were also observed for the polymerizations carried out at different temperatures, but the effect of the side reaction of BTA wilh HQ decreases with deceasing temperature (data not shown herein).

The general validity of the mechanistic model was further verified by comparing the experimental data with the model predictions for the Michael addition polymerizations of BMI/BTA in the presence of HQ in different solvents (NMP, DMAC, or DMF) in the temperature range 383-423 K, as shown in Fig. 2. It should be noted that the calculated maximum rates of the side reaction involving HQ (corresponding to the term -[eta](t) [[B.sub.H].sub.BTA/HQ/0 [f.sup.t](t) in Eq. 4) for the runs with DMF and DMAC (data not shown here) are at least two orders of magnitude lower than that for the run with NMP at 403 K (see the dotted line in Fig. 5b). This is simply because the influence of [eta](t) on the polymerizations in different solvents in increasing order is: DMF < DMAC [much less than] NMP. As expected, the Michael addition polymerization rate increases with increasing temperature. Furthermore, the average ultimate fractional conversion achieved for the polymerizations in different solvents in the temperature range investigated in this study in increasing order is: 0.45 [+ or -] 0,05 (NMP) < 0.56 [+ or -] 0.01 (DMAC) < 0.66 [+ or -] 0.02 (DMF). This is most likely due to the different extents of the influence of the competitive side reaction of BTA with HQ during the early stage of polymerization [i.e., [eta](t)] associated with the solvents used in this work. As aforementioned, the effect of [eta](t) on the polymerizations in different solvents in increasing order is: DMF < DMAC [much less than] NMP. The side reaction of BTA wilh HQ will cause a deviation in the molar ratio of the -C=C- group of BMI to the active hydrogen atoms of the >NH and >[CH.sub.2] groups of BTA from the ideal stoichiometric ratio (1/1). This factor will then result in a greatly reduced ultimate fractional conversion of the -C=C- group of BMI. Thus, as expected, the Michael addition polymerizations of BMI/BTA in the presence of HQ in NMP with the highest proton affinity (i.e.. the largest [eta](t) in the temperature range 383-423 K exhibit the lowest average ultimale fractional conversion.

The data of [K.sub.M] as a function of T thus obtained from the Michael addition polymerizations of BMI/BTA [2/1 (mol/mol)] in different solvents can be expressed in Arrhenius form (Eq. 8), as shown in Fig. 6. The data of [E.sub.a] (= -slope [times] R) and A along with the [R.sup.2] values associated with the least-squares best-fitted straight lines for (the Michael addition polymerizations of BMI/BTA [2/1 (mol/mol)] in different solvents are summarized in Table 4. The relevant solvent proton affinity data available in the literature (6) are also included in this table. The values of [E.sub.a] are estimated to be in the range 46.1-57.0 kJ [mol.sup.-1]). which are quite comparable to that (43 kJ [mol.sup.-1]) obtained from the Michael addition polymerizations of BMI with 4,4'-diaminodiphenylmethane (9). In addition, the values of [E.sub.a] obtained from this study and the literature value (9) are much lower than that (76.3 kJ [mol.sup.-1] ) of the polymerizations of BMI/BTA [2/1 (mol/mol)] in the absence of HQ reported in our previous work (2). This is because the competitive Michael addition and free radical polymerization mechanisms are operative simultaneously in the latter BMI/BTA polymerization system. It is also interesting to note that [E.sub.a] in increasing order is; NMP <DMAC <DMF. This implies that the solvent NMP with the highest proton affinity (i.e., the strongest basicity) acts as the most effective catalyst among the solvents investigated in this work that greatly lowers the energy barrier for the Michael addition polymerization of BMI with BTA. By contrast, the magnitude of the frequency factor A in increasing order is: NMP < DMAC < DMF. As a result of the compensation effect between [E.sub.a] and A, at constant T, [K.sub.M] decreases with increasing solvent proton affinity. The reason for this irend is not clear at this point of time, but it is most likely related to the thermodynamic aspect that A is proportional to exp([DELTA]S/R), where [delta]S is the entropy of activation, which is negative simply because two reacting molecules encounter with each other to form one species (10), It is therefore postulated that, based on the calculated values of A, the absolute value of [delta]S in decreasing order is: NMP > DMAC > DMF.

TABLE 4. Data of [E.sub.a] and A for the Michael addition
polymerizations of BMI/BTA [2/1 i mol/mol )1 in the presence of HQ
(HQ/BTA = 1/1 (w/wl) in different solvents.

         Proton affinity        [E.sub.a]-             inA  [R.sup.2]
       (kJ [moL.sup.-1])  (kJ [mor.sup.-1])  [L/(mol min)]

 NMP               923.4              46.12         10.472     0.9868

 DMAC              908.0              49.51         12.279     0.9905

 DMF               887.5              56.96         15.004     0.9953


CONCLUSIONS

The effect of solvent proton affinity on the kinetics of the isothermal Michael addition polymerizations of BMI and BTA wilh BMI/BTA = 2/1 (mol/mol) in different solvents (NMP, DMAC. and DMF) in the temperature range 383-423 K. were investigated. This was achieved by the complete suppress of the competitive free radical polymer reactions via the addition of a sufficient amount of HQ [BTA/HQ = 1/1 (w/w)]. A mechanistic model was developed to adequately predict the polymerization kinetics before a critical conversion, at which point the diffusion-controlled polymer reactions became the predominant factor during the latter stage of polymerization, was achieved. The side reaction of BTA with HQ that had a significant influence on the early stage of polymerization carried out in NMP was taken into account experimentally via the [[.sub.1]H]-NMR and DSC techniques. By contrast, the side reaction of BTA with HQ did not play an important role in the polymerization system with a solvent characterized by a relatively lower proton affinity such as DMAC or DMF. The activation energy ([E.sub.a]) of the Michael addition polymerization of BMI with BTA in the presence of HQ in increasing order was: NMP < DMAC < DMF, which was correlated quite well with the solvent proton affinity (NMP > DMAC > DMF). This implied that NMP with the highesl proton affinity acted as the most effective catalyst among the solvents investigated in this work that greatly lowered the energy barrier for the Michael addition polymerization of BMI with BTA. Nevertheless, the frequency factor (A) in increasing order was: NMP < DMAC < DMF. As a result of the compensation effect between [E.sub.a] and A, at conslanl temperature, the Michael addition rate constant decreased with increasing solvent prolon affinity.

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(7.) M. Park and Y. Kim, Thin Solid Films, 363, 156 (2000).

(8.) B.D. Mather, K. Viswanalhan, K.M. Miller, T. Long, Prog. Polym. Sci., 31. 487 (2006).

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Fu-En Yu, (1) Jung-Mu Hsu, (2) Jing-Pin Pan, (2) Tsung-Hsiung Wang, (2) Yu-Ching Chiang, (1) Winnie Lin, (1) Jyh-Chiang Jiang, (1) Chorng-Shyan Chern (1)

(1) Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan

(2) Materials and Chemical Research Laboratories, Industrial Technology Research Institute, Chutung, Hsinchu 31015, Taiwan]

Correspondence to: C.S. Chern; e-mail: cschern@mail.ntust.edu.tw

Contract grant sponsor: National Science Council, Taiwan.

DOI 10.1002/pen.23587

Published online in Wiley Online Library (wileyoiilinclibrary.com).

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Author:Yu, Fu-En; Hsu, Jung-Mu; Pan, Jing-Pin; Wang, Tsung-Hsiung; Chiang, Yu-Ching; Lin, Winnie; Jiang, Jy
Publication:Polymer Engineering and Science
Article Type:Report
Date:Mar 1, 2014
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