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Influence of solvent on propagation in cationic polymerization
Eur. Polym. J. Vo[. 22. No. 10, pp. 817 820, 1986 Printed in Great Britain
0014-3057/86 $3.00+0.00 Pergamon Journals Ltd
I N F L U E N C E OF S O L V E N T ON P R O P A G A T I O N IN CATIONIC POLYMERIZATION M. B()LKE, 1 P. HALLPAP, 1 G. HEUBLEIN1 a n d C. WE1SS2 IDepartment of Chemistry, Friedrich-Schiller-University, HumboldtstraBe 10, 6900 Jena and 2Department of Chemistry, Karl-Marx-University, Talstral3e 35, 7010 Leipzig, German Democratic Republic
(Received 11 February 1986) Abstract--The influence of solvent on cationic propagation steps--modelled by ethene homopolymerization--is investigated by means of theoretical models. In order to achieve cationation and the first three propagation steps, the influence of solvent was simulated by a continuum model after calculation for the gas phase at the MINDO/3 level. Characteristic changes, caused by the transition from the gas phase to solution (solvent: CH2C12), were obtained, e.g. an increase of activation barriers and specific alterations of heats of reaction depending on the cationic chain length. The shape of a special potential energy surface for the first propagation step is qualitatively affected by the solvent leading to a change of the character of the activated complex from educt-like (gas phase) to product-like (solution).
INTRODUCTION
Cationic polymerizations are k n o w n as reactions very sensitive to a variety of influences [1, 2]. One of the m o s t i m p o r t a n t conditions which affect ionic reactions is the solvent. In this p a p e r the influence of solvent o n the cationic p r o p a g a t i o n steps is modelled theoretically by m e a n s o f a solvent c o n t i n u u m model. Use is m a d e of the a d v a n t a g e o f q u a n t u m chemical m e t h o d s to separate special interactions of a complex reaction system a n d to investigate t h e m individually. The interactions between the cationic chain end a n d the m o n o m e r in the gas phase have already been investigated h a v i n g considered the first three p r o p a gation steps of the h o m o p o l y m e r i z a t i o n o f ethene as an example [3] [Eqns (1-4)]. H + + CH2~------CH2~CH3--CH~
(1)
C H 3 - - C H ~ + CH2~--------CH2-*C3H7--CH ]
(2)
C 3 H 7 - - C H 2 + CH2~-------CH2~CsHH~CH ~ (3) CsH,--CHf
Ec,V is the product of surface and surface tension, corrected for influence of temperature and coefficient of volume extension. Evdw is calculated by means of Kitaygorodski potential functions with some special gauge constants considering the ratio of Van der Waals radii of the atoms concerned. EeL,depending strongly on the dielectric constant of the solvent, is calculated according to the reaction field theory [7]. In this way the solvation energy for cations is defined by the value of Eel, whereas the leading term in Eqn (5) for uncharged molecules is Evdw . The larger the molecules, the better is their solvation because of higher dispersion interaction. The sum of E~o~vand the heat of formation in the gas phase, AHr, calculated with MINDO/3, should express the stability of the species in solution. The solvent used in the calculations was methylene chloride, typical of solvents used in cationic polymerizations [1,21. The geometrical configuration assumed for the reactants can be seen in Fig. 1. This arrangement considers the preference of planar anticonformational carbon chains and also takes into account the qualification of primary cations as models for cationic chain ends. Symmetrical substituted,
+ CH2~-----CH2--~CvHIs--CH ~ (4)
j
E t h e n e only forms oligomers u n d e r cationic conditions [4]. Nevertheless it is a suitable theoretical model for olefins. O t h e r participants of the reactions, e.g. counterion, a n d reactions in c o m p e t i t i o n with the p r o p a g a t i o n , e.g. isomerization o f the chain end a n d transfer reactions to m o n o m e r , are neglected. They will be subjects of further investigation [5].
/
""-
C --
C/''
~
jR \
/ /p
\ \
METHODS
C
These calculations are carried out at MINDO/3 level [6] employing the program already described [3]. The influence of solvent was considered by means of the extended solvent continuum model, introduced by Huron and Claverie [7-9]. The species to be solvated is located in a shape fitted solvent cavity. Then the solvation energy Esonvis calculated as the sum of energy for cavitation in the solvent continuum Ec~v and of the energy for Van-der-Waals (Evaw) and electrostatic (Eel) interaction between the solvent and the solvated species [Eqn (5)]. Esolv = Eta~ + Evow + Eel
(5)
\ X
X-H,C2Hs,C4H
(a)
9
x
(b)
Fig. 1. Geometrical arrangement of reactants for Eqns (2-4) (a) and symmetry plane a (b) [R and e are independent geometrical variables for a potential energy surface (see further text)]. 817
Gr
818
M. BrLKE et al. Table 1. Heats of activation (AH *) and heats of reaction (AH~)for Eqns (I~) in the gas phase and in solution (values in kJ tool-i) Gas phase Solution (CH2C12) Eqn AH~]~ AH,,~Ic AH~exp AH~]¢¶ AH~,a,¢ (l) --713 -680* 0 (2) + 12 -159 - 128t +58 (3) +25 - 140 - 102t +68 (4) ---135 --1027§ -*Proton affinity of ethene [14]. ?Calculated from experimental heat of formations [15, 16]. §AHf(CsH~7) extrapolated from published data [17]. ¶Calculated with gas phase geometry of activated complexes.
non-classical cations (H-bridged), which are calculated as more stable than the classical ions with semi-empirical quantum chemical methods [I0-12], cannot be obtained in this case due to conservation of the symmetry plane during the optimization of geometry. RESULTS AND DISCUSSION Table 1 contains calculated heats of activation AH * and heats of reaction AH, for Eqns (1-4) in the gas phase and in solution, compared with some experimental results. The comparison shows an overestimation of heats of reaction by M I N D O / 3 , but this difference between the reactions is nearly the same as obtained for experimental values. F o r this reason, some conclusions may be drawn from the values. Cationation C a t i o n a t i o n of the m o n o m e r [Eqn (1)] is an exothermic process resulting from the instability of a free proton. The great exothermic effect and the small steric need of a proton lead to an activation-less process in the gas phase (Fig. 2). In solution, the protonation also seems to proceed without activation [13]. The reaction heat for Eqn (1) is reduced to little
-417 - 105 -115 --137
more than half by the transition from the gas phase to the solvent CH2C12, in the main because of solvation of the proton. Propagation steps Figure 2 shows the energy profiles of the reactions 0 - 4 ) . The energy profiles are calculated from a starting point with 4 m o n o m e r units and a free proton. The decrease of the energy of the polymerizing system is mainly due to the stepwise replacement of g-bonds by g-bonds. This is the thermodynamic foundation of all polymerizations. Comparison of the reactions in the gas phase [3] with those in solution indicates increasing activation barriers in solution. That change should result in a lower rate constant in the more polar medium. The solvent favours the educts in comparison with the activated complexes as the latter have more charge delocalization. This effect is qualitatively in line with the well known Ingold rule. The observed increase of polymerization rate in more polar solvents is achieved by the more pronounced charge separation between cationic chain end and the counterion. It cannot be calculated in the present model as it neglects the counterion.
1 --7
I I I 1600
1400
I m
<3
1200
1
4
C2H 4 -I-
H+
2
3
C2H 4 +
C~,H 5
3
2
C,~H 4 *
C4H 9
I
1200
I
4
t
-
I
5
C a H 4 -~- C 6 H13
1
+ C 8 H17
I
1000
I I
I
I m
i _2
I
800
<3
I i 1000
600
I
i
,....r I 800
400
I
15 i-(kJ. mo1-1 )
Fig. 2. Energy profiles of the model reactions (I-4) in the gas phase and in solution (CH2C12), starting with 4 monomer units and a free proton.
819
Propogation in cationic polymerization The alterations of AHr by transition from the gas phase to the solvent can be attributed to solvation effects, depending on charge distribution and the size of the species in question. The extension of the chain by addition of the first two monomer units leads to a better charge delocalization at the chain end and to less solvation of the products in comparison with the educts. For this reason, the exothermic effects of the first two propagation steps are smaller in solution than in the gas phase. The addition of monomers has for further propagation steps negligible influence on charge distribution at the chain end. In these cases, the solvation energies for the educts and the products are nearly the same. This leads to an equal reaction heat in the gas phase and in CH2C12 for Eqn (4), and probably also for the next steps. Summarizing, the influence of solvent reverses the gas phase order of reaction heats according to chain length. A similar result was obtained by Basilevski et al. [18] investigating Eqn (2) by means of a qualitative different model of solvent consideration. For discussion of an activation barrier for Eqn (2) in the gas phase [18], see also Refs [3, 13]. Bertran et al. calculated the electrophilic attack of a proton [19], a methyl cation [20,21] and an ethyl cation [13] on ethene employing a solvent supermolecule approach. In line with the stated results from the H u r o n Claverie-method, they also found smaller activation heats in the gas phase than in solution. First propagation step
The first propagation step [Eqn (2)], especially the increase of the activation barrier in solution, was investigated in detail with the help of a special potential energy surface [3]. In Fig. 1 the independent geometric parameters R and ~ are shown. They spread the potential energy of the system (C2Hs/C2H4) + (R~-H). Figure 3a contains the energy
function E = f(R, ~) in the gas phase (unit of isoenergetic lines is kJ mol-1). The reaction path goes from the educts (E) through the activated complex ( , ) in the valley of products with different conformations. The activated complex is educt-like. A more detailed discussion of the gas phase potential energy surface and of the connected chemical structures connected has been given [3]. The surface in Fig. 3(2) results after the calculation of Esolvfor all structures which were used to construct the surface in Fig. 3(1). Calculations of the solvent influence on complete potential energy surfaces are scarce at present [22]. More often, investigation of the solvent effect on reaction profile diagrams can be found [23-26]. From Fig. 3 it can be seen easily that even the effect of a relatively nonpolar solvent e.g. CH2CI z alters the shape of the potential energy surface qualitatively. The following points can be noted --increase of activation barrier, --small shifting of the product minima, - - t h e energetic order of product structures changes to the disadvantage of the C-bridged structure V and --there are qualitative changes of the shape in the range of the barrier. The way from the educts to the products in solution does not pass the point of the activated complex in the gas phase. The described changes are understandable because structures of more cyclic character (70 ° ~<~ ~< 110 °) are favoured in the gas phase but less preferred by solvation resulting from more charge delocalization in comparison with open structures with syn-(~ <~70 ~) or anti-(~ ~> l i f t ) conformation. In solution are two different activated complexes ( + ) which are product-like because the conformation of products is already indicated at these
R(m)
45
90 a(o)
"135
180
"~
O
45
90 a(°)
~35
Fig. 3. Potential energy surfaces of the system (C2Hs/C2H4)+ in the gas phase (1) and in solution (2) depending on the parameters R and a (see Fig. 1).
180
820
M. BOLI~ et al.
points. That means that the character of activated complexes changes from educt-like in the gas phase to product-like in solution. This difference was also noted in comparable reactions (attack of methyl cation on ethene and benzene) with the help of a simple super-molecule calculation of solvent influence [21]. By means of a continuum model, such results can only be obtained by investigation o f the potential energy surface in the gas phase and in solution. In this way the heat of activation for Eqn (2) in Table 1 can also be corrected. Because of new structures for activated complexes in solution, the heat of activation A H * is now 33 or 4 2 k J - m o l l instead of 58 k J ' m o l - ~ given in Table 1. This result does not however qualitatively affect the discussion already given. REFERENCES
1. J. P. Kennedy and E. Mar6chal, Carbocationic Polymerization. Wiley, New York (1982). 2. G. Heublein, Zum Ablauf lonischer Polymerisationsreaktionen. Akademieverlag, Berlin (1975). 3. M. B61ke, P. Hallpap, G. Heublein, D. Heidrich and C. Weiss, Eur. Polym. J. 21, 117 (1985). 4. J. P. Kennedy, Cationic Polymerization of Olefins: A Critical Inventory. Wiley, New York (1975). 5. M. B61ke, P. Hallpap, G. Heublein and C. Weiss, in preparation. 6. R. C. Bingham, M. J. S. Dewar and D. H. Lo, J. Am. chem. Soc. 97, 1285 (1975). 7. M-J. Huron and P. Claverie, J. phys. Chem. 76, 2123 (1972). 8. M-J. Huron and P. Claverie, J. phys. Chem. 78, 1853 (1974).
9. M-J. Huron and P. Claverie, J. phys. Chem. 78, 1862 (1974). 10. D. Heidrich, M. Grimmer and H.-J. K6hler, Tetrahedron 32, 1193 (1976). I 1. H. Lischka and H-J. K6hler, J. Am. chem. Soc. 100, 5297 (1978). 12, H. J. Rauscher, D. Heidrich, H-J. K6hler and D. Michel, Theoret. Chim. Acta 57, 255 (1980). 13. J. Bertran and J. Anguiano, J. Molec. Struct. 120, 107 (1985). 14. S. M. Collyer and T. B. McMahon, Chem. Phys. Lett. 87, 909 (1983). 15. D. Cox and G. Pilcher, Thermochemistry o f Organic and Organometallic Compounds. Academic Press, New York (1970). 16. F. P. Lossing and A. Maccoll, Can J. Chem. 54, 990 (1976). 17. F. P. Lossing and J. L. Holmes, J. Am. chem. Soc. 106, 6917 (1984). 18. M. V. Basilevski, G. N. Gerasimov, S. I. Petrochenko and V. A. Tikhomirov, Chem, Phys. $5, 259 (1981). 19. T. Sordo, M. Arumi and J. Bertran, J. Chem. Soc. Perkin Trans. H 708 (1980). 20. J. Bertran, J. Anguiano and A. Oliva, Croat. Chim. Acta 56, 169 (1983). 21. T. Sordo, M, Campillo, A. Oliva and J. Bertran, Chem. Phys. Lett. 85, 225 (1982). 22. J. O. Noell and K. Morokuma, J. phys. Chem. 80, 2675 (1976). 23. P. Demontis, A. Gamba, G. B. Suffritti and M. Simonetta, J. Chem. Soc. Perkin Trans. H 997 (1983). 24. J. Chandrasekhar, S. F. Smith and W. L. Jorgensen, J. Am. chem, Soc. 106, 3049 (1984). 25. H. Z. Cao, M. Allavena, O. Tapia and E. M. Erleth, Chem. Phys. Lett. 96, 458 (1983). 26. J. Koller, M. Hodoscek and D. Hadzi, J. Molec. Struct. 106, 301 (1984).
0014-3057/86 $3.00+0.00 Pergamon Journals Ltd
I N F L U E N C E OF S O L V E N T ON P R O P A G A T I O N IN CATIONIC POLYMERIZATION M. B()LKE, 1 P. HALLPAP, 1 G. HEUBLEIN1 a n d C. WE1SS2 IDepartment of Chemistry, Friedrich-Schiller-University, HumboldtstraBe 10, 6900 Jena and 2Department of Chemistry, Karl-Marx-University, Talstral3e 35, 7010 Leipzig, German Democratic Republic
(Received 11 February 1986) Abstract--The influence of solvent on cationic propagation steps--modelled by ethene homopolymerization--is investigated by means of theoretical models. In order to achieve cationation and the first three propagation steps, the influence of solvent was simulated by a continuum model after calculation for the gas phase at the MINDO/3 level. Characteristic changes, caused by the transition from the gas phase to solution (solvent: CH2C12), were obtained, e.g. an increase of activation barriers and specific alterations of heats of reaction depending on the cationic chain length. The shape of a special potential energy surface for the first propagation step is qualitatively affected by the solvent leading to a change of the character of the activated complex from educt-like (gas phase) to product-like (solution).
INTRODUCTION
Cationic polymerizations are k n o w n as reactions very sensitive to a variety of influences [1, 2]. One of the m o s t i m p o r t a n t conditions which affect ionic reactions is the solvent. In this p a p e r the influence of solvent o n the cationic p r o p a g a t i o n steps is modelled theoretically by m e a n s o f a solvent c o n t i n u u m model. Use is m a d e of the a d v a n t a g e o f q u a n t u m chemical m e t h o d s to separate special interactions of a complex reaction system a n d to investigate t h e m individually. The interactions between the cationic chain end a n d the m o n o m e r in the gas phase have already been investigated h a v i n g considered the first three p r o p a gation steps of the h o m o p o l y m e r i z a t i o n o f ethene as an example [3] [Eqns (1-4)]. H + + CH2~------CH2~CH3--CH~
(1)
C H 3 - - C H ~ + CH2~--------CH2-*C3H7--CH ]
(2)
C 3 H 7 - - C H 2 + CH2~-------CH2~CsHH~CH ~ (3) CsH,--CHf
Ec,V is the product of surface and surface tension, corrected for influence of temperature and coefficient of volume extension. Evdw is calculated by means of Kitaygorodski potential functions with some special gauge constants considering the ratio of Van der Waals radii of the atoms concerned. EeL,depending strongly on the dielectric constant of the solvent, is calculated according to the reaction field theory [7]. In this way the solvation energy for cations is defined by the value of Eel, whereas the leading term in Eqn (5) for uncharged molecules is Evdw . The larger the molecules, the better is their solvation because of higher dispersion interaction. The sum of E~o~vand the heat of formation in the gas phase, AHr, calculated with MINDO/3, should express the stability of the species in solution. The solvent used in the calculations was methylene chloride, typical of solvents used in cationic polymerizations [1,21. The geometrical configuration assumed for the reactants can be seen in Fig. 1. This arrangement considers the preference of planar anticonformational carbon chains and also takes into account the qualification of primary cations as models for cationic chain ends. Symmetrical substituted,
+ CH2~-----CH2--~CvHIs--CH ~ (4)
j
E t h e n e only forms oligomers u n d e r cationic conditions [4]. Nevertheless it is a suitable theoretical model for olefins. O t h e r participants of the reactions, e.g. counterion, a n d reactions in c o m p e t i t i o n with the p r o p a g a t i o n , e.g. isomerization o f the chain end a n d transfer reactions to m o n o m e r , are neglected. They will be subjects of further investigation [5].
/
""-
C --
C/''
~
jR \
/ /p
\ \
METHODS
C
These calculations are carried out at MINDO/3 level [6] employing the program already described [3]. The influence of solvent was considered by means of the extended solvent continuum model, introduced by Huron and Claverie [7-9]. The species to be solvated is located in a shape fitted solvent cavity. Then the solvation energy Esonvis calculated as the sum of energy for cavitation in the solvent continuum Ec~v and of the energy for Van-der-Waals (Evaw) and electrostatic (Eel) interaction between the solvent and the solvated species [Eqn (5)]. Esolv = Eta~ + Evow + Eel
(5)
\ X
X-H,C2Hs,C4H
(a)
9
x
(b)
Fig. 1. Geometrical arrangement of reactants for Eqns (2-4) (a) and symmetry plane a (b) [R and e are independent geometrical variables for a potential energy surface (see further text)]. 817
Gr
818
M. BrLKE et al. Table 1. Heats of activation (AH *) and heats of reaction (AH~)for Eqns (I~) in the gas phase and in solution (values in kJ tool-i) Gas phase Solution (CH2C12) Eqn AH~]~ AH,,~Ic AH~exp AH~]¢¶ AH~,a,¢ (l) --713 -680* 0 (2) + 12 -159 - 128t +58 (3) +25 - 140 - 102t +68 (4) ---135 --1027§ -*Proton affinity of ethene [14]. ?Calculated from experimental heat of formations [15, 16]. §AHf(CsH~7) extrapolated from published data [17]. ¶Calculated with gas phase geometry of activated complexes.
non-classical cations (H-bridged), which are calculated as more stable than the classical ions with semi-empirical quantum chemical methods [I0-12], cannot be obtained in this case due to conservation of the symmetry plane during the optimization of geometry. RESULTS AND DISCUSSION Table 1 contains calculated heats of activation AH * and heats of reaction AH, for Eqns (1-4) in the gas phase and in solution, compared with some experimental results. The comparison shows an overestimation of heats of reaction by M I N D O / 3 , but this difference between the reactions is nearly the same as obtained for experimental values. F o r this reason, some conclusions may be drawn from the values. Cationation C a t i o n a t i o n of the m o n o m e r [Eqn (1)] is an exothermic process resulting from the instability of a free proton. The great exothermic effect and the small steric need of a proton lead to an activation-less process in the gas phase (Fig. 2). In solution, the protonation also seems to proceed without activation [13]. The reaction heat for Eqn (1) is reduced to little
-417 - 105 -115 --137
more than half by the transition from the gas phase to the solvent CH2C12, in the main because of solvation of the proton. Propagation steps Figure 2 shows the energy profiles of the reactions 0 - 4 ) . The energy profiles are calculated from a starting point with 4 m o n o m e r units and a free proton. The decrease of the energy of the polymerizing system is mainly due to the stepwise replacement of g-bonds by g-bonds. This is the thermodynamic foundation of all polymerizations. Comparison of the reactions in the gas phase [3] with those in solution indicates increasing activation barriers in solution. That change should result in a lower rate constant in the more polar medium. The solvent favours the educts in comparison with the activated complexes as the latter have more charge delocalization. This effect is qualitatively in line with the well known Ingold rule. The observed increase of polymerization rate in more polar solvents is achieved by the more pronounced charge separation between cationic chain end and the counterion. It cannot be calculated in the present model as it neglects the counterion.
1 --7
I I I 1600
1400
I m
<3
1200
1
4
C2H 4 -I-
H+
2
3
C2H 4 +
C~,H 5
3
2
C,~H 4 *
C4H 9
I
1200
I
4
t
-
I
5
C a H 4 -~- C 6 H13
1
+ C 8 H17
I
1000
I I
I
I m
i _2
I
800
<3
I i 1000
600
I
i
,....r I 800
400
I
15 i-(kJ. mo1-1 )
Fig. 2. Energy profiles of the model reactions (I-4) in the gas phase and in solution (CH2C12), starting with 4 monomer units and a free proton.
819
Propogation in cationic polymerization The alterations of AHr by transition from the gas phase to the solvent can be attributed to solvation effects, depending on charge distribution and the size of the species in question. The extension of the chain by addition of the first two monomer units leads to a better charge delocalization at the chain end and to less solvation of the products in comparison with the educts. For this reason, the exothermic effects of the first two propagation steps are smaller in solution than in the gas phase. The addition of monomers has for further propagation steps negligible influence on charge distribution at the chain end. In these cases, the solvation energies for the educts and the products are nearly the same. This leads to an equal reaction heat in the gas phase and in CH2C12 for Eqn (4), and probably also for the next steps. Summarizing, the influence of solvent reverses the gas phase order of reaction heats according to chain length. A similar result was obtained by Basilevski et al. [18] investigating Eqn (2) by means of a qualitative different model of solvent consideration. For discussion of an activation barrier for Eqn (2) in the gas phase [18], see also Refs [3, 13]. Bertran et al. calculated the electrophilic attack of a proton [19], a methyl cation [20,21] and an ethyl cation [13] on ethene employing a solvent supermolecule approach. In line with the stated results from the H u r o n Claverie-method, they also found smaller activation heats in the gas phase than in solution. First propagation step
The first propagation step [Eqn (2)], especially the increase of the activation barrier in solution, was investigated in detail with the help of a special potential energy surface [3]. In Fig. 1 the independent geometric parameters R and ~ are shown. They spread the potential energy of the system (C2Hs/C2H4) + (R~-H). Figure 3a contains the energy
function E = f(R, ~) in the gas phase (unit of isoenergetic lines is kJ mol-1). The reaction path goes from the educts (E) through the activated complex ( , ) in the valley of products with different conformations. The activated complex is educt-like. A more detailed discussion of the gas phase potential energy surface and of the connected chemical structures connected has been given [3]. The surface in Fig. 3(2) results after the calculation of Esolvfor all structures which were used to construct the surface in Fig. 3(1). Calculations of the solvent influence on complete potential energy surfaces are scarce at present [22]. More often, investigation of the solvent effect on reaction profile diagrams can be found [23-26]. From Fig. 3 it can be seen easily that even the effect of a relatively nonpolar solvent e.g. CH2CI z alters the shape of the potential energy surface qualitatively. The following points can be noted --increase of activation barrier, --small shifting of the product minima, - - t h e energetic order of product structures changes to the disadvantage of the C-bridged structure V and --there are qualitative changes of the shape in the range of the barrier. The way from the educts to the products in solution does not pass the point of the activated complex in the gas phase. The described changes are understandable because structures of more cyclic character (70 ° ~<~ ~< 110 °) are favoured in the gas phase but less preferred by solvation resulting from more charge delocalization in comparison with open structures with syn-(~ <~70 ~) or anti-(~ ~> l i f t ) conformation. In solution are two different activated complexes ( + ) which are product-like because the conformation of products is already indicated at these
R(m)
45
90 a(o)
"135
180
"~
O
45
90 a(°)
~35
Fig. 3. Potential energy surfaces of the system (C2Hs/C2H4)+ in the gas phase (1) and in solution (2) depending on the parameters R and a (see Fig. 1).
180
820
M. BOLI~ et al.
points. That means that the character of activated complexes changes from educt-like in the gas phase to product-like in solution. This difference was also noted in comparable reactions (attack of methyl cation on ethene and benzene) with the help of a simple super-molecule calculation of solvent influence [21]. By means of a continuum model, such results can only be obtained by investigation o f the potential energy surface in the gas phase and in solution. In this way the heat of activation for Eqn (2) in Table 1 can also be corrected. Because of new structures for activated complexes in solution, the heat of activation A H * is now 33 or 4 2 k J - m o l l instead of 58 k J ' m o l - ~ given in Table 1. This result does not however qualitatively affect the discussion already given. REFERENCES
1. J. P. Kennedy and E. Mar6chal, Carbocationic Polymerization. Wiley, New York (1982). 2. G. Heublein, Zum Ablauf lonischer Polymerisationsreaktionen. Akademieverlag, Berlin (1975). 3. M. B61ke, P. Hallpap, G. Heublein, D. Heidrich and C. Weiss, Eur. Polym. J. 21, 117 (1985). 4. J. P. Kennedy, Cationic Polymerization of Olefins: A Critical Inventory. Wiley, New York (1975). 5. M. B61ke, P. Hallpap, G. Heublein and C. Weiss, in preparation. 6. R. C. Bingham, M. J. S. Dewar and D. H. Lo, J. Am. chem. Soc. 97, 1285 (1975). 7. M-J. Huron and P. Claverie, J. phys. Chem. 76, 2123 (1972). 8. M-J. Huron and P. Claverie, J. phys. Chem. 78, 1853 (1974).
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