Acceleration of Bimolecular Reactions by Solvent Viscosity

Article abstract of DOI:10.1021/jp991066n

We report the first example of acceleration of a bimolecular reaction by increased solvent viscosity. In a series of hydrocarbon solvents of graded viscosity, the rates of two cycloadditions, the Diels-Alder dimerization of cyclopentadiene and the 1,3-dipolar cycloaddition of diphenyldiazomethane with ethyl phenylpropiolate, rise with increasing viscosity to about 1 cP and then fall thereafter. We interpret this rise as viscosity-induced acceleration up to ～1 cP, which cannot be accounted for by current kinetic theory. Several examples from the literature are reinterpreted in these terms, providing further support for our concept.

Full text of DOI:10.1021/jp991066n

J. Phys. Chem. A 1999, 103, 5369-5372
5369
Acceleration of Bimolecular Reactions by Solvent Viscosity1
Kevin A. Swiss and Raymond A. Firestone*
Department of Medicinal Chemistry, Boehringer Ingelheim Pharmaceuticals, Inc., 900 Ridgebury Road,
Ridgefield, Connecticut 06877-0368
ReceiVed: March 26, 1999; In Final Form: May 7, 1999
We report the first example of acceleration of a bimolecular reaction by increased solvent viscosity. In a
series of hydrocarbon solvents of graded viscosity, the rates of two cycloadditions, the Diels-Alder dimerization
of cyclopentadiene and the 1,3-dipolar cycloaddition of diphenyldiazomethane with ethyl phenylpropiolate,
rise with increasing viscosity to about 1 cP and then fall thereafter. We interpret this rise as viscosity-induced
acceleration up to ∼1 cP, which cannot be accounted for by current kinetic theory. Several examples from
the literature are reinterpreted in these terms, providing further support for our concept.
Introduction
There were a few shortcomings in the early study.7 The
viscometry was somewhat inaccurate and was conducted on pure
Viscosity is a measure of the force required to shear through
a given fluid. Remarkably, the effect of solvent viscosity on
reaction rates is a question that chemists seldom consider.
Current kinetic theory2,3 holds that the rates of bond-making
reactions that have significant activation barriers are independent
of viscosity at low viscosities, i.e., those of common mobile
solvents, or gases at pressures well above the falloff region.
This is defined as the collision-controlled regime, where en-
counters between the reactants are plentiful, and the rate is de-
pendent on collision-dependent energy transfer.
However, consideration of the nature of enzymic catalysis4
led us to predict different behavior, i.e., a positive effect of
viscosity in the collision-controlled regime. In addition to the
usual catalytic means such as proximity effects and push-pull,
there are two features peculiar to enzymes, the catalytic cleft
and the “ball of wax”,5 i.e., a preponderance of chemically un-
reactive amino acids, whose function was explained as creating
a zone of high viscosity in which reactions are accelerated. The
acceleration comes about because, according to the new theory,
bond-making reactions having significant activation barriers are
particularly sensitive to vibrational energy. Bond formation, it
was proposed, takes longer than a single vibration, and therefore
occurs more efficiently between mutually slow-moving reac-
tants, one of which is vibrationally excited, than between
vibrationally cold reactants with high line-of-centers translational
energy.6 Of course, at high viscosity encounter control still
reigns, so that were the viscosity high throughout the entire
solvent the reaction would still be very slow. The beauty of
enzymes is that they offer a cleft of high viscosity to promote
bond formation and yet avoid encounter control because the
solvent is a mobile one.1
solvents rather than the reaction mixtures themselves, owing to
solubility problems. The Diels-Alder reaction had been done
in a series of glymes rather than the preferred hydrocarbon
solvents, and the reactions chosen, while bond-making in nature,
were both unimolecular, which precluded any investigation of
the changeover from collision to encounter control.
We now report two new studies that surmount all the above
shortcomings and provide more powerful data supporting the
prediction of positive rate-viscosity correlation for bimolecular
reactions under collision control. As the viscosity is progres-
sively raised, the rates first rise and then fall.
To obviate the possibility that alterations in viscosity are
accompanied by alterations in other solvent propertiessmost
likely polarity-relatedsthat might affect the rate, reactions were
chosen that exhibit essentially no effect of polarity on the rate,
namely Diels-Alder9 and 1,3-dipolar cycloadditions.10 Ex-
amples were chosen that proceed at moderate temperatures in
the least interactive possible solvents, and concentrations were
kept low to minimize microscopic inhomogeneities arising from
aggregation or thermal effects.
Cyclopentadiene is soluble in nonpolar media, and its
dimerization is particularly well-studied. There are already hints
in the literature of a positive effect of viscosity on the rate.11
In a kinetic study in 1939, the data showed that in mobile
solvents the rate varied little and was a simple function of neither
polarity nor viscosity, but in paraffin oil the rate was twice that
in CCl4, and in neat cyclopentadiene it increased rapidly 3.3×
toward the end, i.e., as the medium changed into the more vis-
cous dicyclopentadiene.12 Proceeding from any solvent into the
gas phase involves a significant and discontinuous drop in
viscosity,7 and the rate fell to 0.22× that in paraffin oil.12 The
gas-liquid rate effect is a common one7 and is suggested to be
responsible for the correlation of Diels-Alder rate with solvent
porosity.13
Clearly, the vibrational-activation theory clashes head-on with
conventional theory, at least in the collision-controlled regime.
The first experimental test was published in 1981 and verified
the theory’s prediction of a positive effect of viscosity on the
rate.7 Two unimolecular bond-making reactions, an intramo-
lecular Diels-Alder and a Claisen rearrangement, were run in
a solvent series of similar nature but gradually increasing vis-
cosity and were indeed found to accelerate with rising viscosity.
Since that time, several papers have appeared describing
phenomena that could be interpreted as supporting our thesis.8
Another aspect of the gas-liquid rate effect is the observation
that DA rates in CO2 show enormous sharp increases as the
pressure is raised from the sub- into the supercritical region.
During this transit, but not below or above it, the apparent ∆Vq
jumps to huge negative values,14 -750 mL/mol.15 This cannot
be a true volume effect, and we attribute it to a discontinuity in
10.1021/jp991066n CCC: $18.00 © 1999 American Chemical Society
Published on Web 06/17/1999

5370 J. Phys. Chem. A, Vol. 103, No. 27, 1999
Swiss and Firestone
Figure 1. Relative rate constant vs viscosity for cyclopentadiene
dimerization in various common solvents at 40 °C.17
Figure 2. Relative rate constant vs viscosity of cyclopentadiene
dimerization, 25 °C. Solvents used: (1) n-octane; (2) n-decane; (3)
n-undecane; (4) n-dodecane; (5) n-tridecane; (6) n-tetradecane; (7)
n-heptadecane.
viscosity arising from sudden change in phase. A rise in polarity
cannot account for the phenomenon since it would affect the
rate negatiVely.16
Another paper reported cyclopentadiene dimerization rates
in a large group of solvents.17 When their rate constants are
plotted against solvent viscosity, there is scatter at low viscosities
but a clear correlation emerges overall (Figure 1).11
Results and Discussion
We have measured the effect of viscosity on the rates of two
bond-making bimolecular reactions, the dimerization of cyclo-
pentadiene (reaction 1) and the 1,3-dipolar cycloaddition of
Figure 3. Relative rate constant vs microviscosity of cyclopentadiene
dimerization, 25 °C. Solvents used: (1) n-octane; (2) n-decane; (3)
n-undecane; (4) n-dodecane; (5) n-tridecane; (6) n-tetradecane; (7)
n-heptadecane.
duplicates. To minimize local heat effects with this exothermic
reaction, reactions were stirred, and concentrations were the
lowest that produced good data. The overall picture is the same
whether scaled to macro- or microviscosity.
At the low end of the viscosity scale, rates rise sharply as
viscosity rises. This observation cannot be accounted for by
current kinetic theory2,3 (vide supra). At ca. 1.3 cP (correspond-
ing to ca. 0.5 cP microviscosity) the rate levels off and falls
thereafter as viscosity continues to rise.
Reaction 2 produced a similar picture, shown in Figure 4.
Once again the rate rises and then falls as viscosity is
progressively increased. The crossover point is at about 2.1 cP
(i.e., 0.75 cP microviscosity), close to that of reaction 1. The
maximum positive slopes of reduced rate constant (k/ko) vs
viscosity for reactions 1 and 2 are 1.87/cP (for data points 1-4)
and 0.17/cP (for data points 2-5), respectively. The maximum
positive slopes for reduced rate constant versus microviscosity
(ηµ) are 5.47/cP and 1.17/cP. We attribute the smaller slope for
reaction 2 to preassociation of the more polar reactants, which
reduces their relative translation prior to entering the TS. For
the cyclopentadiene reaction in various solvents of differing
macroviscosity shown in Figure 1,17 we calculate a slope of
0.60/cP for all data, and 1.28/cP using data only from 0.21 to
1.0 cP inclusive.
diphenyldiazomethane with ethyl phenylpropiolate18 (reaction
2). Both reactions are known to be largely insensitive to solvent
polarity, and to further ensure that the rate effects stemmed
primarily from variations in viscosity, all solvents were pure
linear saturated hydrocarbons. Only the chain length was varied,
not the temperature or pressure.
The viscosity experienced by the reactant molecules (micro-
viscosity) is not the same as that measured by the viscometer
(macroviscosity). One would expect that micro- and macrovis-
cosity would be alike when the solute and solvent molecules
are the same size, but not when there is a great disparity in
size.19 As the hydrocarbon chains grow longer and longer, the
relatively small cyclopentadiene molecules contact a smaller
and smaller fraction of the entire solvent chains. Thus micro-
viscosity, an increasingly local phenomenon, should rise more
slowly than macroviscosity, whose measurement always in-
volves the entire length of the hydrocarbon chains. This
expectation is borne out by measurements of microviscosity
reported for toluene molecules in linear saturated hydrocarbons,
the very ones we are using. Microviscosity indeed rises more
slowly than macroviscosity as the chain length grows.20
The results for cyclopentadiene are depicted in Figures 2 and
3. Viscosities were measured on the reaction mixtures them-
selves, not the pure solvents, and points 1, 2, 4, and 6 are
Cycloaddition rates vs solvent of the same dipolarophile with
C-methyl-N-phenyl sydnone at 140 °C 21 show the same vis-

Acceleration of Bimolecular Reactions
J. Phys. Chem. A, Vol. 103, No. 27, 1999 5371
Figure 5. Viscosity vs reduced rate constant of intramolecular Diels-
Alder reaction, reaction 3, 100 °C. Solvents used: (1) glyme; (2)
diglyme; (3) triglyme; (4) tetraglyme.
Figure 4. Viscosity vs relative rate constant of DPDM-EPP reaction,
30 °C. Solvents used: (1) n-octane; (2) n-dodecane; (3) n-tridecane;
(4) n-tetradecane; (5) n-pentadecane; (6) n-hexadecane; (7) n-hepta-
decane.
This program arose from the hypothesis that enzymes
accelerate reactions in part because their active sites are always
zones of high viscosity.4,7 However, active sites also have other
attributes, most notably their capability, presumably honed
through eons of evolution, of snugly fitting around their transi-
tion states (TS’s) in a lock-and-key manner.28 There is a dif-
ference between the two concepts, for a key experiences con-
tainment but not viscosity, but distinguishing between them
seems difficult. However, we have found a way to do this by
using tiny shapeless bits of viscous polyethylene widely dis-
persed in an excess of mobile solvent, which catalyze a Claisen
rearrangement >12.8-fold.1 This case cannot be accounted for
by the lock-and-key model (which of course remains valid in
other circumstances) and supports the premise of the present
paper.
cosity dependence.11 Relative rates and viscosities (η, cP) at
140 °C in the hydrocarbon solvents, where dielectric constants
are almost identical: mesitylene 92 (0.23), p-cymene 99 (0.32),
Decalin 220 (0.42-0.58), paraffin oil 237 (2-3).21 Other
examples of viscosity-induced bimolecular acceleration: addi-
tion of methyl methacrylate to the growing polymer chain is
faster in PhCN ((0.98) than in toluene (0.55);22 reaction of
excited 9-cyanoanthracene with 1,3-cyclohexadiene decelerates
with rising viscosity (encounter control), but intracage reaction
accelerates.23
We have accurately redone the viscometry for the intramo-
lecular Diels-Alder reaction of ref 8 using the actual reaction
mixtures (in this case glymes) and find that the corrected slope
of reduced rate constant k/ko vs macroviscosity η is 0.34/cP
(Figure 5), less that that of reaction 1. This is expected because
the relative translation of the two reactive moieties in the
intramolecular Diels-Alder reaction is more restricted than that
of two independent cyclopentadiene molecules and therefore
has less to lose at elevated viscosity.
There is scant precedent known to us where elevated viscosity
has been recognized as an accelerating factor in a bond-forming
reaction at ordinary viscosities.29 The rate of conformational
rearrangement of cyclohexane increases with pressure at mod-
erately low pressures, attributed by the authors to the pressure-
induced viscosity increase.30 This is of course a rotation and
not a bond-forming reaction. Furthermore, it is possible that
pressure and not viscosity is the agent here, since the first motion
in a chair-to-chair rearrangement involves movement of a set
of axial protons away from each other. This opens up space
between them which solvent molecules may now enter, increas-
ing the packing fraction and making the TS effectively smaller
than the reactants.
At ultralow pressure (and viscosity) there is the so-called
falloff region where inter alia bond-forming reactions slow,
owing to the paucity of third-body collisions capable of cooling
off the energized products. Even small pressure increases restore
normal reaction rates.31 This is a situation where bond-making
rates indeed rise with increased viscosity, but one far removed
from the realm of everyday chemistry where our attention is
centered.
We report k vs η directly, for parsimony’s sake. However,
when this plot is made for numerous Diels-Alder cases where
the pressure rather than the solvent is varied (using η calculated
from data in the literature24), linear relationships are seen on
log-log but not simple plots.25 These plots have significance
because an appreciable portion of the pressure-induced accelera-
tion stems from pressure-induced viscosity increases. It is
noteworthy that these log-log plots exhibit a downward
departure from linearity as viscosities rise above ca. 1-2 cP,26,27
just as they do with reactions 1 and 2.
Conclusions
The fact that elevated pressure affects reaction rates to a
significant degree through viscosity as well as volume effects
requires a revision of the pressure variant of the Arrhenius eq
4,25 since an appreciable portion of the apparent ∆Vq arises from
For two bimolecular bond-forming reactions, as the viscosity
is progressively increased, the rates first rise and then fall. Other
solvent properties such as polarity cannot account for the results.
The rising portion, predicted by the vibrational-activation theory,
is without precedent in preexisting theory or experiment.
Whether it is a universal phenomenon or restricted to only some
reactions can only be determined by investigating a greater
variety of reactions.
[d(ln k)/dp] ) -∆Vq/RT
viscosity and not volume effects.27
(4)

5372 J. Phys. Chem. A, Vol. 103, No. 27, 1999
Swiss and Firestone
(2) Kramers, H. A. Physica 1940, 7, 284.
Experimental Section
(3) (a) Leffler, J. E.; Grunwald, E. Rates and Equilibria of Organic
Reactions; Wiley: New York, 1963; p 57. (b) Burshtein, A. I.; Khudyakov,
I. V.; Yakobson, B. I. Prog. React. Kinet. 1984, 13, 221-305. (c)
Aleksandrov, I. V.; Gol′danskii, V. I. Chem. Phys. 1984, 87, 455. (d) le
Noble, W. J.; Kelm, H. Angew. Chem., Int. Ed. Engl. 1980, 19, 841.
(4) Firestone, R. A.; Christensen, B. G. Tetrahedron Lett. 1973, 389.
(5) Luisi, P. L. Naturwissenschaften 1979, 66, 498.
(6) Jaffe, S. B.; Anderson, J. B. J. Chem. Phys. 1969, 51, 1057.
(7) Firestone, R. A.; Vitale, M. A. J. Org. Chem. 1981, 46, 2160.
(8) (a) Sternbach, D. D.; Rossana, D. M. Tetrahedron Lett. 1982, 23,
303. (b) Dolbier, W. R., Jr.; Seabury, J. J. Am. Chem. Soc. 1987, 109, 4393.
(c) Dunams, T.; Hoekstra, M.; Pentaleri, M.; Liotta, D. Tetrahedron Lett.
1988, 29, 3745. (d) Dolbier, W. R., Jr.; Weaver, S. L. J. Org. Chem. 1990,
55, 5, 711. (e) Metz, P.; Seng, D.; Frohlich, R.; Wibbeling, B. Synlett 1996,
741. (f) Valgimigli, L.; Ingold, K. U.; Lusztyk, J. J. Org. Chem. 1996, 61,
7947.
All reagents and solvents with the following exceptions were
purchased from Aldrich Chemical Co. and used as is. Cyclo-
pentadiene (distilled fresh each time and stored at -78 °C) was
cracked from dicyclopentadiene (Lancaster Synthesis Ltd.).
Diphenyldiazomethane was prepared by the method of Smith
and Howard.32 Cannon-Ubbelohde semi-micro viscometers were
purchased from Cannon Instrument Co. A precision kinematic
viscosity bath was used and temperatures were calibrated
between this and the reactions using a digital thermometer. UV-
vis spectrophotometry was run on a Perkin-Elmer Lambda 3.
Example of a Cyclopentadiene Kinetic Run. Into a weighed
25-mL volumetric flask was added approximately 20 mL of
hydrocarbon solvent; then cold cyclopentadiene (ca. 0.200 g)
and hydrocarbon solvent were added to the line (to make a ∼0.1
M solution). The solution was weighed (for density) and then
thoroughly mixed. A small magnetic flea was added and the
flask was placed in a constant-temperature bath at 25 °C and
magnetically stirred. Aliquots (ca. 1 g) were removed every 24-
48 h and diluted to 250 mL total volume in HPLC-grade hexane.
The concentration of cyclopentadiene of the diluted aliquots was
determined by UV spectrophotometry (ꢀ ) 3390, λmax ) 241
nm). After the last data point, the viscosity of the actual reaction
mixture was determined at 25 °C. Viscosity in cP was
determined by the following equation: η (cP) ) density × time
× (viscometer constant). Data points 1, 2, 4, and 6 (shown with
error bars) are duplicates.
(9) Sauer, J. Angew. Chem., Int. Ed. Engl. 1967, 6, 16-33.
(10) Huisgen, R. Angew. Chem., Int. Ed. Engl. 1963, 2, 633.
(11) Our interpretation, not the authors’.
(12) Benford, G. A.; Kaufmann, H.; Khambata, B. S.; Wasserman, A.
J. Chem. Soc. 1939, 381.
(13) Firestone, R. A.; Saffar, S. G. J. Org. Chem. 1983, 48, 4783.
(14) Paulitis, M. E.; Alexander, G. C. Pure Appl. Chem. 1987, 59, 61.
(15) Ikushima, Y.; Saito, N.; Srai, M. J. Phys. Chem. 1992, 96, 2293.
(16) Nakagawa, K.; Ishii, Y.; Ogawa, M. Chem. Lett. 1977, 21.
(17) Coster, G.; Pfeil, E. Chem. Ber. 1968, 101, 4248.
(18) Huisgen, R.; Stangl, H.; Sturm, H. J.; Wagenhofer, H. Angew. Chem.
1961, 73, 170.
(19) Akesson, E.; Hakkarainen, A.; Laitinen, E.; Helenius, V.; Gillbro,
T.; Korppi-Tommola, J.; Sundstrom, V. J. Chem. Phys. 1991, 95, 6508.
(20) Sun, Y.-P.; Saltiel, J. J. Phys. Chem. 1989, 93, 8310.
(21) Huisgen, R.; Gotthardt, H. Chem. Ber. 1968, 101, 1059.
(22) Fernandez-Garcia, M.; Martinez, J. J.; Madruga, E. L. Polym.
Commun. 1997, 39, 991.
Example of a DPDM-EPP Kinetic Run. Into a weighed
25-mL volumetric flask was added diphenyldiazomethane (ca.
230.1 mg) and approximately 20 mL of hydrocarbon solvent.
Ethyl phenylpropiolate (ca. 1.7 g, 7-10-fold excess) was added,
and hydrocarbon solvent was filled to the mark, all at 30 °C.
The solution was weighed (for density) and then thoroughly
mixed. A 0.1-mm cuvette was filled and placed in a thermostated
cell holder in the spectrophotometer. Absorbance over time was
measured and plotted (in our hands, DPDM gave ꢀ ) 100, λmax
) 525 nm). The viscosity was measured at the same temperature
using an appropriate-sized viscometer and constant-temperature
bath. Viscosity in cP was determined by the following equa-
tion: η (cP) ) density × time × (viscometer constant). All
data points are duplicated.
(23) Kitazawa, M.; Yabe, T.; Hirata, Y.; Okada, T. J. Mol. Liq. 1995,
65/66, 321.
(24) Bridgman, P. W. The Physics of High Pressure; G. Bell & Sons:
London, 1949.
(25) To be published in a separate article.
(26) The downward slope in rates beyond 1-2 cP in reactions 1 and 2
and under pressure were regarded at first as incursions into the encounter-
controlled regime. However, it was pointed out that this ought to occur
only at higher viscosity and suggested instead that the viscous solvents limit
the relative freedom of movement of the reactants in the microenvironment
of the encounter pair while having no critical influence on the diffusion of
the reactants in the bulk solution. We thank Dr. Keith U. Ingold for this
suggestion.
(27) Based on comparison of the slope of k vs η for reaction 1 and for
P vs η in common solvents with the slope of k vs P in Diels-Alder
reactions; for a review of volumes of activation see: Asano, T.; le Noble,
W. J. Chem. ReV. 1978, 78, 407.
(28) Pauling, L. Nature 1948, 161, 707. Wolfenden, R. Acc. Chem. Res.
1972, 5, 10. Page, M. I. Int. J. Biochem. 1979, 10, 471.
(29) With the possible exception of ref 8a,b,d.
(30) Hasha, D. L.; Eguchi, T.; Jonas, J. J. Am. Chem. Soc. 1982, 104,
2290.
Supporting Information Available: Tabular listing and
plots of all solvent rates. This material is available free of charge
via the Internet at http://pubs.acs.org.
(31) Mozurkewich, M.; Lamb, J. J.; Benson, S. W. J. Phys. Chem. 1984,
88, 8, 6435. These authors report that the rate of reaction of HO• with CO
rises 2.5× from its low-pressure limit with the addition of SF6 bath gas,
which removes excess energy by collision, preventing reversal.
(32) Smith, L. I.; Howard, K. L. Organic Syntheses; Wiley: New York,
1955; Collect. Vol. 3, p 351.
References and Notes
(1) Vibrational Activation V. Paper IV: Catalysis of Claisen Rear-
rangement by Low-MW Polyethylene. Swiss, K. A.; Firestone, R. A. J.
Org. Chem. 1999, 64, 2158.