Brooklyn, of the temperature dependence of these samples with variable degrees of
polymerization precisely fit Lifson’s partition function predictions. The smaller
energy, which could be termed a chiral structural deuterium isotope effect, was near
to a single small calorie per mole of units, while the larger energy, the cost of a
helical reversal, was near to 4,000 cal/mol [7].
The changes observed for the optical activity (a measure of the excess helical
sense), as a function of temperature and degree of polymerization, fit the picture of
the cooperative phenomenon. The change in the optical activity of the deuterated
polyisocyanate as a function of degree of polymerization, below about 1,000 units,
was almost linear with increasing chain length and with a very small dependence on
temperature. The samples with higher degrees of polymerization, on the other hand,
showed no dependence of the optical activity on chain length, but exhibited a very
large dependence of the optical activity on temperature.
A helical reversal energy of about 4,000 cal/mol of individual units translates, at
ambient temperature, to approximately one reversal for every 1,000 units. Short
chains with degrees of polymerization substantially below 1,000 units would
therefore be almost entirely free of helical reversals. The amplification of the chiral
deuterium isotope effect would therefore increase with degree of polymerization,
because there are no interruptions on the conformational state of the chain, until
reaching a chain length at which helical reversals became probable. For this reason,
the excess helical sense would increase with degree of polymerization as would,
therefore, the optical activity as observed experimentally (see above).
For longer chains in which helical reversals were probable, the limit to the
amplification of the chiral deuterium isotope effect would no longer depend on
the chain length but rather on the number of units between reversals. The amplification would therefore strongly depend on temperature because the probability of a
helical reversal along the chain backbone depends exponentially on temperature,
following the Boltzmann equation, e
ÀE/RT , where E is the excess energy of the
helical reversal.
The results on the deuterated polyisocyanate described above begged the question of how small the chiral influence could be. An experiment was designed in
which poly(n-hexyl isocyanate) with no preference for helical sense was dissolved
in a series of chiral enantiomerically pure solvents. In every solution, the CD
spectrum at the wavelength of the helical chromophore showed an excess helical
sense. Remarkably, fitting these data as a function of temperature and degree of
polymerization to Lifson’s partition function showed that the energy term per mole
of units favoring one helical sense, as a consequence of the chiral solvent, was less
than 0.1 cal/mol. Moreover, the excess helical sense, left-handed for some solvents
and right-handed for other solvents, could not be made sense of from structural
considerations. These data, and the inability to generate a structural interpretation,
demonstrated the limits to structural theory. It follows that structural interpretations
are not possible (the foundations of physical organic chemistry) for cooperative
systems in which properties involve minute, but amplified energies. Energy differences below several hundred calories per mole do not allow assigning structural
interpretation for the source of the observations [8].
268
M.M. Green
polymerization precisely fit Lifson’s partition function predictions. The smaller
energy, which could be termed a chiral structural deuterium isotope effect, was near
to a single small calorie per mole of units, while the larger energy, the cost of a
helical reversal, was near to 4,000 cal/mol [7].
The changes observed for the optical activity (a measure of the excess helical
sense), as a function of temperature and degree of polymerization, fit the picture of
the cooperative phenomenon. The change in the optical activity of the deuterated
polyisocyanate as a function of degree of polymerization, below about 1,000 units,
was almost linear with increasing chain length and with a very small dependence on
temperature. The samples with higher degrees of polymerization, on the other hand,
showed no dependence of the optical activity on chain length, but exhibited a very
large dependence of the optical activity on temperature.
A helical reversal energy of about 4,000 cal/mol of individual units translates, at
ambient temperature, to approximately one reversal for every 1,000 units. Short
chains with degrees of polymerization substantially below 1,000 units would
therefore be almost entirely free of helical reversals. The amplification of the chiral
deuterium isotope effect would therefore increase with degree of polymerization,
because there are no interruptions on the conformational state of the chain, until
reaching a chain length at which helical reversals became probable. For this reason,
the excess helical sense would increase with degree of polymerization as would,
therefore, the optical activity as observed experimentally (see above).
For longer chains in which helical reversals were probable, the limit to the
amplification of the chiral deuterium isotope effect would no longer depend on
the chain length but rather on the number of units between reversals. The amplification would therefore strongly depend on temperature because the probability of a
helical reversal along the chain backbone depends exponentially on temperature,
following the Boltzmann equation, e
ÀE/RT , where E is the excess energy of the
helical reversal.
The results on the deuterated polyisocyanate described above begged the question of how small the chiral influence could be. An experiment was designed in
which poly(n-hexyl isocyanate) with no preference for helical sense was dissolved
in a series of chiral enantiomerically pure solvents. In every solution, the CD
spectrum at the wavelength of the helical chromophore showed an excess helical
sense. Remarkably, fitting these data as a function of temperature and degree of
polymerization to Lifson’s partition function showed that the energy term per mole
of units favoring one helical sense, as a consequence of the chiral solvent, was less
than 0.1 cal/mol. Moreover, the excess helical sense, left-handed for some solvents
and right-handed for other solvents, could not be made sense of from structural
considerations. These data, and the inability to generate a structural interpretation,
demonstrated the limits to structural theory. It follows that structural interpretations
are not possible (the foundations of physical organic chemistry) for cooperative
systems in which properties involve minute, but amplified energies. Energy differences below several hundred calories per mole do not allow assigning structural
interpretation for the source of the observations [8].
268
M.M. Green