Crystal Growth & Design
Article
reaction cavity analyzed but also elasticity compensating strains
caused by a reaction and protecting crystals from crack-
ing.42−46 The feedback was the factor responsible for kinetics
in the case of various compounds.43,44,47−50 Sometimes the
analysis of one or several individual intermolecular contacts
provided valuable information connected to the proceeding
photochemical reactions in crystals. For instance, hydrogen
bonds were given as the reason for photochemical inertia51−53
or activity.18,54 π···π interactions had a positive influence on
reactivity by preorientating molecules in crystals55,56 or a
negative impact by impeding atomic shifts.20,57
Scheme 2. Graphical Representation of the Geometrical
Parameters Describing Susceptibility to the Norrish-Yang
Reaction
The above-described factors are connected with internal
crystal structures. It should be added that, except for these,
there are other factors, which are external, such as radiation
wavelength, temperature, and pressure.59
The kinetics of a photochemical reaction in a crystal can be
described in terms of the Johnson-Mehl-Avrami-Kolgomorov
(JMAK) model by the following equation:58,60
• Δthe CO···H angle between the atoms of the
carbonyl group and γ-hydrogen; the ideal value is 90°−
120°.11
• θthe C−H···O angle between γ-carbon, γ-hydrogen,
and carbonyl oxygen; the ideal value is 180°.13
P = 1 − exp(−kt)n
where:
P is product content.
k is reaction rate.
t is time.
• ωthe torsion angle describing the deviation of the γ-
hydrogen from the plane of the carbonyl group; the ideal
value is 0°.14
The above-given ideal values are also valid in the case of the
formation of a five-membered ring, except for the value of
parameter D, which in such a situation should be less than 3.4
Å.15
n is the Avrami exponent.
The n parameter provides the information about dimension-
ality of product growth D. For n equal to 2, 3, or 4 the
formation of product proceeds in 1, 2, or 3 dimensions,
respectively. In the case when n is 1, there are no vectors of
product propagation, and product molecules occur independ-
ently and randomly. In such a situation, domains that could
cause undesirable phase separation are not formed, and a
reaction is homogeneous. It should be mentioned that certain
circumstances arose in which the values of the Avrami
exponent were significantly different from integers.61,62 In
practice the logarithmic form of the JMAK equation, known as
the Avrami plot, is used. The linear dependence between
ln[−ln(1 − P)] and ln t justifies the use of the model.
The JMAK model was applied to photochemical reactions
such as the [2 + 2] photodimerization of α-trans-cinnamic,61,63
β-cinnamic,64 o-methoxycinnamic, and o-ethoxycinnamic
acids65 and the [4 + 4] photodimarization of 9-anthracene-
carboxylic acid.66 It was also used for the description of the
kinetics of the Norrish-Yang reaction in crystals of ammonium
and benzylaminium 4-(2,4,6-triisopropylbenzoyl)benzoates.
The analyses performed revealed a homogeneous mechanism
with autoinhibition for the ammonia salt, n = 0.84, and a
hybrid mechanism (homogeneous and one-directional) for the
benzylamine salt, n = 1.44(4).18 A very interesting phenom-
enon was met in the case of the benzylidene oxazolone
derivative, where the kinetics significantly changed at a certain
stage of the process, as it was evidenced by two straight lines
having different slopes in the Avrami plot. During the first
stage, the reaction was homogeneous, n = 1.1(2), and during
the second one it proceeded homogeneously with auto-
inhibition, n = 0.33(6). The observed autoinhibition was
connected with certain, yet gradual, degradation of a crystal.67
In this paper, we aim to reveal and explain on structural
grounds the differences in the unique kinetics of the Norrish-
Yang reaction in crystals in the case of 1,3,5,7-tetraazatricyclo-
[3.3.1.13,7]decane 4-(2,4,6-triisopropylbenzoyl)benzoate by
means of X-ray diffraction and additionally by Raman
spectroscopy.
At times, the analysis of parameter d only enabled the
rationalization of photochemical reactivity in crystals, as it was
in the case of the Yang cyclization of α-1-norbornylacetophe-
none derivatives.2,8 The analysis of d and Δ explained the
predominant formation of a five-membered ring (not four-
membered) for phenylethaneaminium 4-(2,4,6-
triisopropylbenzoyl)benzoate.7
Nevertheless, there were also cases when the analysis of all
five parameters provided valuable results, for instance, when
explaining why only one of two o-isopropyl groups was
reactive6,16−18 and why there were differences in the reactivity
of three salts of 4-(2,4,6-triisopropylbenzoyl)benzoic acid.18
However, there were cases where the analysis of the
geometrical parameters merely explained the occurrence of
the reaction but did not provide the answer as to why only one
of the two fragments having a similar geometry took part in the
reaction.19 In terms of the geometrical demands for
benzophenones, the role of the dihedral angle between a
carbonyl group and a benzene ring was also emphasized.20
According to the topochemical postulate, a photochemical
reaction proceeds in crystals when there is the possibility of
breaking old bonds and forming new ones. Such a reaction is
easier when the required atomic shifts are small and a reaction
cavity21−27 does not significantly change its geometry.28,29
However, when there is free space close to the reacting
molecular fragments, the reaction can occur, although the
necessary shifts and changes are significant. Moreover, the
existence of such a free space can cause a crystal lattice to
better accommodate a strain caused by the appearance of
product molecules. The analysis of the size and shape of a
reaction cavity helped to explain the photochemical reactivity
of many compounds.22,24−27,30−32 It was reported that a big
reaction cavity of suitable shape facilitated a photochemical
reaction33−35 and a small cavity of unsuitable shape disabled a
reaction.20 The geometry of a reaction cavity was responsible
for the reaction rate,36−40 the reaction direction, and the
obtained products.5,19,41 Not only was the geometry of a
5062
Cryst. Growth Des. 2020, 20, 5061−5071