SI, PI, GI (pure, Sigma-Aldrich) were recrystallized from ethanol (reagent grade, POCH, Poland). Dimethylsulfoxide (DMSO, pure, Avocado, Germany) was dried over molecular sieves 4A (POCH, Poland), while EO and PO (racemate) (pure, Fluka, Switzerland) and sodium hydroxide (reagent grade, POCH, Poland) were used as received.

Weighed sample of imide was placed in 50 cm³ volumetric flask and dissolved in ca 30 cm³ DMSO. After dissolving of imide and NaOH as catalyst the temperature of the solution was raised to 25˚C, 30˚C, 35˚C, 40˚C, 45˚C or 50˚C (±0.05˚C). Oxiranes (EO or PO) as liquids stored in refrigerator were transferred into the flask, the volume was adjusted with DMSO and then the flask was immediately closed to avoid evaporation of boiling oxirane and weighed. The concentration of oxirane was calculated based on mass of substrates used. The solutions prepared in that way were then rapidly transferred into thermostated dilatometer.

The influence of catalyst concentration on the rate of reaction was studied at constant concentration of imide and EO (1.0 mol/dm³). The sodium hydroxide concentration was varied within 0.05 ÷ 0.20 mol/dm³ region with 0.05 mol/dm³ step. The influence of imide concentration on the rate of reaction was studied at constant concentration of EO (0.25 mol/dm³) and catalyst (0.20 mol/dm³) with variable imide concentration within 2 ÷ 4 mol/dm³ region.

The temperature dependence was obtained for the system with 1.0 mol/dm³ imide and oxirane and 0.20 mol/dm³ NaOH concentrations within 25˚C ÷ 40˚C for the reaction with EO and 35˚C ÷ 50˚C for the reaction with PO with 5˚C intervals. The temperature range for kinetic measurements is limited from lower side by long reaction time (2 weeks for EO to 1.5 months for PO), which precludes the good accuracy of measurement, and from the higher side by boiling of oxiranes in reaction mixture (above 40˚C for EO and 50˚C for PO).

Kinetics of reaction was studied by dilatometry, i.e. by measuring volume contraction of reaction mixture, as it was described before [5] . Relative concentration of oxirane (b) was defined as

b = c B c 0B (3)

where: c_0B, c_B-corresponding to initial and instantaneous concentrations of oxirane, mol/dm³.

In order to establish the rate low, the substitution method was applied. The values of relative concentration of oxirane, c_B obtained for 0.2 - 0.8 region with 0.05 step and reaction time were put into the kinetic law equations of various orders. Considering the system with EO as standard, the relative reactivity of PO (r_PO) was used as the ratio of the rate constants at the same temperature:

r PO = k PO k EO (4)

where: k_PO, k_EO-rate constants for PO and EO, respectively.

Relative reactivity of imides was analyzed in analogous manner using succinimide as standard.

The activation energy (ΔG^≠) was calculated from [15] :

Δ G ≠ = R T ⋅ ( 23764 − ln k T ) (5)

where: R-gas constant [J/mol・K],

T-temperature of measurement, [K],

k-rate constant.

By plotting ΔG^¹ versus T a straight line was obtained with activation enthalpy (ΔH^¹) and entropy (ΔS^¹) of the reaction as the coefficients of the line [15] :

Δ G ≠ = Δ H ≠ − T ⋅ Δ S ≠ (6)

The products of reactions were isolated after full kinetic run. The DMSO was distilled off under reduced pressure and N-(hydroxyalkyl)imides were isolated as solids, which were recrystallized from ethanol or benzene. Pure products were characterized by melting point, and by the IR spectra (ALPHA FT-IR BRUKER spectrometer). The yield was estimated based on chromatographic analysis (LC chromatograph KB 5901, prod. COBRABID, Poland), as described in [5] .

Conductometric measurements were performed for solutions of imides, sodium hydroxide and mixture of them in DMSO in thermostated 20 cm³ cell at 20˚C (±0.1).

The rate law for the reaction of SI with EO was obtained by substituting the instantaneous values of relative oxirane concentration, b (Equation (3)) and reaction time into kinetic equations of various orders (Table 1). It has been found that reaction of SI with EO obey 3/2 order rate low (Table 1).

V = − d c B d t = k 3 / 2 c 3 / 2 (7)

The reaction depends on catalyst concentration. The relationship between rate constant derived from Equation (7) and catalyst concentration was:

k 3 / 2 = k ′ 3 / 2 c cat n (8)

When plotting lgk_3/2 = f (gc_cat) the n ≈ 0.5 was obtained (Figure 1). In order to determine power coefficient for oxirane concentration and imide concentration

the kinetics was followed at high excess of imide (8 - 16-fold) in relation to oxirane to keep c AH ≫ c B . Thus c_AH = const. was assumed. Then the order of reaction for oxirane was 1 (Table 2). This results in the following equation:

k 1 = k ′ 1 c AH p (9)

According to kinetic data kinetic order for imide groups was p ≈ 0.5 (Figure 2). Thus the kinetic law describing the reaction of SI with EO is:

V = k c cat 1 / 2 c AH 1 / 2 c B (10)

Other imides (PI, GI) react with EO and PO according to the same rate law (Table 3).

Electronic inductive effect is mostly responsible for reactivity of oxiranes as it was already discussed in [5] :

Higher reactivity of EO than PO was expected, because electrophilicity of C-1 in PO is weakened due to electrodonation from methyl group. Experimental rate constants for reactions of EO and PO with SI and PI are 2.1-2.6 times higher for EO than for PO (Table 3). The reactivity of SI and PS with oxiranes is almost the same, while GI is more reactive (Table 4). We tentatively attributed this to difficult stabilization of glutarimide anion due to its out-of-plane distortion in comparison with planar other imide anions. Determined rate constants of reactions between oxiranes and imides enabled us to establish the following order of reactivity for imides and oxiranes, which was the same as for analogous reactions catalyzed by triethylamine [5] :

GI > PI ≥ SI and EO > PO (11)

Gibbs activation energy (ΔG^≠) for these reactions was determined in function of temperature. The plots ΔG^≠ = f (T) are linear (Figure 3) which means that the same mechanism was ruling the kinetics within the studied temperature range. Averaged activation enthalpy, entropy and Gibbs energy, determined using Eyring formula, are collected in Table 5. The value of entropy changes suggests two-molecule intermediate state because dividing the value of ΔS^¹ by 50 J/mol K the value of changes in entropy contributed to restriction of translation, rotation and oscillation of one mol of molecules involved in intermediate state [15] gives ca 2, which corroborate well with proposed further mechanism of reaction (vide infra; elementary reaction 14).

The intermediate state in case of reaction with GI is more restricted. This might be the largest limitation of rotational degrees of freedom at intermediate state of non-planar hexa-membered ring of GI. The relationship of changes in enthalpy vs. entropy of activation for all studied systems is shown in Figure 4. The relationship is isokinetic, which indicates that all the reaction within the series obey the same mechanism [15] .

Based on experimentally derived kinetic law (10) for reaction of cyclic imides (AH) with oxiranes (B) in presence of sodium hydroxide s catalyst (Cat) the following elementary reaction can be postulated:

− dissociation of NaOH in DMSO:

NaOH ⇄ Na + + OH −

Cat ⇄ k − 1 k 1 at + + C − (12)

− formation of imide anions (A⁻) in reaction of hydroxyl anions (C⁻) from catalyst:

AH + C − ⇄ k − 2 k 2 A − + HC (13)

− reaction of imide anion with oxirane with formation of alcoholate (AB⁻):

A − + B → k 3 AB − (14)

− neutralization of alcoholate with recovery of catalytic anion:

AB − + HC → k 4 ABH + C − (15)

The acronyms under formula in Schemes 13 - 15 will be then used in kinetic equations of elementary reactions.

I assume that:

1) Dissociation of NaOH is fast reaction (12);

2) Reaction of hydroxyl group with imide is also fast hydrogen cation transfer (13);

3) Rate limiting of the whole process is attack of imide anion on oxirane (14);

4) Neutralization of alcoholate is also fast reaction (15), the oxirane consumption is equal to imide anion consumption, i.e.:

V gen = − d c B d t = d c A − d t = k 3 c A − c B (16)

The concentration of c A − can be found from stationary state condition [15] :

d c A − d t = k 2 c AH c C − − k − 2 c A − c HC − k 3 c A − c B = 0 (17)

Because

c A − = c HC (18)

then

d c A − d t = k 2 c AH c C − − k − 2 c A − 2 − k 3 c A − c B = 0 (19)

and further

c A − = − k 3 c B + k 3 2 c B 2 + 4 k − 2 k 2 c AH c C − 2 k − 2 (20)

From 2 and 3 it results in: k 3 c B ≪ and

k 3 c B ≪ 4 k − 2 k 2 c AH c C − (21)

This enables to simplify relationship (20) to:

c A − = 4 k − 2 k 2 c AH c C − 2 k − 2 = K 2 c AH c C − (22)

where:

K 2 = k 2 k − 2 (23)

Introducing (22) to Equation (16) one can obtain:

V gen = k 3 K 2 c AH 1 / 2 c C − 1 / 2 c B (24)

Assuming that:

c C − = c cat (25)

and substituting (25) to (24) gives:

V gen = k 3 K 2 c cat 1 / 2 c AH 1 / 2 c B (26)

The Equation (26) can be simplified into:

V gen = k c cat 1 / 2 c AH 1 / 2 c B (27)

where:

k = k 3 K 2 (28)

Derived Equation (27) is in accordance with experimental one (10) indicating that propsed mechanism is kinetically proper. The compatibility of derived and experimental equations occurs provided a dissociation of NaOH in DMSO is irreversible, i.e. k_-1 = 0. If only partial dissociation of NaOH is taken into accout, the following relationship can be derived:

V gen = k c cat 1 / 4 c AH 1 / 2 c B (29)

which is not in accordance with the experimental one.

In order to verify the proposed mechanism and the adopted assumption we have experimentally studied:

− the equilibrium between imide and sodium hydroxide in DMSO (13);

− the consecutive products in studied systems.

The equilibrium between reagents in imide-sodium hydroxide system was studied by straightforward measurements of conductance of 1-molar solution of SI and PI imides in DMSO, separately for 0.05 mol/dm³ NaOH solution in DMSO. The solubility of NaOH in neat DMSO limited using concentration of NaOH for conductivity measurement in contrary to its solubility in DMSO in presence of imides, with which it reacts (13). In kinetic experiments the NaOH solubility was as high as 0.2 mol/dm³. Then conductivity measurement was performed for mixture of 1.00 M imide and 0.05 M sodium hydroxide in DMSO (Table 6). The conductivity of NaOH in DMSO is much higher than conductance of nest DMSO, while the conductivity of imide solution in DMSO is only slightly higher than that of the solvent. Finally, the conductivity of mixture of imide and NaOH solution is considerably higher than additive conductance of component solutions. This may indicate a partial dissociation of sodium imidates in DMSO in presence of water formed upon reaction (13). Further evidences on equilibrium (13) were provided by H-NMR spectroscopy (Figure 5). The imide proton resonance of succinimide at 11 ppm (Figure 5(a)) disappeared upon addition of sodium hydroxide into the solution of SI in DMSO-d₆ (Figure 5(b)). Also the residual water resonance at 3.3 ppm in the spectrum of SI shifted downfield to 4.2 ppm and its intensity increased considerably due to water released in reaction (13). At the same time methylene proton resonance (2.5 ppm) was shifted up field (up to 2.2 ppm) as could be expected for succinimidate anion. Similar behavior was observed for PI-NaOH solution in DMSO-d₆.

We have analyzed the products of reaction mixtures used for kinetic measurements by chromatography. We have found that post-reaction mixtures contained 98% - 99% pure N-(hydroxyalkyl)imides. No unreacted imides were detected in contrary to earlier analogous mixtures in presence of triethylamine catalyst [5] . After recrystallization of products the IR spectra and melting temperatures were compared with the products isolated earlier [4] confirming the identity of products isolated hereof.

Heating of solution of N-(2-hydroxyalkyl)imide in DMSO in presence of oxirane and NaOH catalyst at 40˚C for 48 hours did not result in further contraction of volume of the mixture, again suggesting that no further reaction of N-(2-hydroxyalkyl)imide with oxirane took place. Thus the reaction system applied here can be exploited as synthetic route to obtain N-(2-hydroxyalkyl)imides with high yield not only for monoimides but also for multifunctional imides of mentioned earlier isocyanuric, barbituric, and uric acids.