# Kinetics of Polycycloaddition of Flexible α-Azide-ω-Alkynes Having Different Spacer Length

^{1}

^{2}

^{*}

## Abstract

**:**

_{8}vs. C

_{12}) between functional groups are synthesized. Their bulk polymerization kinetics is studied by differential scanning calorimetry (DSC) and parameterized with the aid of isoconversional methodology. The monomer with a shorter hydrocarbon spacer has somewhat greater reactivity. The effect is traced to a moderate increase in the effective value of the preexponential factor that arises from the fact that the respective monomer has a higher initial molar concentration in itself. The techniques of GPC and NMR provide additional kinetic and mechanistic insights into the studied reaction.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

_{2}, 60 Å, 0.04–0.063 mm, Merck, Rahway, NJ, USA), sodium azide (>99%, Corvine Chemicals and Pharmaceuticals, Hyderabad, India), sodium sulfate (anhydrous, >99%, Khimprom-M, Yaroslavl, Russia) were purchased and used as received. Tetrahydrofuran (>99.5%, Chimmed, Moscow, Russia) was additionally distilled over sodium hydroxide. α-azide-ω-alkynes (Figure 1) have been synthesized according to the known synthetic protocol [10]. The purity of synthesized monomers was estimated from respective

^{1}H NMR spectra and found to be not less than 98%.

**1-azido-8-(prop-2-yn-1-yloxy)octane (8AA)**.

^{1}H NMR (400 MHz, CHCl

_{3}-d1, δ, ppm): 1.33 (m, 8H, CH

_{2}), 1.59 (m, 4H, CH

_{2}), 2.41 (t, 1H, J = 2.3 Hz, ≡CH), 3.25 (t, 2H, J = 6.9 Hz, CH

_{2}-N), 3.51 (t, 2H, J = 6.6 Hz, CH

_{2}-CH

_{2}-O), 4.13 (d, 2H, J = 2.3 Hz, O-CH

_{2}-C≡).

^{13}C NMR (101 MHz, CHCl

_{3}-d1, δ, ppm): 26.13, 26.78, 28.95, 29.20, 29.38, 29.59, 51.61, 58.17, 70.34, 74.19, 80.17. IR (cm

^{−1}): 3304 (≡CH, ν), 2933, 2858, 2095 (N

_{3}, ν), 1464, 1354, 1264 (C-N, ν), 1101 (C-O-C, ν) (Figures S1–S3 in the Supplementary Materials).

**1-azido-12-(prop-2-yn-1-yloxy)dodecane (12AA)**.

^{1}H NMR (400 MHz, CHCl

_{3}-d1, δ, ppm): 1.27 (m, 16H, CH

_{2}), 1.59 (m, 4H, CH

_{2}), 2.41 (t, 1H, J = 2.3 Hz, ≡CH), 3.25 (t, 2H, J = 7.0 Hz, CH

_{2}-N), 3.50 (t, 2H, J = 6.6 Hz, -CH

_{2}-CH

_{2}-O-), 4.13 (d, 2H, J = 2.3 Hz, O-CH

_{2}-C≡).

^{13}C NMR (101 MHz, CHCl

_{3}-d1, δ, ppm): 26.23, 26.86, 28.98, 29.29, 29.56, 29.60, 29.65, 29.67, 51.64, 58.15, 70.46, 74.15, 80.22. IR (cm

^{−1}): 3308 (≡CH, ν), 2927, 2855, 2095 (N

_{3}, ν), 1466, 1354, 1261 (C-N, ν), 1102 (C-O-C, ν). (Figures S4–S6 in the Supplementary Materials).

#### 2.2. Methods

^{−1}. Polystyrene standards were used for the GPC calibration. The

^{1}H and

^{13}C NMR experiments were carried out on a Bruker AVANCE III NMR spectrometer operating at 400 MHz with CDCl

_{3}as a solvent.

^{1}H NMR analyses of the polymers were performed on the samples with incomplete conversion (~90%) for their better solubility in deuterated chloroform (Figures S7 and S8 in the Supplementary Materials). Chemical shifts are reported in delta (δ) units in parts per million (ppm). IR spectra were recorded on a Bruker Vertex 70 FTIR spectrometer.

^{−1}argon flow. Temperature was raised from 25 to 250 °C at the heating rates of 0.5, 1.0, 2.0, and 4.0 °C min

^{−1}. The samples were placed into 40 µL Al pans and sealed under argon. The sample mass in all runs was 5.0 ± 0.2 mg. Isothermal polymerization (130 °C, 2 h) of both monomers has been performed inside the same DSC instrument in 40 µL aluminum pans hermetically sealed in argon.

## 3. Calculations

_{α}. Unlike simpler rigid methods, this method allows one to eliminate a systematic error in E

_{α}incurred when E

_{α}varies considerably with α [16]. The elimination of the error is accomplished via piecewise integration that assumes E

_{α}to be constant only over a narrow integration range, Δα. In the present computations Δα was kept to be 0.01. E

_{α}was determined as the value that secures the minimum of the function:

_{α}on α. The trapezoidal rule was applied to determine numerically the values of the $J\left[{E}_{\alpha},{T}_{i}\left({t}_{\alpha}\right)\right]$ integrals. A minimum of Equation (1) was found by the COBYLA non-gradient method from the NLopt library. The error bars for the E

_{α}values were evaluated as described elsewhere [17].

_{α}on α was obtained by plugging the E

_{α}values into the compensation effect equation

_{i}and E

_{i}pairs into Equation (3). Each of these pairs was found by inserting various reaction models, f

_{i}(α) into the linearized form of the rate equation:

_{i}(α) model, plotting the left-hand side of Equation (4) against the reciprocal temperature permits evaluating lnA

_{i}and E

_{i}from the respective intercept and slope of the straight line. As established earlier [18], the use of four models, namely the power law (P2, P3, P4) and Avrami-Erofeev (A2), suffices for accurate calculations.

_{α}were employed to establish the numerical form of the integral reaction model by Equation (5):

_{α}is the time to reach the conversion α at isothermal temperature, T.

## 4. Results and Discussion

_{1}and C

_{2}are the concentrations of isomeric triazoles, C is the concentration of the monomer in the reaction mixture, n is the reaction order, k

_{1}and k

_{2}are the rate constants of the formation of two isomeric 1,2,3-triazole units. The temperature dependence of the rate constant is expressed by the Arrhenius Equation (8), where the index i equals 1 or 2 to identify the parameters of the two respective competing reactions.

_{0}means the concentration of the monomer in itself. It should be also noted, that the C

_{0}value in the Equation (10) is taken relative to the standard state (i.e., 1 mol L

^{−1}) that permits avoiding the confusion with the concentration-dependent units of the preexponential factor when the molecularity of a reaction differs from one [25].

_{1}= E

_{2}) [20]. In this case the reaction kinetics can be expressed by a simple nth-order reaction rate Equation (11)

^{−1}) shift the reaction to the temperatures where the monomers may start to decompose [20]. As one can see from Figure 3, DSC curves for the

**8AA**monomer are shifted to lower temperature compared to those for

**12AA**that indicates that the former is more reactive. The difference between the corresponding peak temperatures is ~4–5 °C. The measured average heats of the reaction are 1130 ± 50 J g

^{−1}(236 ± 10 kJ mol

^{−1}) and 790 ± 30 J g

^{−1}(210 ± 8 kJ mol

^{−1}) for the

**8AA**and

**12AA**monomers, respectively. The obtained values agree with the literature data for the heats of azide-alkyne cycloaddition reactions, which usually are within the range of 210–270 kJ mol

^{−1}[26].

_{α}and pre-exponential factor A

_{α}on conversion presented in Figure 4. One can observe an insignificant variation of both parameters with conversion for the studied monomers. This suggests that the E

_{1}and E

_{2}values, characterizing competing steps of forming isomeric triazolic units during polymerization, are close to each other for both monomers. The average values of E

_{α}are 85 ± 2 and 86 ± 2 kJ mol

^{−1}for

**8AA**and

**12AA**, respectively. Similar values of the activation energy are reported for other bulk AAPC reactions [13,24]. The average values of lnA

_{α}are equal to 20.0 ± 0.5 and 20.1 ± 0.4, respectively (A

_{α}in s

^{−1}).

_{α}and A

_{α}values in Equation (5) yields numerical values of g(α) displayed in Figure 5. The dependencies of g(α) on α are consistent with the nth-order reaction model. This is readily visualized by fitting the integral form of this model (Equation (13)) to the experimental g(α) data.

^{2}) values are grouped in Table 1. It is seen that the nth-order reaction model produces fits of good quality and yields n that equals 2. This value is expected naturally considering the bimolecular mechanism of the studied reaction.

_{ef}and E

_{1}the latter parameter has been fixed at the value equal to the respective mean value of E

_{α}(Figure 4). The A

_{ef}and n values have been optimized during fitting. The resulting kinetic parameters of the reaction are presented in Table 1. It is seen that the optimized values of the natural logarithm of the preexponential factors (Table 1) are only insignificantly smaller than the mean lnA

_{α}determined independently from the compensation effect (Figure 4). The n values are also smaller than those estimated via isoconversional analysis (Equation (13)), which is probably a result of mutual correlation between n and A

_{ef}. On the other hand, these n values still round off to 2.

_{n}values of 15,600 and 17,200 g mol

^{−1}for

**8AA**and

**12AA**, respectively. The amount of cyclization products in both cases does not exceed few percent and the contribution of intramolecular reactions can be neglected, as it was assumed previously.

^{1}H NMR spectra of the obtained polymers afford estimating the ratio of 1,4- to 1,5-disubstituited triazolic fragments formed during polymerization as 1.8 in both cases (Figure 6). The same ratio of isomers has recently been reported for the bulk azide-alkyne cycloaddition between phenyl propargyl ether and 1-azidodecane [20]. It is worth noting that the ratio of the isomeric triazolic fragments in that case was found to be equal to the ratio of the preexponential factors (i.e., A

_{ef,}

_{1}/A

_{ef,}

_{2}= 1.8) [20].

**8AA**monomer with a shorter spacer possesses somewhat higher reactivity than

**12AA**. Per our hypothesis, this difference most likely relates to the higher initial molar concentration of

**8AA**monomer that arises from its lower molar mass. Based on the corresponding molar masses of the

**8AA**and

**12AA**monomers (209.3 and 265.4 g mol

^{−1}) and assuming that both monomers have the same density, one can easily find that for

**8AA**the C

_{0}value in Equation (10) and, thus, A

_{ef,1}should be 1.3 times higher than the corresponding values for

**12AA**. Assuming for simplicity that E and n are unaffected by the spacer length, the 1.3 increase in the effective preexponential factor should cause similar increase in the polymerization rate of

**8AA**relative to that of

**12AA**as long as the rates are compared at the same α and T values. To perform such comparison we have calculated the isoconversional-isothermal factor Z

_{α,T}defined by Equation (14) [27]. Isothermal polymerization rate values have been calculated from the non-isothermal ones with the help of the technique of isoconversional predictions (Equation (6)).

_{α,T}value averaged over the whole conversions range has turned out to be 1.30 ± 0.04. The value of Z

_{α,T}is almost independent of the chosen temperature because of the closeness of the effective activation energies for both monomers (Table 1). Remarkably, the obtained Z

_{α,T}value matches exactly the rate increase expected from the increase in C

_{0}and A

_{ef,}

_{1}values. This apparently reinforces the idea that the effect of the hydrocarbon spacer length on the reactivity of α-azide-ω-alkynes is primarily associated with the monomer’s molar mass and its initial concentration in itself.

## 5. Conclusions

## Supplementary Materials

^{1}H NMR spectrum of 1-azido-8-(prop-2′-yn-1′-yloxy)octane (8AA) (CDCl

_{3}-d1, 25 °C), Figure S2:

^{13}C NMR spectrum of 1-azido-8-(prop-2′-yn-1′-yloxy)octane (8AA) (CDCl

_{3}-d1, 25 °C), Figure S3: FTIR spectrum of 1-azido-8-(prop-2′-yn-1′-yloxy)octane (8AA), Figure S4:

^{1}H NMR spectrum of 1-azido-12-(prop-2′-yn-1′-yloxy)dodecane (12AA) (CDCl

_{3}-d1, 25 °C), Figure S5:

^{13}C NMR spectrum of 1-azido-12-(prop-2′-yn-1′-yloxy)dodecane (12AA) (CDCl

_{3}-d1, 25 °C), Figure S6: FTIR spectrum of 1-azido-12-(prop-2′-yn-1′-yloxy)dodecane (12AA), Figure S7:

^{1}H NMR spectrum of polymer based on 1-azido-8-(prop-2′-yn-1′-yloxy)octane (8AA) (CDCl

_{3}-d1, 25 °C), Figure S8:

^{1}H NMR spectrum of polymer based on 1-azido-12-(prop-2′-yn-1′-yloxy)dodecane (12AA) (CDCl

_{3}-d1, 25 °C).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**DSC curves of studied polycycloaddition reaction for

**8AA**(solid lines) and

**12AA**(dashed lines) monomers (numbers denote heating rates in °C min

^{−1}).

**Figure 4.**Isoconversional values of activation energy (circles and squares) and preexponential factor (triangles and diamonds) for studied for

**8AA**(red symbols) and

**12AA**(blue symbols) monomers.

**Figure 5.**Integral form of nth-order reaction model fit to the experimental g(α) data for

**8AA**(

**A**) and

**12AA**(

**B**) monomers.

**Figure 6.**Comparison integral intensity of C4-H and C5-H protons of triazolic units in polymers based on

**8AA**(

**A**) and

**12AA**monomers (

**B**).

Monomer | Fit to | E_{1}/kJ mol^{−1} | ln(A_{ef}/s^{−1}) | n | r^{2} |
---|---|---|---|---|---|

8AA | Equation (13) | - | - | 1.99 ± 0.01 | 0.98 |

Equation (11) | * 85 ± 2 | 19.67 ± 0.02 | 1.64 ± 0.04 | 0.99 | |

12AA | Equation (13) | - | - | 2.00 ± 0.01 | 0.98 |

Equation (11) | * 86 ± 2 | 19.71 ± 0.02 | 1.65 ± 0.03 | 0.99 |

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**MDPI and ACS Style**

Galukhin, A.; Aleshin, R.; Nosov, R.; Vyazovkin, S.
Kinetics of Polycycloaddition of Flexible α-Azide-ω-Alkynes Having Different Spacer Length. *Polymers* **2023**, *15*, 3109.
https://doi.org/10.3390/polym15143109

**AMA Style**

Galukhin A, Aleshin R, Nosov R, Vyazovkin S.
Kinetics of Polycycloaddition of Flexible α-Azide-ω-Alkynes Having Different Spacer Length. *Polymers*. 2023; 15(14):3109.
https://doi.org/10.3390/polym15143109

**Chicago/Turabian Style**

Galukhin, Andrey, Roman Aleshin, Roman Nosov, and Sergey Vyazovkin.
2023. "Kinetics of Polycycloaddition of Flexible α-Azide-ω-Alkynes Having Different Spacer Length" *Polymers* 15, no. 14: 3109.
https://doi.org/10.3390/polym15143109