# Free-Radical Propagation Rate Coefficients of Diethyl Itaconate and Di-n-Propyl Itaconate Obtained via PLP–SEC

^{*}

## Abstract

**:**

^{–1}·s

^{–1}and E

_{a}= 17.5 kJ·mol

^{−1}for DEI and A = 1.0 L·mol

^{–1}·s

^{–1}and E

_{a}= 17.5 kJ·mol

^{−1}for DnPI.

## 1. Introduction

_{p}, is one of the kinetic key parameters that describe how fast the chain-growth reaction proceeds and how sensitive it is to changes in reaction conditions such as temperature and concentration of reactants. Measuring kinetic coefficients in radical polymerization is important for understanding and optimizing radical polymerization processes, as it allows to predict and control the behavior of the reaction under different conditions and in addition enables to predict the properties of the resulting polymer. The kinetic information can thus be used to design new polymers with specific properties, optimize reaction conditions for industrial-scale production, and troubleshoot problems that arise during polymerization.

## 2. Materials and Methods

_{2}SO

_{4}. The mixture was boiled under reflux for 5 h. Then, the alcohol was removed using a rotary evaporator. The residue was poured in a 5-times excess of ice water, the phases were separated, and the organic phase was neutralized with a 10 wt.%-solution of NaHCO

_{3}in water. Afterwards, the product was dried over CaCl

_{2}. The purity was determined by NMR and was found to be >95 %.

^{1}H NMR (300 MHz, CDCl

_{3}, δ, see Scheme 1): 6.31 (s, 1H; C7), 5.68 (s, 1H; C7), 4.11 (t, J = 6.8 Hz, 2H; C3), 4.04 (t, J = 6.8 Hz, 2H; C9), 3.33 (s, 2H; C5), 1.65 (m, 4H; C2+C10), 0.92 (q J = 7.3 Hz, 6H; C1+C11);

^{13}C NMR (75 MHz, CDCl

_{3}, δ): 170.9 (C4), 166.4 (C8), 134.3 (C6), 128.2 (C7), 66.72 (C3/C9), 66.6 (C3/C9), 37.9 (C5), 22.06 (C2+C10), 10.5 (C1+C11).

^{−1}(DEI) and 1.025 g·mL

^{−1}(DnPI).

^{6},10

^{4},10

^{3}Angstrom) which was embedded in a PSS TCC6000 column oven at 35 °C. THF at a flow rate of 1 mL·min

^{−1}was used as the solvent. The detector was an Agilent 1260 RID G1362A. Access to absolute molecular weight distributions was obtained by a PS-PMMA calibration in conjunction with the Mark-Houwink-constants of DEI and DnPI, which have been determined previously [15]. These values refer to the solvent toluene, but may also be used for THF, as suggested by Szablan et al. [7].

## 3. Results

#### 3.1. Prediction of Arrhenius Parameters for DEI

_{p}(T), can be calculated from the partition functions ${Q}_{\mathrm{n}}$ of the involved molecules n and the electronic barrier height ${E}_{0}$ (see Equation (1)). κ denotes a correction factor in order to account for tunneling (assumed to be equal to 1 here and will be left out in the following), $c$ is the inverse of the volume used in the translational partition function, k

_{B}is the Boltzmann constant, R the universal gas constant, and $m$ is the molecularity of the reaction [21].

_{p}can be calculated directly by Equations (3) and (4). The formulae for calculating the individual entropy components can be found in the Supporting Information.

_{j}denotes the frequency of the j-th vibration and h is the Planck constant.

#### 3.2. PLP Experiments

_{i}and the inflection point at the low molecular weight side of the peak typically yields the most precise results [26]. The inflection points were determined by evaluating the maxima of the derivative of the molar mass distribution, as shown in Figure 1.

#### 3.2.1. Diethyl Itaconate

_{Inf}, were extracted from complete molar mass distributions obtained via size-exclusion chromatography.

_{p}is chain-length independent and is called the “consistency criterion” of PLP-SEC. It was introduced for distinguishing the additional PLP peaks from any other occurring peaks that are not kinetically relevant.

_{p}for short macroradicals up to chain lengths of ca. 5 [31,32]—is reflecting a real chain-length dependency up to longer chain-lengths or is an SEC artifact [33,34]. PLP-SEC alone is apparently not capable of deciding this open question and it is now generally accepted that the k

_{p}data obtained are estimates subject to uncertainty, due to such as yet unexplained effects.

_{p}data, a regular Arrhenius fit is employed (see Figure 4). The observed chain-length dependency of k

_{p}is not taken into account, but is accepted as uncertainty; consequently, the Arrhenius parameters, given in Table 3, will be average values over the whole chain length regime. It can already be noted here that these Arrhenius parameters fit very well to the ones obtained for other itaconates, but this will be discussed in greater detail below.

#### 3.2.2. Di-n-Propyl Itaconate

## 4. Discussion

_{p}at a given temperature were used for revealing family behavior of monomers. In the case of linear alkyl methacrylates, k

_{p}(at 50 °C) increases linearly with the length of the side chain [34]. For itaconates, we find an opposite trend: as indicated in Figure 8, k

_{p}clearly decreases with increasing size of the ester groups. This can possibly be reasoned by a pre-structuring effect of the monomer, as has also been put forward by Haehnel et al. [35]. For alkyl methacrylates, longer side chains lead to a more structured monomer bulk. Due to stronger dispersive interactions, the longer side chains align more pronouncedly with each other. This effect also aligns the olefinic bonds such that propagation is easily possible and promoted with ester groups size. Itaconates, however, have two side chains. This allows for two different patterns of alignment. The first is identical to the one discussed for methacrylates. The second pattern is not stacked, but shifted, in a zig-zag motif. This alignment increases the distance of the olefinic bonds, leading to decreased propagation rates. Apparently for itaconates, the second pattern is preferred. This interesting effect might be confirmed by MD simulations in the future.

## 5. Conclusions

_{p}clearly decreases with increasing size of the ester groups. This behavior is different to other monomers and can possibly be explained by a pre-structuring effect of these rather sterically hindered monomers.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Formulae for Calculating the Individual Entropy Components

## Appendix B

#### Structures of the Reactants, Transition State and Product on UHF/6-31g(d) Level of Theory

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**Figure 1.**Detail of a representative molar mass distribution (

**blue**) from PLP of DEI and its derivative (

**red**). The molar masses L

_{i}were obtained from the maxima of the derivative curve.

**Figure 2.**Ratio of molar masses of inflection points for all DEI samples. Blue points show the ratio of the second inflection point to the first one, while the red points show the ratio of the third inflection point to the second one.

**Figure 3.**Obtained propagation rate coefficients, k

_{p}, for DEI as function of initiator concentration, c

_{Ini}. An average of the ${k}_{\mathrm{p}}$ values extracted from the different inflection points is used here. Triangles refer to a laser repetition rate of 0.5 Hz, while circles refer to 1 Hz, and squares to 2 Hz.

**Figure 4.**Arrhenius fit for ${k}_{\mathrm{p}}$ of DEI. The indicated uncertainties in ln(k

_{p}) result from the standard deviation of the measurements for the respective temperature, while for the uncertainty in T

^{−1}an uncertainty of ΔT = 2 K was assumed. The obtained Arrhenius parameters are shown in Table 3.

**Figure 5.**Ratio of molar masses of inflection points for all DnPI samples. Blue points show the ratio of the second inflection point to the first one, while the red points show the ratio of the third inflection point to the second one. Data points that significantly deviate from the expected ratios have been omitted from the analysis according to the consistency criterion of PLP-SEC.

**Figure 6.**Obtained propagation rate coefficients for DnPI as a function of initiator concentration, c

_{Ini}. An average of the ${k}_{\mathrm{p}}$ values extracted from the different inflection points is used here. Stars refer to a laser repetition rate of 0.25 Hz, while triangles refer to 0.5 Hz.

**Figure 7.**Arrhenius fit for ${k}_{\mathrm{p}}$ of DEI. The indicated uncertainties in ln(k

_{p}) result from the standard deviation of the measurements for the respective temperature, while for the uncertainty in T

^{−1}an uncertainty of ΔT = 2 K was assumed. For 30 °C, only one data point exists, consequently the uncertainty in ln(k

_{p}) was assumed to be similar to the other values. The obtained Arrhenius parameters are shown in Table 5.

**Figure 8.**Values of k

_{p}at 50 °C for the family of itaconates using Arrhenius parameters from Table 6.

**Table 1.**Calculated electronic barriers, E

_{0}, and Arrhenius parameters (prefactor, A, and activation energy, E

_{A}) for the propagation step of DEI at 20 °C. The frequencies used for the calculation were used unscaled as well as scaled by their respective scaling factors.

Method | E_{0} [kJ·mol^{–1}] | A [L·mol^{–1}·s^{–1}] | E_{A} [kJ·mol^{–1}] |
---|---|---|---|

UHF/6-31G(d) | 12.7 | $2.0\cdot {10}^{3}$ | 22.6 |

UHF/6-31G(d) scaled | 12.7 | $3.3\cdot {10}^{3}$ | 22.3 |

B3LYP/def2-TZVP | 13.8 | $1.4\cdot {10}^{4}$ | 22.7 |

B3LYP/def2-TZVP scaled | 13.8 | $1.5\cdot {10}^{4}$ | 22.7 |

**Table 2.**PLP-SEC data for DEI: initiator concentration, c

_{Ini}, temperature T, total number of pulses, n

_{pulses}, laser pulse frequency, ν, molecular weight at the various inflection points, M

_{inf}, and the average k

_{p}of all obtained inflection points.

c_{Ini}[mol·L ^{–1}] | T/K | n_{pulses} | ν [Hz] | M_{inf1}[g·mol ^{–1}] | M_{inf2}[g·mol ^{–1}] | M_{inf3}[g·mol ^{–1}] | k_{p}[L·mol ^{–1}·s^{–1}] |
---|---|---|---|---|---|---|---|

0.022 | 343.15 | 2000 | 1 | 25,400 | 42,800 | - | 22.4 |

0.022 | 343.15 | 2000 | 2 | 15,400 | 27,700 | - | 28.0 |

0.040 | 343.15 | 2000 | 1 | 26,600 | 42,800 | - | 23.0 |

0.040 | 343.15 | 2000 | 2 | 15,200 | 28,000 | - | 28.0 |

0.026 | 333.15 | 1000 | 0.5 | 43,000 | 73,800 | 108,800 | 18.5 |

0.026 | 333.15 | 4000 | 1 | 25,100 | 44,900 | 65,600 | 22.2 |

0.047 | 333.15 | 2400 | 0.5 | 44,700 | 79,100 | 116,500 | 19.7 |

0.047 | 333.15 | 4000 | 1 | 23,600 | 44,500 | - | 22.0 |

0.022 | 323.15 | 2000 | 1 | 20,000 | 36,400 | 54,300 | 18.0 |

0.022 | 323.15 | 2000 | 0.5 | 35,700 | 63,100 | 96,100 | 15.9 |

0.061 | 323.15 | 2000 | 1 | 19,780 | 36,400 | - | 18.2 |

0.061 | 323.15 | 2000 | 0.5 | 35,100 | 61,120 | - | 15.7 |

0.033 | 313.15 | 2000 | 1 | 16,320 | 30,050 | - | 15.0 |

0.051 | 313.15 | 2000 | 1 | 15,700 | 29,800 | - | 14.7 |

0.051 | 313.15 | 2000 | 0.5 | 29,100 | 52,300 | - | 13.2 |

0.027 | 303.15 | 2000 | 1 | 12,510 | 23,310 | 35,790 | 11.5 |

0.027 | 303.15 | 2000 | 0.5 | 23,500 | 42,900 | 65,000 | 10.6 |

0.046 | 303.15 | 2000 | 1 | 12,490 | 23,420 | - | 11.6 |

0.046 | 303.15 | 2000 | 0.5 | 23,100 | 42,900 | 64,200 | 10.5 |

**Table 3.**Experimental Arrhenius parameters for chain-length-averaged k

_{p}of DEI, obtained via PLP-SEC.

A [L·mol^{–1}·s^{–1}] | E_{A} [kJ·mol^{–1}] |
---|---|

(1.1 ± 0.3) · 10^{4} | 17.5 ± 0.6 |

**Table 4.**PLP data for DnPI: initiator concentration, c

_{Ini}, temperature T, total number of pulses, n

_{pulses}, laser pulse frequency, ν, molecular weight at the various inflection points, M

_{inf}, and the average k

_{p}of all obtained inflection points.

c_{Ini}[mol·L ^{–1}] | T/K | ν [Hz] | M_{inf1}[g·mol ^{–1}] | M_{inf2}[g·mol ^{–1}] | M_{inf3}[g·mol ^{–1}] | k_{p}[L·mol ^{–1}·s^{–1}] |
---|---|---|---|---|---|---|

0.074 | 333.15 | 0.25 | 70,800 | 129,100 | - | 16.5 |

0.049 | 333.15 | 0.25 | 70,200 | 127,900 | 193,900 | 16.2 |

0.074 | 333.15 | 0.5 | 41,300 | 72,800 | 111,900 | 18.7 |

0.049 | 333.15 | 0.5 | 41,100 | 72,500 | 110,000 | 18.5 |

0.074 | 323.15 | 0.25 | 61,800 | 115,200 | - | 14.6 |

0.049 | 323.15 | 0.25 | 61,200 | 113,500 | - | 14.4 |

0.074 | 323.15 | 0.5 | 33,930 | 61,600 | - | 15.8 |

0.049 | 323.15 | 0.5 | 35,000 | 61,000 | - | 16.0 |

0.074 | 313.15 | 0.25 | 47,200 | 92,800 | - | 11.4 |

0.049 | 313.15 | 0.25 | 50,500 | 93,400 | 136,800 | 11.6 |

0.074 | 313.15 | 0.5 | 26,200 | 49,800 | - | 12.5 |

0.049 | 313.15 | 0.5 | 28,400 | 48,400 | - | 12.8 |

0.049 | 303.15 | 0.5 | 19,400 | 39,100 | - | 9.5 |

0.074 | 293.15 | 0.25 | 12,100 | 22,400 | 32,700 | 2.8 |

0.049 | 293.15 | 0.25 | 12,400 | 20,700 | 32,100 | 2.7 |

0.074 | 293.15 | 0.5 | 16,100 | 29,600 | - | 7.5 |

0.049 | 293.15 | 0.5 | 14,300 | 30,100 | - | 7.1 |

**Table 5.**Experimental Arrhenius parameters for chain-length-averaged k

_{p}of DnPI, obtained via PLP-SEC.

A [L·mol^{–1}·s^{–1}] | E_{A} [kJ·mol^{–1}] |
---|---|

(1.0 ± 0.5) · 10^{4} | 17.5 ± 1.2 |

**Table 6.**Comparison of Arrhenius prefactors and activation energies for ${k}_{\mathrm{p}}$ of different itaconic acid esters. DMI = Dimethyl itaconate, DnBI = Di-n-butylitaconate and DCHI = Dicyclohexylitaconate.

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**MDPI and ACS Style**

Meyer, E.; Weege, T.; Vana, P.
Free-Radical Propagation Rate Coefficients of Diethyl Itaconate and Di-n-Propyl Itaconate Obtained via PLP–SEC. *Polymers* **2023**, *15*, 1345.
https://doi.org/10.3390/polym15061345

**AMA Style**

Meyer E, Weege T, Vana P.
Free-Radical Propagation Rate Coefficients of Diethyl Itaconate and Di-n-Propyl Itaconate Obtained via PLP–SEC. *Polymers*. 2023; 15(6):1345.
https://doi.org/10.3390/polym15061345

**Chicago/Turabian Style**

Meyer, Enno, Tobias Weege, and Philipp Vana.
2023. "Free-Radical Propagation Rate Coefficients of Diethyl Itaconate and Di-n-Propyl Itaconate Obtained via PLP–SEC" *Polymers* 15, no. 6: 1345.
https://doi.org/10.3390/polym15061345