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Abstract

In this article, coumarin-based random copolymer which can be utilized for atom transfer radical polymerization was investigated both theoretically and experimentally. The thermal degradation mechanism and the activation energies (E _a) were obtained by means of the Coats–Redfern (CR), Tang, and Flynn–Wall–Ozawa (FWO) methods. The thermal degradation reaction mechanism for random copolymer obeyed the phase boundary model (contracting volume, R ₃) of solid-state mechanism. The thermodynamic properties in the range from 100 K to 500 K have been obtained. The calculated HOMO–LUMO energy gap and electronic properties, such as chemical hardness (η), electron affinity (A), chemical potential (μ ₀), global softness (ζ), electronegativity (χ), global electrophilicity (ω), and dipole moment (μ), were investigated and discussed. The molecular electrostatic potential analysis of the random copolymer was also computed.

Keywords

DFT coumarin HOMO–LUMO MEP thermogravimetric analysis decomposition activation energy

Introduction

Coumarin and derivatives play an important role as versatile, because of their applications in photochemistry, medicinal chemistry, and synthetic chemistry. Many of these compounds have found to be active as excellent laser dyes at near-ultraviolet to green wavelength,¹ fluorescent probes,² bactericides, antibacterial agent, anti-allergy compound, anti-diabetic, cardiovascular agents, control of anti-aging, diagnostic probes for amyloid accumulation disease, therapeutic agents for fibrosis and their chances as skin-whitening compounds, fluorescent brighteners, ³ antimicrobial,⁴ antifungal,⁵ anti-inflammatory,⁶ anticoagulant,⁷ antitumor,⁸ and free radical scavenging activity especially the superoxide anions generated by activated neutrophils and to investigate neuronal circuits in tissues.⁹

In recent years, the polymers containing coumarin have attracted great attention as a consequence of these significant properties. The polymers containing coumarin have also been incorporated in a wide variety of functional materials, such as a two-photon optical memory,¹⁰ photoinduced bendable actuator, ¹¹ and reversible cluster formation.¹² The thermal degradation study of polymers, which are used to determine the upper temperature limit of use for a polymeric material, is very important for polymer science in many cases. Therefore, the use of thermogravimetric data for the determination of kinetic parameters has been under great attention. For this purpose, thermogravimetric analysis (TGA) is a technique largely used due to the information provided by a simple thermogram and its simplicity.¹³ To forecast the lifetime as thermal of materials, the thermal decomposition analysis which is especially useful for the study of polymeric materials can be utilized.^14
–16 This analysis can ensure important information relating to critical applications, such as defense, aerospace, and service performance.¹⁵ Currently, quantum mechanical calculations with density functional theory (DFT) are very popular in theoretical modeling due to their accuracy and efficiency with regard to the assessment of molecular properties.¹⁷ Most of the physical and chemical properties of monomer and polymer can be estimated by various computational methods.^18,19 In addition, by adding a monomeric unit to the polymer chain, the thermal properties of a polymer can be significantly modified.²⁰ This coumarin-based random copolymer can be used for the preparation of various photoresponsive polymers, which has become the focus of interest, as well as thermal decomposition and theoretical studies on designing polymers containing coumarin using the DFT method. So, the main purpose of this work was to obtain the thermal behavior and quantum chemical studies of the structure and reactivity of the coumarin-based random copolymer, which can be used as a macroinitiator for the preparation of designing various polymers.

Experimental and theoretical details

The TGA data of the random copolymer were obtained from our previous study.²¹ The activation energy (E _a) calculations were made using different methods with the help of this data. Thermogravimetric measurements were obtained from a TGA-50 instrument under flowing nitrogen atmosphere. The thermal stability of random copolymer was determined with the help of TGA at various heating ratios, such as 5, 15, 25, and 35°C min^–1. The random copolymer was heated from the room temperature to 500°C. The decomposition E _as which are determined using the Coats–Redfern (CR), Tang, and Flynn–Wall–Ozawa (FWO) methods at various heating ratios are summarized below. All the quantum chemical calculations of the random copolymer were carried out using DFT with hybrid Becke–3–Lee–Yang–Parr (B3LYP)^22
–24 combined with 6–311 + G(d, p) basis set using GaussView molecular visualization program²⁵ and Gaussian 09W package program²⁶ without any constraint on the molecular geometry.

Thermogravimetric analysis

TGA provides general information about the comprehensive reaction kinetics rather than the particular reactions. The reaction rate (% min⁻¹) for the decomposition reaction is described as shown below²⁷:

\frac{d α}{d t} = k (T) f (α)

where k(T) is rate constant and depends on temperature, α is the relative decomposition conversion, t is time, and f(α) is a function of the conversion depend on the mechanism. The reaction rate constant is stated by the Arrhenius equation:

k (T) = A exp (- \begin{matrix} E \\ R T \end{matrix})

where A (min⁻¹) is the pre-exponential factor, E (J mol⁻¹) is the E _a, and R is the gas constant (8.314 J mol⁻¹ K⁻¹).

If the temperature of the sample is changed by a controlled and constant heating rate (β = dT/dt), equations (1) and (2) result in:

\frac{d α}{d t} = A exp (- \begin{matrix} E \\ R T \end{matrix}) f (α)

The integration form of equation (3) is generally expressed as:

g (α) = \int_{0}^{α_{p}} \frac{d α}{f (α)} = \frac{A}{β} \int_{0}^{T_{p}} exp (- \begin{matrix} E \\ R T \end{matrix}) d t

where g(α) is the integral form of kinetic model. This equation is well known in the literature and frequently used the reaction mechanisms of solid-state reactions. Different kinetic methods based on this equation were used in this study.

FWO method

FWO method has generally been used in the investigation of the E _a of solid-state reactions as shown in the decomposition processes of polymers.^28,29 Equation (4) is integrated by means of the Doyle approximation³⁰ and is usually described by the following equation:

log β = log [\frac{A E}{g (α) R}] - 2.315 - \frac{0.457 E}{R T}

The E _a at different degrees of conversion can be obtained from a plot of log β versus 1000/T.

Tang method

The following equation has been suggested by Tang and can be described as³¹:

ln (\frac{β}{T^{1.894661}}) = ln [\frac{A E}{R g (α)}] + 3.635041 - 1.894661 ln E - \frac{1.001450 E}{R T}

The slope of the straight line for the plot of ln (β/T ^1.894661) versus 1000/T is used to determine the E _a.

CR method

CR method³² uses an asymptotic approximation for the resolution of equation (4) and it is given by:

ln \frac{g (α)}{T^{2}} = ln \frac{A R}{β E} - \frac{E}{R T}

The different expressions of integral function of conversion for thermal degradation are given in Table 2. The E _a can be obtained from a plot of ln (g(α)/T ²) versus 1000/T.

Results and discussion

Kinetic analysis

Thermal degradation behavior of random copolymer was determined by way of TGA at several heating rates (5, 15, 25, and 35°C min⁻¹). To abstain from the overlapping of inflection point temperatures, we used 10°C min⁻¹ intervals between measurements.³³ With the help of equation (5) or the FWO method, the decomposition E _a can be obtained from a slope of log β versus 1000/T at different degrees of conversion. This equation was derived from the Doyle approach, therefore we have worked at the low degrees of conversion such as intervals from 3% to 18%. The straight lines in Figure 1 are almost parallel, this indicates that this method can be applied to the experimental values of random copolymer at conversion degrees from 3 to 18%. The E _a related to the different degrees of conversion was determined using the FWO method and given in Table 1. As it can be seen in Table 1, the average value of the E _a for random copolymer was found to be 208.38 kJ mol⁻¹.

Figure 1.

FWO plots of coumarin-based random copolymer at different degrees of conversion. FWO: Flynn–Wall–Ozawa.

Table 1.

Using FWO and Tang methods, calculated E _a of coumarin-based random copolymer.

FWO method			Tang method
α (%)	E _a (kJ mol⁻¹)	R ²	E _a (kJ mol⁻¹)	R ²
3	191.7496	0.9354	192.0825	0.9321
5	218.2561	0.9964	220.3175	0.9965
7	240.5602	0.9774	241.4128	0.9769
9	220.3847	0.9639	221.1394	0.9632
12	214.2174	0.9804	215.7182	0.9792
15	186.7466	0.9893	187.4085	0.9889
18	186.7466	0.9893	185.6983	0.9893

FWO: Flynn–Wall–Ozawa; E _a: activation energy.

With the help of equation (6) or the Tang method, the decomposition E _a can be obtained from the slopes of ln (β/T ^1.894661) versus 1000/T at different degrees of conversion. The straight lines in Figure 2 are almost parallel, this indicates that this method can be applied to the experimental values of random copolymer at conversion degrees from 3 to 18%. The E _a related to the different degrees of conversion was determined using the Tang method and given in Table 1. As it can be seen in Table 1, the average value of the E _a for random copolymer was found to be 209.11 kJ mol⁻¹. Table 1 also indicates that this E _a which was obtained by the Tang method was very close to that of 208.38 kJ mol⁻¹ obtained by the FWO method. Compared to other methods, the Tang and FWO methods are more advantageous, but they do not have the basic knowledge of the reaction mechanism for determining the E _a. These methods have been utilized for control of a mechanism of thermal degradation models.³⁴ The different thermal degradation processes listed in Table 2 and the decomposition E _a can be determined from a slope of ln (g(α)/T ²) versus 1000/T. The decomposition E _as obtained by CR method for random copolymer are listed in Table 3 for each heating rate and mechanism. The kinetic thermal analysis indicated that the E _a value (R ₃) obtained using the CR method was in good agreement with those obtained using the Tang and FWO methods.

Figure 2.

Tang plots of coumarin-based random copolymer at different degrees of conversion.

Table 2.

Algebraic expressions of g(α) for the most frequently used mechanisms of the solid-state processes.

Symbol	g(α)	Solid-state process
Sigmoidal curves
A ₂	[−ln(1 − α)]^1/2	Nucleation and growth [Avrami equation 1] Avrami–Erofeev model
A ₃	[−ln(1 − α)]^1/3	Nucleation and growth [Avrami equation 2] Avrami–Erofeev model
A ₄	[−ln(1 − α)]^1/4	Nucleation and growth [Avrami equation 3] Avrami–Erofeev model
Deceleration curves
R ₁	α	Phase boundary model (one-dimensional movement)
R ₂	[1 − (1 − α)^1/2]	Phase boundary model (contracting area)
R ₃	[1 − (1 − α)^1/3]	Phase boundary model (contracting volume)
D ₁	α ²	One-dimensional diffusion (1-D) model
D ₂	(1 − α)ln(1 − α) + α	Two-dimensional diffusion (2-D) model
D ₃	[1 − (1 − α)^1/3]²	Three-dimensional diffusion (Jander equation)
D ₄	(1−2/3α) − (1 − α)^2/3	Three-dimensional diffusion (Ginstling–Brounshtein equation)
F ₂	1/(1 − α)	Random nucleation with two nuclei on the individual particle
F ₃	1/(1 − α)²	Random nucleation with three nuclei on the individual particle

Table 3.

E _a of coumarin-based random copolymer calculated by the CR method for the solid-state processes at various heating ratios (from 5°C min⁻¹ to 35°C min⁻¹).

	5°C min⁻¹		15°C min⁻¹		25°C min⁻¹		35°C min⁻¹
Mechanism	E _a (kJ mol⁻¹)	R ²	E _a (kJ mol⁻¹)	R ²	E _a (kJ mol⁻¹)	R ²	E _a (kJ mol⁻¹)	R ²
A ₂	93.4992	0.9799	92.4849	0.9587	84.86931	0.9973	97.0326	0.9902
A ₃	61.7098	0.9799	61.038	0.9587	56.0164	0.9973	64.0385	0.9902
A ₄	46.7504	0.9799	46.24081	0.9587	42.4363	0.9973	48.5146	0.9902
R ₁	179.466	0.9815	177.1464	0.9563	162.7632	0.9894	186.0174	0.9965
R ₂	183.2073	0.9807	181.029	0.9575	166.2301	0.9972	190.0082	0.9898
R ₃	184.4876	0.9805	182.3592	0.9579	167.419	0.9972	191.38	0.9899
D ₁	358.932	0.9815	354.3011	0.9563	325.518	0.9971	372.0266	0.9894
D ₂	363.8872	0.981	359.4308	0.9571	330.1074	0.9972	377.3059	0.9896
D ₃	368.9836	0.9805	364.7186	0.9579	334.838	0.9972	382.7516	0.9899
D ₄	365.5666	0.9808	361.1768	0.9574	331.6704	0.9972	379.1018	0.9897
F ₂	15.2869	0.9236	15.8689	0.9952	14.1845	0.9822	16.3295	0.9889
F ₃	30.5747	0.9236	31.7378	0.9952	28.369	0.9822	32.6598	0.9889

CR: Coats–Redfern; Ea: activation energy.

HOMO and LUMO analysis

The optimized structure of random copolymer is demonstrated in Figure 3 with proper atomic labeling. The molecular orbitals are calculated with the optimized geometry. HOMO and LUMO are the main orbitals playing a part in chemical reactions and very useful for chemists and physicists. These orbitals indicate the path the molecule interacts with other species and are very important parameters for quantum chemistry that helps to illustrate the kinetic stability and chemical reactivity of the molecules.^35,36 The energy of LUMO relevant to electron affinity and the related orbital acts as an electron acceptor, while the energy of HOMO directly relevant to the ionization potential and the related orbital acts as an electron donor.³⁷ The 3-D drawing of MOs (HOMO and LUMO) mapped with molecular orbitals for both two and three units is demonstrated in Figure 4. As it can be seen in Figure 4 for both, the positive phase is bluish green and the negative one is greenish. Moreover, it can be seen from Figure 4, the energy gap of HOMO–LUMO decreases from two units to three units and is 4.5483 eV and 4.5315 eV, respectively. The energy gap between HOMO and LUMO, dipole moment, electronegativity, softness, chemical hardness, electrophilicity index, electron affinity, and ionization potential has been calculated with B3LYP/6–311 + G(d, p) level in the gas phase. The obtained data are listed in Table 4. The quantum chemical descriptors have been used in the DFT theory of chemical reactivity for defining the reactive sites of the molecular systems and are connected with the electronic structure and the mechanism which play a part in the covalent bond formation as a result of reaction between the electrophiles and the nucleophiles.³⁸ Energies of LUMO and HOMO have been used to calculate global chemical reactivity descriptors, such as electronegativity, chemical hardness, chemical potential, global softness, and global electrophilicity index.^39
–41

Figure 3.

Optimized molecular structure of the coumarin-based random copolymer assuming x and y = 1. The red, gray, white, and green spheres correspond to oxygen, carbon, hydrogen, and chlorine atoms, respectively.

Figure 4.

Optimized HOMO and LUMO orbitals of coumarin-based random copolymer (for two and three units, respectively).

Table 4.

Calculated some parameters of coumarin-based random copolymer at DFT/B3LYP/6–311 + G(d, p).

	Values (eV)
Parameter	For two units	For three units
SCF energy	–44860.7653	–54273.2245
Dipole moment (µ)	6.7847 Debye	7.5611 Debye
E _HOMO	–6.9282	–6.8431
E _LUMO	–2.3799	–2.3116
Energy gap (ΔE = E _LUMO − E _HOMO)	4.5483	4.5315
Chemical potential (μ ₀)	–4.6540	–4.5773
Electronegativity(χ)	4.6540	4.5773
Electron affinity (A)	2.3799	2.3116
Ionization energy (I)	6.9282	6.8431
Hardness(η)	2.2741	2.2657
Global electrophilicity (ω)	4.7622	4.6235
Global Softness (ζ)	0.4397	0.4413

DFT: density functional theory.

Using Koopmans’ theorem, these chemical descriptors are calculated as follows:

Chemical hardness (η) can be expressed as:

η = \frac{E_{LUMO} - E_{HOMO}}{2}

Softness (ς) can be expressed as:

ς = \frac{1}{η}

Chemical potential (µ) can be expressed as:

µ = \frac{E_{LUMO} + E_{HOMO}}{2}

Electronegativity (χ) can be expressed as:

χ = - \frac{(E_{LUMO} + E_{HOMO})}{2}

Global electrophilicity (ω) can be expressed as:

ω = \frac{μ^{2}}{2 η}

The larger energy gap between LUMO and HOMO for the two units (E _LUMO − E _HOMO = 4.5483) as compared to three units (E _LUMO − E _HOMO = 4.5315) suggests that three units is less reactive than two units. Further, from Table 4, it can be seen that higher values of the global electrophilicity index for the two units ( $ω = 4.7622$ ) suggest that it is more electrophilic than three units (ω = 4.6235). Besides, from Table 4, it can be seen that higher values of softness for three units (ζ = 0.4413) suggest that it is softer than two units (ζ = 0.4397).

Thermodynamic properties

Based on vibration analysis, the statistical thermodynamic functions such as entropy (S), specific heat capacity (C), and enthalpy (H) and some thermodynamic parameters such as rotational constants, the zero–point vibrational energies, and rotational temperatures, which obtained theoretical harmonic frequencies of random copolymer (for two and three units) were calculated by B3LYP/6–311 + G(d, p) and the results at 298.15 K in ground state were presented in Tables 5 and 6. According to Table 6, because of the molecular vibrational intensities increase with temperature, the thermodynamic functions are increasing with temperature ranging from 100 K to 500 K. The correlation equations between heat capacity, entropy changes, enthalpy, and temperatures are fitted by quadratic formulas. The relevant correlation graphs for two units of random copolymer are as demonstrated in Figure 5 and the corresponding fitting equations are as follows:

Figure 5.

Correlation graphic of thermodynamic parameters and temperature for coumarin-based random copolymer (for two units).

Table 5.

Calculated thermodynamic parameters of coumarin-based random copolymer in gas phase at 298.15 K.

	Values
Parameter	For two units	For three units
Heat capacity (cal mol⁻¹·K)
Total	96.697	127.181
Translational	2.981	2.981
Rotational	2.981	2.981
Vibrational	90.735	121.220
Energy (thermal; kcal mol⁻¹)
Total	249.079	334.459
Translational	0.889	0.889
Rotational	0.889	0.889
Vibrational	247.301	332.682
Entropy (cal mol⁻¹·K)
Total	184.102	220.939
Translational	43.698	44.395
Rotational	36.545	37.628
Vibrational	103.859	138.917
Zero-point vibrational energy (kcal mol⁻¹)	232.66440	312.86780
Rotational constants (GHz)
X	0.52445	0.20247
Y	0.05743	0.05453
Z	0.05341	0.04900
Rotational temperatures (K)
	0.02517	0.00972
	0.00276	0.00262
	0.00256	0.00235

Table 6.

Calculated thermodynamic parameters of coumarin-based random copolymer in gas phase at different temperatures for two and three units, respectively.

Temperature(K)	H (kcal mol⁻¹)		C (cal mol⁻¹·K)		S (cal mol⁻¹·K)
100	235.396	316.307	42.513	56.356	110.637	124.435
200	241.278	324.046	70.399	93.170	150.306	176.619
300	249.854	335.291	97.191	127.823	184.713	221.743
400	261.075	349.967	122.812	161.212	216.817	263.732
500	274.695	367.783	144.949	190.285	247.117	303.366

Δ H = 232.0016 + 0.02073 T + 1.29436 \times 10^{- 4} T^{2} (R^{2} = 0.9999)

C = 12.0528 + 0.31158 T - 9.04929 \times 10^{- 5} T^{2} (R^{2} = 0.9998)

S = 69.5562 + 0.42965 T - 1.50293 \times 10^{- 4} T^{2} (R^{2} = 0.9997)

The relevant correlation graphs for three units of random copolymer are as demonstrated in Figure 6 and the corresponding fitting equations are as follows:

Figure 6.

Correlation graphic of thermodynamic parameters and temperature for coumarin-based random copolymer (for three units).

Δ H = 311.8094 + 0.02779 T + 1.68464 \times 10^{- 4} T^{2} (R^{2} = 0.9999)

C = 16.6262 + 0.40767 T - 1.19614 \times 10^{- 4} T^{2} (R^{2} = 0.9998)

S = 70.369 + 0.56598 T - 2.01679 \times 10^{- 4} T^{2} (R^{2} = 0.9997)

The related fitting factors (R ²) of entropy, heat capacity, and enthalpy for both two and three units (random copolymer) are 0.9998, 0.9997, and 0.9999, respectively. It is observed from Table 6 and the related fitting equations that the value of these thermodynamic properties is increased with both temperature and when one passes from two to three units. All the thermodynamic data provide useful information for further research on the coumarin-based random copolymer. These parameters can be utilized to predict reaction mechanism and compute the other thermodynamic energies related to thermodynamic functions.

Molecular electrostatic potential surfaces analysis

The molecular electrostatic potential (MEP) is a very important feature and used to guess molecular reactive regions and widely used as a reactivity surface exhibiting most possible regions for the electrophilic attack. A 3-D plot of MEP and electrostatic potential of random copolymer is demonstrated in Figure 7. The potential has been especially helpful as an indicator of the sites or regions of a molecule. Electrostatic potential is connected with electronegativity, dipole moment, partial charges, and region of chemical reactivity of the molecule. Such surfaces indicate the size, shape, region, and charge density of chemical reactivity of the molecules.

Figure 7.

Electrostatic potential surfaces of coumarin-based random copolymer (for three units).

The different colors on the map result from different values of the electrostatic potential. The electrostatic potential increases in the order red (electron rich region and partly negative charge) < orange (less electron rich region) < yellow (slightly electron rich region) < green (neutral) < blue (electron deficient and partly positive charge). The maximum positive regions are nucleophilic regions and seen as blue color, and the maximum negative regions are electrophilic regions and seen as red color. Therefore, molecular electrostatic potential (Figure 7, below) clearly indicates the presence of high negative charge on the oxygen atoms. Furthermore, we can say that the negative electrostatic potential (ESP) is seen as a reddish or a yellowy blob and is located more over the oxygen atoms (Figure 7, top). The contour maps such as positive, negative, and both charges of random copolymer are demonstrated in Figure 8. As shown in Figure 8, the contour map supports the negative and positive potential regions of the random copolymer in accordance with the molecular electrostatic potential surfaces. MEP, V(r) at a given point r(x, y, z) in the vicinity of a molecule, is described as the interaction energy between a positive test charge (a proton) located at r and the electrical charge generated from the molecule nuclei and electrons. For the system worked, the V(r) values are computed by the following equation⁴²:

Figure 8.

Molecular electrostatic potential contour surface of coumarin-based random copolymer (for three units).

V (r) = \sum Z_{A} / | R_{A} - r | - \int ρ (r') / | r' - r | d^{3} r

where $ρ (r')$ and $r'$ are the electronic density functions of the molecule and the dummy integration factor, respectively. Z_A is defined as the charge of nucleus A located at R_A .

Conclusions

DFT calculations were used for the two and three units which can take part as repeating units in the random copolymer. Firstly, the molecular structure of random copolymer was determined theoretically using the DFT calculations. Molecular electrostatic potential, electrostatic potential, and contour surfaces, which help in the determination of electrophilic and nucleophilic sites in the molecule as well as possible reaction path, are determined. The electronic and thermodynamic properties for two and three units of random copolymer were calculated. These quantum chemical calculations may help to understand the activity and properties of the coumarin-based random copolymer. Secondly, the thermal decomposition kinetic analyses were performed using the CR, Tang, and FWO methods. The thermal decomposition mechanisms for random copolymer obeyed a deceleration R ₃ type, which is a solid-state process based on phase boundary model (contracting volume).

Footnotes

Acknowledgements

The author is grateful to Prof. Dr. Kadir Demirelli and Bitlis Eren University for supporting the Gaussian software of this study.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Coumarin-based random copolymer

Abstract

Keywords

Introduction

Experimental and theoretical details

Thermogravimetric analysis

FWO method

Tang method

CR method

Results and discussion

Kinetic analysis

HOMO and LUMO analysis

Thermodynamic properties

Molecular electrostatic potential surfaces analysis

Conclusions

Footnotes

Acknowledgements

Declaration of Conflicting Interests

Funding

References