Introduction

Poly(ε-caprolactone), PCL, is an attractive class of polyester due to its biocompatibility and biodegradability. PCL is one of the biodegradable polymers used in biomedical and pharmaceutical industries as a resorbable material and drug delivery systems [1]. PCL can be normally synthesized by ring-opening polymerization (ROP), in which high molecular mass can be obtained by a conventional coordination-insertion ROP of ε-caprolactone (ε-CL) monomer with metal alkoxide initiators or metal carboxylate [2, 3]. A large variety of metal alkoxide initiators with different oxidation states have been reported for ROP of cyclic ester monomers such as Al [4], Zn [5], Mg [6], Ti [7, 8], Sn [9–14]. Among these, organotin initiators have been widely used in industrial applications and academic research, especially for tin(IV) alkoxides. Tin(IV) alkoxides such as tributyltin alkoxides (nBu3SnOR), dibutyltin dialkoxides (nBu2Sn(OR)2) [9], and cyclictin(IV) alkoxides [10], which contain a reactive Sn–O bond, can effectively initiate the coordination-insertion ROP of ε-CL. Kricheldorf and co-workers [11] reported the efficiency of tributyltin derivatives such as tributyltin methoxide (nBu3SnOMe), tributyltin chloride (nBu3SnCl), tributyltin acetate (nBu3SnOAc), and tributyltin thioacetate (nBu3SnSAc) in the bulk polymerization of ε-CL. These nBu3SnOR are an attractive class of initiators because they can be easily synthesized by the nucleophilic substitution of tributyltin chloride. Moreover, they are more stable to oxygen and soluble in common organic solvents [9, 11]. Also, the syndiotactic of desirable polyester can be effectively controlled using nBu3SnOMe [15, 16]. However, there are a few reports on the kinetics of ROP of cyclic ester monomers initiated by nBu3SnOR [9, 11], therefore their kinetic information is needed for more understanding on their catalytic behavior. In previous reports [9, 11], only 1H-NMR as a time consuming technique was used to determine kinetic parameters such as  % conversion (% α), rate constant of polymerization (k p), and half-life of polymerization (t 1/2). But an activation energy (E a) has not been reported before, due to the complicated processes of E a determination from the 1H-NMR technique. Thus, in this present work, an effective differential scanning calorimetry (DSC) technique is introduced to determine both kinetic and thermodynamic parameters of ROP of ε-CL.

Recently, DSC has been used to study the kinetics of ROP of cyclic ester monomers [17–20]. DSC provides a continuous history of the heat evolved during the polymerization which can be analyzed kinetically, either by the isothermal or non-isothermal methods. These two methods can be used to determine various useful kinetic and thermodynamic parameters. Isoconversional methods have been applied to non-isothermal kinetic data in order to investigate the dependence of E a on monomer conversion (α) [7, 21–23]. To our best knowledge, the kinetics and thermodynamics information of ROP of ε-CL initiated by the synthesized nBu3SnOnBu using DSC has not been reported before.

In this work, we are the first to report both the isothermal and non-isothermal DSC methods on investigation of the bulk ROP of ε-CL initiated by various concentrations of the synthesized nBu3SnOnBu. The kinetic parameters such as apparent rate constants (k app), degree of aggregation (m), and E a were determined. The dependence of E a with monomer conversion as polymerization proceeds was observed by the Friedman [24], Kissinger–Akahira–Sunose (KAS) [25] and Flynn–Wall–Ozawa (FWO) [26–28] isoconversional methods. In addition, the thermodynamic parameters such as activation enthalpy (ΔH ≠) and entropy (ΔS ≠ ) were determined by isothermal DSC technique.

Experimental

Materials

Commercial ε-CL monomer (Acros Organics) was purified by fractional distillation under reduced pressure over calcium hydride. Toluene (Carlo Erba) and n-butanol (Sigma-Aldrich) were purified by distillation over sodium metal. Tributyltin chloride (Acros Organics) was used as received without purification.

Synthesis of tributyltin n-butoxide

Tributyltin n-butoxide (nBu3SnOnBu) was synthesized by the nucleophilic substitution of tributyltin chloride (nBu3SnCl) by sodium n-butoxide (NaOnBu) in dry toluene. The reaction mixture was heated and then refluxed for 6 h as described in literature [29]. The obtained nBu3SnOnBu was purified by vacuum distillation and its identification was confirmed by proton nuclear magnetic resonance spectroscopy (1H-NMR) on a Bruker DPX-400 NMR spectrometer operating at 400 MHz in deuterated chloroform (CDCl3).

DSC measurements

Non-isothermal method

Kinetic studies of the ROP of ε-CL initiated by 1.0, 1.5, and 2.0 mol% of synthesized nBu3SnOnBu were carried out by means of DSC (Perkin–Elmer DSC-7). For each sample, about 6–10 mg was accurately weighed into an aluminum pan and then hermetically sealed. The samples were heated over temperature range of 20–300 °C at heating rates of 5, 10, 15, and 20 °C min−1 under a nitrogen atmosphere in order to observe the amount of heat liberated from the polymerization reaction. The E a was determined by the methods of Kissinger and Ozawa. The dependence of E a with monomer conversion was analyzed by the Friedman, KAS, and FWO isoconversional methods.

Isothermal method

For isothermal DSC polymerization, the sample was prepared similar to the non-isothermal method. The samples were held for 4 h to ensure the completion of polymerization at selected temperatures, which predicted from non-isothermal experiments (temperature prior to exotherm start). For thermodynamic studies, the k app determined from the isothermal method was used to estimate the thermodynamic parameters for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu. The m value was determined from isothermal DSC polymerization of ε-CL initiated by 0.5–2.0 mol% of nBu3SnOnBu at 165 °C.

Bulk polymerization of ε-caprolactone

ε-CL monomer with 0.125, 0.250, 0.500, and 1.000 mol% of nBu3SnOnBu initiator were weighed into dry glass vials and capped in a controlled atmosphere glove box under dry nitrogen. The reaction vials were immersed in a pre-heated silicone oil bath at a constant temperature of 120 °C for 72 h. At the end of polymerization, the vials were immersed into the ice bath to stop the polymerization reaction. Then, the obtained crude PCLs were dissolved in chloroform and re-precipitated in cold methanol before drying in a vacuum oven at 45 °C until the constant mass. The molecular mass and polydispersity index (PDI) of the synthesized PCLs were determined by Water e2695 gel permeation chromatography (GPC) at 35 °C with refractive index and viscosity detectors. Tetrahydrofuran (THF) was used as an eluent with flow rate of 1.0 mL min−1.

Poly(ε-caprolactone)s characterization

The obtained crude PCLs were characterized using a Bruker DPX-400 NMR spectrometer. Spectra were recorded using 5 mm o.d. tubes, deuterated chloroform as solvent and tetramethylsilane (TMS) as the internal standard at room temperature. The 1H-NMR spectra were recorded at a resonance frequency with 32 scans, a 3.5 s acquisition time and a 6 µs pulse width.

Non-isothermal and isothermal DSC data analysis

ROP of cyclic ester monomers is exothermic due to the covalent bond formation of monomers. The heat released from polymerization can be observed by exothermic curve of DSC. The kinetic of ROP can be investigated by both non-isothermal and isothermal methods. For non-isothermal DSC experiment, ROP occurred under different constant heating rates. The onset temperature of polymerization increases with increasing heating rate resulting in a shift of the exothermic peak to a higher temperature range. The fraction of monomer conversion (α) can be determined from the heat released at any time (ΔH t) divided by total heat of polymerization (ΔH total). The E a can be determined by the methods of Kissinger and Ozawa [30–35]. The Kissinger method is based on the relationship between the heating rate (β) and the temperature at maximum rate of polymerization (T m) which is shown in Eq. (1).

$$ \frac{{{\text{d[ln(}}\beta /T_{\text{{m}}}^{2} ) ]}}{{{\text{d(}}1 /T_{\text{{m}}} )}} = - \frac{{E_{\text{{a}}} }}{R} $$
(1)

Therefore, the value of E a can be obtained from the slope of a plot of ln(β/T 2m ) against 1/T m, where R is the gas constant. For Ozawa method, Doyle’s approximation of log p(x) ≅ −2.315 − 0.457E a/RT for x = E a/RT > 20 is used and the relationship of log β and 1/T m yields the following Eq. (2).

$$ \log \beta = {\text{constant}} - 0.457\frac{{{{E}}_{\text{a}} }}{{{\text{RT}}_{\text{{m}}} }} $$
(2)

Nowadays, isoconversional methods have been applied to non-isothermal kinetics data to investigate the dependence of E a with α. These methods allow multiple step processes to be detected via the dependence of E a with α [21].

Friedman [24] showed the relationship of the natural logarithm of reaction rate, \( \ln ({\text{d}}\alpha /{\text{d}}t) \), as a function of the reciprocal temperature, as shown in Eq. (3). This equation enables the E a to be determined for each fraction of α, where A is the frequency factor and f(α) is the function of monomer conversion.

$$ \ln \left( {\frac{{{\text{d}}\alpha }}{{{\text{d}}t}}} \right) = \ln \left( {Af\left( \alpha \right)} \right) - \frac{{E_{\text{{a}}} }}{RT} $$
(3)

This equation also implies that the reaction rate is only a function of temperature at a constant value of α. Therefore, E a can be simply obtained from the slope of the plot of \( \ln ({\text{d}}\alpha /{\text{d}}t) \) against 1/T.

KAS method [25] is based on a linear relationship between ln(β/T 2) and the inverse of the temperature (1/T).

$$ \ln \left( {\frac{\beta }{{T^{ 2} }}} \right) = \ln \left( {\frac{ - RAf'(\alpha )}{{E_{\text{{a}}} }}} \right) - \frac{{E_{\text{{a}}} }}{RT} $$
(4)

From Eq. (4), E a can be determined from the slope of the plot of ln(β/T 2) against 1/T. This method does not require knowledge of f’(α) and it only assumes that the process follows the same mechanism for a given conversion regardless of the polymerization temperature.

FWO method [26–28] using Doyle’s approximation of the temperature integral is possible to obtain a complete evaluation of E a throughout the whole conversion as shown in Eqs. (5) and (6).

$$ \ln \beta = \ln \left( {\frac{{AE_{\text{{a}}} }}{R}} \right) - \ln g(\alpha ) - 5.331 - 1.052\left( {\frac{{E_{\text{{a}}} }}{RT}} \right) $$
(5)
$$ g(\alpha ) = \int\limits_{0}^{\alpha } {\frac{{{\text{d}}\alpha }}{f(\alpha )}} $$
(6)

where g(α) is the integral conversion function. For a constant α, the E a can be determined from the slope of the plot of ln β versus 1/T.

To support the kinetic results from non-isothermal method, the isothermal method is used to determine the kinetic parameters for ROP of cyclic ester monomer as previously reported [17, 18]. The polymerization of lactones and lactides using metal alkoxides initiator is a first-order reaction with respect to monomer concentration as described in previous works [35–38]. So, the first-order reaction model was employed to determine the k app as shown in Eq. (7) [17]. E a can be derived from the Arrhenius equation (when k app = A exp(−E a /RT)) in Eq. (8).

$$ - \ln (1{ - }\alpha ) {\text{ = k}}_{\text{app}} t $$
(7)
$$ - \ln (1{ - }\alpha ) {\text{ = A}}_{ \exp } \left( { - \frac{{E_{{\text{a}}} }}{RT}} \right)t $$
(8)

where α is the fraction of monomer conversion, A is the frequency factor, R is the gas constant, and t is the polymerization time.

Results and discussion

Synthesis and characterization of tributyltin n-butoxide initiator

The nBu3SnOnBu initiator can be synthesized by the nucleophilic substitution of nBu3SnCl with NaOnBu in dry toluene as shown in the reaction below.

$$ n{\text{Bu}}_{ 3} {\text{SnCl}}({\text{s}}) + {\text{NaO}}n{\text{Bu}}(1) \to n{\text{Bu}}_{ 3} {\text{SnO}}n{\text{Bu}}(1) + {\text{NaCl}}({\text{s}}) $$

The NaCl was precipitated out from the solution and the crude nBu3SnOnBu was obtained and purified by vacuum distillation resulting in 76 % yield. The purified nBu3SnOnBu is characterized by 1H-NMR as shown in Fig. 1.

Fig. 1
figure 1

1H-NMR spectrum of the synthesized nBu3SnOnBu initiator in CDCl3

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From Fig. 1 the proton chemical shift of 0.90 ppm (a, h) is the triplet of methyl chain end (–CH3), 0.95–1.60 ppm (b, c, d, f, g) is the multiplet of methylene proton (–CH2–) of four n-butyl groups and 3.65–3.70 ppm (e, e′) is the triplet of methylene proton connected to oxygen (–O–CH2–). The chemical shift in the range from 3.60 to 3.70 ppm shows two complex peaks which may be caused by the aggregation of nBu3SnOnBu. However, in the polymerization process, the aggregation of nBu3SnOnBu should be decreased by the solubilization of monomer which is described later in the determination of the degree of aggregation of nBu3SnOnBu section.

Kinetic analysis for ROP of ε-CL initiated by tributyltin n-butoxide initiator

The polymerization measurement under dynamic condition provides a good alternative means of obtaining useful kinetic information over different temperature ranges. For non-isothermal DSC polymerization, each sample was heated from 20 to 300 °C at heating rates of 5, 10, 15, and 20 °C min−1 and the obtained DSC curves are shown in Fig. 2. The average heats of ROP of ε-CL using 1.0, 1.5, and 2.0 mol% nBu3SnOnBu initiator are 172.3, 176.1, 165.7 J g−1, respectively.

Fig. 2
figure 2

Non-isothermal DSC curves for ROP of ε-CL at heating rates of 5, 10, 15, and 20 °C min−1 initiated by 1.0 mol% of nBu3SnOnBu

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From Fig. 2, under dynamic condition the temperatures at which the reaction starts and completes increase with increasing of heating rate as does the size of exothermic peak. As the initiator concentration increases, the polymerization exotherms shift to lower temperature range at all heating rates indicating the higher rate of polymerization. Moreover, each DSC curve shows broad exotherm which may be caused by the slow propagation (r p) rate because this initiator contains only one active site (Sn–O) with three n-butyl groups which reduce the nucleophilic strength of initiator and cause the steric effect in the coordination of monomer. Although, the size of exothermic peak and the reaction rate increases with increasing heating rate, the time to complete polymerization decreases. At low heating rates, the calorimetric signal is small, but the polymerization time is long. The opposite result occurs at higher heating rates when the liberation of heat accompanying polymerization reduces the time to complete reaction.

These are in good agreement with our previous work [7], which are clearly supported by the plots of monomer conversion as a function of polymerization temperature as shown in Fig. 3. The results showed that the polymerization completed faster at higher heating rate for all initiator concentrations. At the constant heating rate of 5 °C min−1 as shown in Fig. 3(b), the polymerization was found to complete faster at higher nBu3SnOnBu concentrations.

Fig. 3
figure 3

Plots of monomer conversion as a function of polymerization temperature at different heating rates for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu (a) and plots of conversion as a function of polymerization temperature of ROP of ε-CL initiated by 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu at heating rate of 5 °C min−1 (b)

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To support the effect of heating rate and initiator concentration, plots of polymerization rate as a function of polymerization temperature are shown in Fig. 4.

Fig. 4
figure 4

Plots of reaction rate as a function of polymerization temperature at different heating rates for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu (a) and plots of reaction rate as a function of polymerization temperature of ROP of ε-CL initiated by 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu at heating rate of 5 °C min−1 (b)

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The results in Fig. 4(a) show that the rate of polymerization increased with increasing of the heating rate because the polymerization shifts to higher temperature range, related to the higher energy obtained in system. The dependency of the polymerization rate with the heating rate shown in Fig. 4(a) is similar to the polymerization of ε-CL with 1.5 and 2.0 mol% of nBu3SnOnBu. In Fig. 4(b), as a concentration of nBu3SnOnBu increased at heating rate of 5 °C min−1, the reaction rate was found to increase due to the more active site (Sn–O) available to initiate ROP of ε-CL.

The values of E a and ΔH total are determined by the plots of Kissinger (Eq. (1)) and Ozawa (Eq. (2)) methods as shown in Fig. 5. The obtained values of E a, summarized in Table 1, were used to compare and support the influence of initiator concentration on polymerization rate.

Fig. 5
figure 5

Plots of ln(β/T 2m ) (a) and log (β) (b) against 1,000/Tm based on the methods of Kissinger and Ozawa for activation energy determination of ROP of ε-CL initiated by nBu3SnOnBu

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Table 1 Kinetic parameters for ROP of ε-CL initiated by 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu determined for non-isothermal DSC
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From Table 1, T m increased with heating rate but decreased when the concentration of the initiator increased. In addition, the values of E a determined from Kissinger method are lower than that of Ozawa method at all initiator concentrations. This is not clear for the difference in E a values, but the small variation in E a compared in each initiator concentration is probably caused by the difference in mathematic approximation which is used in each method. However, the obtained E a from each method gave the same trend on the decrease in E a as the increasing initiator concentration. So, the increase in concentration of nBu3SnOnBu has a profound effect on the ROP of ε-CL by reducing the energy required to initiate the polymerization. Furthermore, in the non-isothermal condition, the values of collision frequency (A) of monomer with reactive center (Sn–O) increased with increasing of initiator concentration. This finding is similar to the non-isothermal DSC polymerization of glycolide with zinc octoate (Zn(Oct)2) reported by Mazzaro and co-workers [18].

To support the kinetic results from non-isothermal DSC data, the isothermal method was used to investigate the initiative behavior of nBu3SnOnBu in ROP of ε-CL. The isothermal DSC curves for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu are shown in Fig. 6.

Fig. 6
figure 6

Isothermal DSC curves for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu at 155, 160, 165, and 170 °C

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The same results as non-isothermal DSC method were observed with broad DSC curves showing the slow propagation step. It is worth noting that the polymerization occurred faster at higher temperature; however, polymerization still took longer time to complete due to the slow propagation step as described earlier. Moreover, from isothermal DSC curves shown in Fig. 6, the relationships between the monomer conversion and the polymerization time were plotted and illustrated in Fig. 7. The results from Fig. 7(a) showed that the monomer conversion is generally close to 1 (complete polymerization), faster at higher temperature due to higher energy obtained in reaction mixture that increased the rate of polymerization. The obtained results from Fig. 7(a) are similar to the polymerization of ε-CL with 1.5 and 2.0 mol% of nBu3SnOnBu. As the concentration of nBu3SnOnBu increases at 165 °C (Fig. 7(b)), the complete conversion is faster which is similar to the results obtained from non-isothermal method.

Fig. 7
figure 7

Plots of monomer conversion as a function of polymerization time for ROP of ε-CL at different temperatures initiated by 1.0 mol% of nBu3SnOnBu (a) and plots of monomer conversion as a function of polymerization time for ROP of ε-CL initiated by 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu at 165 °C (b)

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From the plots of −ln(1-α) against polymerization time (Eq. (7)) shown in Fig. 8, the k app was determined from the slope of these plots. This was considered as steady-state of polymerization reaction (0.2 < α < 0.6) and diffusion control would not affect the rate of propagation. The first-order rate plots have a good linearity with R 2 > 0.99. From the obtained k app, the E a can be calculated from Arrhenius plots of −ln(k app) versus 1,000/T as shown in Fig. 9. The kinetic parameters determined from isothermal DSC are summarized in Table 2.

Fig. 8
figure 8

First-order rate plots for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu: a 155, b 160, c 165, and d 170 °C

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Fig. 9
figure 9

Arrhenius plots of −ln(k app) as a function of reciprocal temperature (1,000/T) for ROP of ε-CL initiated by 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu

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Table 2 Kinetic parameters for ROP of ε-CL initiated by 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu determined from isothermal DSC
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From Table 2, the values of k app increased with increasing of temperature and initiator concentration because at higher temperature the initiators and monomers collide each other more frequently with accumulating energy surpassing the E a resulting in higher k app. At high initiator concentrations, more active sites for polymerization increase the rate of polymerization and reduce the energy required for driving the polymerization to occur. The values of A decreased with increasing of initiator concentration which are similar to the isothermal DSC polymerization of ε-CL initiated by Ti(IV) alkoxide reported by Li et al. [17]. The decreasing of E a as a function of nBu3SnOnBu concentration from isothermal DSC has the same trend as the results from non-isothermal DSC. The determined E a values from isothermal method are close to those of non-isothermal method suggesting that the DSC method is convenient and reliable to obtain the kinetic parameters especially E a values of the ROP of ε-CL.

Bulk ring-opening polymerization and mechanistic aspect

The ROP of ε-CL initiated by nBu3SnOnBu occurs via the conventional coordination-insertion mechanism as shown in Scheme 1. The coordination-insertion mechanism comprises two steps. The first step is the coordination of monomer and initiator molecule by the interaction of carbonyl oxygen of ε-CL and the second step is the acyl-oxygen cleavage of ε-CL by the attack of −OnC4H9 group, then the new ε-CL will insert into the propagating species (nBu3SnOnBu-opened ε-CL). As the propagation step proceeds, the PCL will be formed.

Scheme 1
scheme 1

Coordination insertion mechanism for ROP of ε-CL initiated by nBu3SnOnBu

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This well-known mechanism was confirmed by the 1H-NMR spectrum of crude PCL synthesized from isothermal DSC polymerization of ε-CL at 170 °C as shown in Fig. 10. As shown, the methyl proton of four n-butyl groups was found at 0.90 ppm (a, s) and the small peak at 3.65 ppm (e) was assigned as –Sn–O–CH2– of living polymer chain [10, 39]. The spectrum reveals that the polymerization is nearly complete with 98 % of monomer conversion which is determined from the intensity of PCL peak divided by the summation of intensity of PCL and ε-CL peaks [39]. However, there is still a small amount of monomers left in the crude PCL indicating by the monomer peaks at 2.65 (a′) and 4.22 (e′) ppm which are attributed to –CH2–CO– and –CH2–O– of the ε-CL monomer ring, respectively. So, this observation can be used to confirm that ROP of ε-CL initiated by nBu3SnOnBu proceeds via the coordination-insertion mechanism.

Fig. 10
figure 10

1H-NMR spectrum of crude PCL in CDCl3 synthesized by isothermal DSC polymerization of ε-CL initiated by 1.0 mol% of nBu3SnOnBu at 170 °C

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From the bulk ROP of ε-CL at 120 °C, the molecular mass of PCL increased with increasing of monomer to initiator concentration ([M]/[I]) ratio and it was successfully controlled by adjusting the [M]/[I] ratio as listed in Table 3. In addition, this synthesis condition gave the  % yield of PCL higher than 85 %. At high initiator concentration or low [M]/[I] ratio, the nBu3SnOnBu initiated polymerization faster resulting in the low molecular mass PCL as shown in Table 3. Moreover, the synthesized PCL show PDI values close to 2 due to the occurrence of transesterification reaction.

Table 3 Number average molecular mass (\( \bar{M}_{\text{n}} \)), mass average molecular mass (\( \bar{M}_{\text{w}} \)), polydispersity index (PDI) and  %yields of PCLs from bulk polymerization of ε-CL at 120 °C for 72 h using different nBu3SnOnBu concentrations
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Determination of the thermodynamic parameters

The thermodynamic parameters such as enthalpy (ΔH ≠) and entropy of activation (ΔS ≠) were used to describe the order of transition state (TS) of activated complex of ε-CL initiated by nBu3SnOnBu as similar to the estimation of the thermodynamic parameters for ROP of l-lactide with tin(IV) alkoxides reported by Chrisholm and co-workers [40]. The thermodynamic parameters of transition state can be simply determined by the Eyring equation [41]. In this work, the Eyring equation was modified using the k app values obtained from isothermal DSC (see Table 2) and the new expression is shown in Eq. (9).

$$ \ln \left( {\frac{{k_{\rm app} }}{T}} \right) = \ln \left( {\frac{{k_{{\text{B}}} }}{h}} \right) + \frac{{\Delta S^{ \ne } }}{R} + \ln \left[ I \right]{}_{0} - \frac{{\Delta H^{ \ne } }}{RT} $$
(9)

where k app is the apparent rate constant of polymerization, k B is the Boltzmann constant, h is the Plank’s constant, ΔH ≠is the activation enthalpy, ΔS ≠is the activation entropy, and [I]0 is the initial concentration of nBu3SnOnBu. From the Eq. (9), the values of ΔH ≠ and ΔS ≠can be calculated from the slope and extrapolated intercept of the linear plot of −ln(k app/T) versus 1,000/T (as shown in Fig. 11), respectively.

Fig. 11
figure 11

Plot of −ln(k app/T) against 1,000/T for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu

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From Fig. 11, the plot has a good linearity with R 2 = 0.946. The obtained values of ΔH ≠ and ΔS ≠are 70.5 kJ mol−1 and −100.3 J mol−1 K−1, respectively. The result shows that DSC is also a convenient method to estimate the thermodynamic parameters for ROP of ε-CL. The negative value of ΔS ≠indicates that the transition state (TS) has a restricted (highly ordered) orientation, resulting in the ensured formation of PCL.

Determination of the degree of aggregation (m) of nBu3SnOnBu

Metal alkoxide initiators generally exist as molecular aggregates in equilibrium with monomeric species. They normally have significantly different reactivities depending on the degree of aggregation (m). The m value of metal alkoxides can be determined from the method of Penczek and co-workers [42, 43] from a kinetic plot of ln(k app) versus ln[I]0 as shown in Eq. (10).

$$ \ln (k_{\rm app} ) = 1/m\,\ln [I]_{0} + C $$
(10)

where k app is the apparent rate constant, [I]0 is the initial concentration of initiator, m is the degree of initiator aggregation, and C is a constant. The plot of ln(k app) versus ln[nBu3SnOnBu]0 is shown in Fig. 12, and the m value is calculated from the slope of this plot. In addition, the order of the reaction (n) with respect to initiator concentration can also be determined by 1/m. The kinetic parameters that used to determine the values of m and n are summarized in Table 4.

Fig. 12
figure 12

Plot of ln(k app) against ln[nBu3SnOnBu]0 for the ROP of ε-CL initiated by 0.5, 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu at 165 °C

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Table 4 The values of apparent rate constant (k app), degree of aggregation (m), and reaction order to initiator (n) for ROP of ε-CL initiated by 0.5, 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu at 165 °C
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In according to Fig. 12, the slope of the plot of ln(k app) versus ln[I]0 is 0.92 (= 1/m) which, therefore, gives a degree of aggregation (m) of 1.08. This m value (closed to 1) suggests that, within the initiator concentration ([nBu3SnOnBu]0 ≤  2.0 mol%) used in this study, the initiator is in non-aggregated form (high solubility in monomer).

Isoconversional kinetic analysis

The dependence of E a with α can also be investigated by isoconverisonal methods. In general, for a single step polymerization, the E a is constant for all α which is different from a multi-step polymerization [20, 21]. The differential method (Friedman) and the integrated methods ((KAS) and (FWO)) were used in this work to investigate the dependence of E a with α [44, 45]. These three methods were applied to non-isothermal kinetic data to determine E a from the ROP of ε-CL initiated by a selected initiator concentration (1.0 mol%). The results from kinetic plots of each method (Fig. 13) show that the Friedman method has the less uniform of the plots, caused by the uncertainty in the determination of polymerization rate (dα/dt). Moreover, this method has no mathematic approximation that makes the obtained values of E a higher than KAS and FWO methods [7, 46]. The dependence of E a with α shown in Fig. 14 indicates that the E a is not constant for the whole range of α which is different from Ti(IV) alkoxides initiating system as reported by Meelua et al. [7]. This might be caused by the difference in the rate of initiation (r i) and the rate of propagation (r p) of this initiating system. This finding agrees with the report of Kricheldorf and co-workers [11] that the r i is faster than r p in ROP of ε-CL initiated by nBu3SnOMe. The E a determined from Friedman, KAS, and FWO methods for ROP of ε-CL using 1.0 mol% nBu3SnOnBu as initiator are 73–92, 67–81, and 72–86 kJ mol−1, respectively. The values of E a determined from isoconversional method are close to those of isothermal and non-isothermal methods.

Fig. 13
figure 13

Plots of a −ln(dα/dt), b −ln(β/T 2) and c −ln(β) against 1000/T based on the methods of Friedman, KAS, and FWO, respectively for ROP of ε-CL initiated by 1.0 mol% of nBu3SnOnBu

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Fig. 14
figure 14

Plots of E a as a function of monomer conversion obtained from Friedman, KAS, and FWO isoconversional methods

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Conclusions

The DSC, proven as a fast and convenient technique with non-isothermal and isothermal methods, has been used to investigate the kinetics and thermodynamics of ROP of ε-CL initiated by the synthesized nBu3SnOnBu. For the kinetic parameters, the activation energies (E a) of the reaction at 1.0, 1.5, and 2.0 mol% of nBu3SnOnBu were found to be 78–83, 61–66, and 60–65 kJ mol−1 for non-isothermal method, and 74.2, 65.8, and 62.0 kJ mol−1 for isothermal method, respectively. The obtained E a values from both methods show the same trend as a function of initiator concentration, indicating that the DSC method is reliable to study the kinetics of ROP of ε-CL initiated by nBu3SnOnBu. Moreover, the non-aggregation of the synthesized nBu3SnOnBu initiator in monomers was confirmed by the isothermal method. For the thermodynamic parameters, the ΔH ≠and ΔS ≠of the reaction using the isothermal DSC were observed to be 70.5 kJ mol−1 and −100.3 J mol−1 K−1, respectively. The negative value of ΔS ≠ implies that the highly ordered transition state of nBu3SnOnBu and ε-CL is observed. The dependence of E a with monomer conversion was further investigated by isoconversional method and the determined E a is close to the non-isothermal and isothermal methods. Finally, the molecular mass of PCL was effectively controlled by the [M]/[I] ratio. Our present investigation for kinetic and thermodynamic parameters on the ROP of ε-CL with synthesized nBu3SnOnBu initiator using DSC technique both non-isothermal and isothermal method has proven to be rapid and effective, which could be practical to the most ROP of cyclic esters with other initiators.