Experimental Design (2⁴) to Improve the Reaction Conditions of Non-Segmented Poly(ester-urethanes) (PEUs) Derived from α,ω-Hydroxy Telechelic Poly(ε-caprolactone) (HOPCLOH)

Abstract

Aliphatic unsegmented polyurethanes (PUs) have garnered relatively limited attention in the literature, despite their valuable properties such as UV resistance and biocompatibility, making them suitable for biomedical applications. This study focuses on synthesizing poly(ester-urethanes) (PEUs) using 1,6-hexamethylene diisocyanate and the macrodiol α,ω-hydroxy telechelic poly(ε-caprolactone) (HOPCLOH). To optimize the synthesis, a statistical experimental design approach was employed, a methodology not commonly utilized in polymer science. The influence of reaction temperature, time, reagent concentrations, and solvent type on the resulting PEUs was investigated. Characterization techniques included FT-IR, ¹H NMR, differential scanning calorimetry (DSC), gel permeation chromatography (GPC), optical microscopy, and mechanical testing. The results demonstrated that all factors significantly impacted the number-average molecular weight (M_n) as determined by GPC. Furthermore, the statistical design revealed crucial interaction effects between factors, such as a dependence between reaction time and temperature. For example, a fixed reaction time of 1 h, with the temperature varying from 50 °C to 61 °C, did not significantly alter M_n. Better reaction conditions yielded high M_n (average: 162,000 g/mol), desirable mechanical properties (elongation at break > 1000%), low levels of unreacted HOPCLOH in the PEU films (OH/ESTER response = 0.0008), and reduced crystallinity (ΔH_m = 11 J/g) in the soft segment, as observed by DSC and optical microscopy. In contrast, suboptimal conditions resulted in low M_n, brittle materials with unmeasurable mechanical properties, high crystallinity, and significant amounts of residual HOPCLOH. The best experimental conditions were 61 °C, 0.176 molal, 8 h, and chloroform as the solvent (ε = 4.8).

1. Introduction

Polyurethanes (PUs) are extensively used across a wide range of industries due to their excellent mechanical properties, chemical resistance, and the versatility of their synthesis. Conventionally, PUs are synthesized from two key components: (1) a diisocyanate (O=C=N-R-N=C=O) and (2) a macrodiol (HOROH). The use of a catalyst is optional but can enhance the reaction efficiency [1]. PUs find applications in diverse fields, including adhesives [2,3], foams [4,5], coatings [6,7,8,9], and medical devices [10,11,12].

For biomedical applications, aliphatic diisocyanates such as 1,6-hexamethylene diisocyanate (HDI), isophorone diisocyanate (IPDI), and trans-1,4-cyclohexane diisocyanate (CHDI) are often preferred. This preference stems from the fact that PUs derived from aliphatic diisocyanates decompose into less toxic byproducts compared to those synthesized from aromatic diisocyanates [13,14,15,16]. Additionally, aliphatic PUs exhibit superior resistance to ultraviolet (UV) radiation compared to their aromatic counterparts. This improvement is attributed to the absence of UV-absorbing aromatic rings in their structure [17,18], making aliphatic PUs more suitable for applications requiring prolonged exposure to sunlight.

The second essential component for PU synthesis, the macrodiol, often comprises linear or branched aliphatic polyesters, specifically α,ω-hydroxy telechelic polyesters synthesized via ring-opening polymerization. Examples of such polyesters include poly(3-hydroxybutyrate) (P3HB) [19,20] and polylactic acid (PLA) [21,22].

Another notable example of a macrodiol utilized in PU synthesis is α,ω-hydroxy poly(ε-caprolactone) (HOPCLOH), a biodegradable oligoester [23,24]. The combination of HDI and macrodiols derived from aliphatic polyesters leads to the formation of aliphatic poly(ester-urethanes) (PEUs). The synthesis of non-segmented PEUs derived from HOPCLOH and aliphatic diisocyanates presents opportunities to investigate the relationship between their structure and properties [25,26]. Despite the significance of this class of aliphatic PEUs and their potential applications, research in this area remains limited. In contrast, a significant body of work has focused on PUs synthesized from aromatic diisocyanates [27,28,29,30,31].

A critical parameter in polymer synthesis and the resulting properties is the number-average molecular weight (M_n), as many physical characteristics of polymers are directly influenced by this value. Notably, for PEUs derived from PCL and HDI, M_n is often not reported in the literature. This omission is partly attributed to the cross-linked nature or poor solubility of some of these polymers [23,32,33,34,35,36].

Our group previously conducted a systematic study on the influence of the molar ratio of reactants, commonly referred to as the isocyanate index (HDI/HOPCLOH), on polymer properties [37]. The isocyanate index is a key determinant of M_n, cross-linking density, and chain branching in the resulting PEUs. Indices greater than 1 typically promote higher cross-linking densities or increased branching [36,38,39,40,41], while indices below 1 often result in incomplete polymerization. This incomplete reaction leads to low M_n values and little to no cross-linking or branching [42,43,44], ultimately producing PEUs with poor mechanical properties. Therefore, understanding and optimizing the diisocyanate index is essential for improving the performance of these materials.

Another critical factor influencing polymerization is reaction temperature. Proper control of the temperature can significantly impact the outcome of the process. For instance, some polyurethanes can be synthesized at ambient temperature [45,46]. It is well established that increasing the reaction temperature accelerates reaction kinetics in PU synthesis [47]. However, higher temperatures also increase the likelihood of side reactions, such as allophanate cross-linking or branching [48], which can alter the structural and mechanical properties of the polymer. Conversely, insufficient reaction temperatures [49] may result in low M_n values due to incomplete reactions. Thus, the reaction temperature must be carefully optimized to balance reaction kinetics with the structural integrity of the synthesized polymer [38,50,51].

The choice of solvent is another significant factor, as it can influence the reaction mechanism [52,53,54,55] and its ability to dissolve both the reactants and the growing polymer chains [31,56,57]. Adequate solubility is critical for preventing premature gelation during the reaction process. To mitigate the risk of gelation or excessive viscosity during polymerization, it is common practice to introduce a suitable quantity of solvent when an increase in viscosity is observed [39,58,59].

Time and concentration are two critical parameters that significantly influence the kinetics of polymer synthesis [60,61]. Concentration, in particular, plays a pivotal role by increasing the frequency of molecular collisions, thereby enhancing both catalytic effects (such as favoring the diffusion of a metal catalyst) and the autocatalytic activity of urethane groups [62,63]. To synthesize PEUs with the desired properties, it is essential to appropriately adjust these and other factors in the reaction process. Several methodological approaches can be employed to optimize reaction conditions and achieve specific or multiple desired outcomes.

The trial-and-error method is a traditional approach that involves systematically refining reaction conditions based on prior results. While this method offers flexibility and allows for continuous improvement, it can be time-consuming and inefficient, often leading to local rather than global optimization [64].

In contrast, machine learning (ML) experimentation is an advanced and more powerful approach. ML models can simulate polymerization processes, predict the effects of reaction parameters, and explore larger reaction spaces, thereby increasing the likelihood of identifying optimal conditions [65]. However, ML approaches require substantial computational resources and expertise in data modeling. Additionally, challenges such as overfitting—where the model becomes overly tailored to the training data and performs poorly on new datasets [65,66]—can reduce the reliability and generalizability of these predictions.

Among the various alternatives for experimental design, 2ⁿ factorial designs are a classic and practical option. This method offers a systematic approach to improving polymerization reaction conditions and provides a more efficient exploration of the reaction space compared to iterative experimentation [67,68]. While less complex and resource-intensive than machine learning-based approaches, the 2ⁿ factorial design remains highly effective in identifying critical factors.

A key advantage of the 2ⁿ factorial design is its ability to evaluate multiple factors and their interactions in a structured and straightforward manner, making it an excellent starting point for optimizing reaction parameters [69]. Additionally, it is often advisable to begin with a linear mathematical model, as it is simpler and more interpretable compared to more complex techniques, such as response surface models or machine learning models. The linear nature of the 2ⁿ factorial design provides a solid foundation for identifying significant factors and interactions, which can later inform the development of more advanced optimization strategies. Notably, the 2ⁿ factorial design is highly adaptable and can be extended to create response surface models or serve as a basis for training machine learning models [70], effectively bridging the gap between simplicity and advanced optimization techniques.

In this study, a preliminary investigation was conducted to explore the factors influencing the synthesis of PEUs. Specifically, the study examined (1) starting material concentrations (HOPCLOH and HDI), (2) reaction temperature, (3) reaction time, and (4) solvent type. A 2⁴ factorial design (two levels per factor, with four factors) was employed to systematically investigate and optimize the reaction conditions. This approach allowed for a deeper understanding of how these factors influence the number-average molecular weight (M_n), whether high or low. The factorial design enabled the identification of both the main effects of each factor and their interactions, offering a structured framework for optimizing polymerization conditions and guiding future studies.

2. Experiment

2.1. Materials

The materials utilized in this study were sourced from Sigma-Aldrich (now Merck, Darmstadt, Germany) and were characterized by their respective high purity levels: ε-caprolactone (CL) with a purity of 97%, 1,8-octanediol at 98%, ammonium heptamolybdate tetrahydrate ((NH₄)₆Mo₇O₂₄⋅4H₂O) at 99%, 1,6-hexamethylene diisocyanate (HDI) at 99.0%, and two anhydrous solvents: (a) chloroform (dielectric constant 4.8) at ≥99%, containing amylenes as a stabilizer, and (b) acetonitrile (dielectric constant 38) at 99.8%. The glassware was dried in an oven at 100 °C overnight before use. Polymerization reactions were conducted using an IKA^® RET basic magnetic stirrer hot plate with a metal flask carrier (100 mL) and a flask inlay (25 mL), operating at a voltage of 115 V.

2.2. Preparation of α,ω-Hydroxy Telechelic Poly(ε-caprolactone) (HOPCLOH)

The synthesis of α,ω-hydroxy telechelic poly(ε-caprolactone) (HOPCLOH) was carried out via bulk polymerization. In a typical reaction, using a dry round-bottom flask (250 mL), the following substances were added: (a) ε-caprolactone (CL) (126.7 g, 1.35 mol) as the monomer, (b) 1,8-octanediol (15.0 g, 0.136 mol) as the initiator, and (c) ammonium decamolybdate, synthesized in situ from ammonium heptamolybdate (0.084 g), which functioned as the catalyst. After 1 h, the oligomeric macrodiol HOPCLOH was obtained in the form of a waxy substance. The resulting product exhibited a number-average molecular weight (M_n), as determined by ¹H NMR, of 1177 g/mol. HOPCLOH: ¹H NMR (500 MHz, CDCl₃, ppm): δ 4.04 (t, [-CH₂-O-], PCL and t, [-CH₂-O-CO], Oct), 3.64 (t, 4H, [(-CH₂-OH)₂], PCL and [(-CH₂-OH)₂], Oct), 2.31 (t, 2H, (-CH₂-CO-O-), PCL), 1.64 (m, 4H, [(CH₂)₂], PCL), 1.58 (q, 4H, [(CH₂)₂], Oct), 1.36 (t, 2H, [CH₂], PCL), 1.32 (s, 8H, [CH₂]₄, Oct). ¹³C NMR (125 MHz CDCl₃, ppm): δ 173.65 [-O-CO-(CH₂)₅-OH] PCL hydroxyl terminal group, 173.45 [-O-CO-(CH₂)₅-] PCL, 64.31 [-CH₂-O-CO-] oct, 64.01 [-CH₂-O-CO-] PCL, 62.37 [-O-CO-(CH₂)₄-CH₂-OH, ester] PCL, 34.12 [-O-CO-CH₂-(CH₂)₄-OH, hydroxyl terminal group] PCL, 34.01 [-CH₂-CO-O-, ester] PCL, 32.18 [-O-CO-(CH₂)₃-CH₂-CH₂-OH, ester]. IR (cm⁻¹): 3459 (ν, O-H, hydroxyl), 2936 (ν_as, CH₂, PCL), 2864 (ν_s, CH₂, PCL), 1722 (ν, C=O, PCL), 1164 (ν_as, C-(C=O)-O, PCL), 731 (ρ, CH₂, PCL). DSC: ΔH_m = 85 J/g, T_m1 = 39 °C, T_m2 = 43 °C x_i (%) = 63%.

2.3. Synthesis of Poly(ester-urethanes) (PEUs) from HOPCLOH

The initial conditions for the synthesis of poly(ester-urethanes) (PEUs) were outlined in previous studies [23,71]. The molar ratio of 1,6-hexamethylene diisocyanate (HDI) to macrodiol (HOPCLOH) was set at 1.14:1. The experiments were conducted in this way (PEUs). The specific conditions were as follows: 0.2960 g (0.00176 mol) of HDI and 1.991 g (0.00154 mol) of HOPCLOH, which had a theoretical degree of polymerization (DP) of 10 [experimentally, M_n(NMR) = 1177 g/mol, as determined by ¹H NMR, considering 8% unreacted diol (1,8-octanediol) in the original HOPCLOH], were introduced into a 25 mL round-bottom flask, previously dried in an oven overnight. The polymerization reaction was performed using chloroform or acetonitrile as the solvent at concentrations of 0.089 or 0.176 molal. The reaction was conducted at 50 °C or 61 °C for 1 h or 8 h (see Scheme 1). Following the polymerization process, the resulting PEU solution was transferred onto a Teflon plate bordered by a glass ring, and the solvent was allowed to evaporate over a period of 12 h or until it had fully evaporated. PEU-20: ¹H NMR (500 MHz, CDCl₃, ppm): δ 4.73 (s, ¹H, [NH], urethane), 4.05 (t, 2H, [CH₂O], PCL and t, 2H, [CH₂O], Oct), PCL and [(-CH₂-OH)₂], Oct), 3.63 (t, 4H, [(-CH₂-OH)₂], PCL and [(-CH₂-OH)₂], Oct), 3.14 (t, 4H, [(-CH₂-NH-CO-O-)₂], urethane), 2.31 (t, 2H, (-CH₂-CO-O-), PCL), 1.64 (m, 4H, [(CH₂)₂], PCL and q, 4H, [CH₂)₂], Oct), 1.47 (q, 4H, [(CH₂)₂], urethane), (1.37 (q, 2H, [CH₂], PCL, and q, 4H, [CH₂]₂, urethane), 1.32 (s, 8H, [CH₂]₄, Oct. ¹³C NMR (125 MHz, CDCl₃, ppm): IR (cm⁻¹): 3339 (ν, N–H, urethane), 2937 (ν_as, CH₂, PCL), 2858 (ν_s, CH₂, PCL), 1720 (ν, free C=O, PCL), 1681 (ν, C=O, overlapping hydrogen-bonded urethane.) 1625 cm⁻¹: ν(N–H) (urea) 1536 (δ, N–H, urethane), 1465 (δ_s, CH₂, PCL), 1190 (ν_as, C-(C=O)-O, PCL), 1043 (ν_as, O-C-C, PCL), 732 (ρ, CH₂, PCL). DSC (soft segment (PCL)): ΔH_m = 31 J/g, T_m = 43 °C, x_i (%) = 23%.

2.4. Experimental Design

All statistical analyses were conducted using the Minitab 19^® software [72], with a significance threshold of α = 0.05 applied to all statistical tests [69]. To optimize the reaction conditions for maximizing the number-average molecular weight (M_n) of the PEUs, a comprehensive list of factors potentially influencing M_n was developed. A 2ⁿ factorial experimental design was employed, where the number 2 indicated two levels in each factor, and n represented the number of factors. Consequently, the current experimental design used four factors: (1) type of solvent, (2) temperature, (3) reaction time, and (4) concentration of reagents (

Table 1. The four factors are shown with their two levels of 2⁴ factorial design.

Levels	Factors				Total Experiments 32
	Temperature (°C)	HOPCLOH Concentration (Molality)	Reaction Time (h)	Solvent Type (Dielectric Constant)
High level	61	0.176	8	Acetonitrile (38)
Low level	50	0.089	1	Chloroform (4.8)

). To visualize the experiments in the 2⁴ experimental design, all 16 treatments are presented in Table S1, where each treatment was duplicated, resulting in a total of 32 experimental runs. Additional factors that might affect M_n were held constant to control variability. The sequence of these runs was randomized to reduce the risk of systematic bias. During each run, relative environmental humidity (expressed as a percentage) was monitored to determine whether a positive correlation existed between this covariate and M_n.

3. Measurements

3.1. Fourier Transform Infrared Spectroscopy (FT-IR)

Infrared spectra were obtained using the attenuated total reflectance (ATR) technique with a Perkin-Elmer Spectrum One FT-IR spectrometer and a Perkin-Elmer Spectrum Two FT-IR spectrometer.

3.2. Nuclear Magnetic Resonance (NMR)

¹H and ¹³C NMR spectra were recorded at room temperature using a Bruker Avance III HD 500 MHz spectrometer, with CDCl₃ as the solvent. Chemical shifts (δ) are reported in parts per million (ppm) and were referenced to the residual solvent signal: ¹³C at δ = 77.16 ppm and ¹H at δ = 7.26 ppm.

3.3. Gel Permeation Chromatography (GPC)

For PEUs, a PerkinElmer gel permeation chromatograph (200 Series LC pump) equipped with a refractive index detector (IR 200a) was used. ResiPore columns (Polymer Laboratories, Long Beach, CA, USA) were conditioned at 70 °C, with a flow rate of 0.3 mL/min using HPLC-grade dimethylformamide (DMF) containing 0.1 wt% LiBr as the mobile phase. Calibration was performed using polystyrene standards (Polymer Laboratories).

3.4. Mechanical Properties

Tensile measurements were conducted using a Zwick/Roell Z005 instrument (Zwick/Roell, Singapore) equipped with a 500 N load cell. The tensile tests were performed at a test speed of 200 mm/min. Type 3 dumbbell-shaped test pieces (according to ISO 37) were cut from the films.

3.5. Differential Scanning Calorimetry (DSC)

Thermograms were obtained using a DSC Q200 instrument. The experiments consisted of several cycles: (1) heating from 25 °C to 100 °C, (2) isothermal hold for 1 min at 100 °C, (3) cooling from 100 °C to −30 °C, (4) isothermal hold for 1 min at −30 °C, and (5) final heating from −30 °C to 100 °C. The entire cycle was performed at a heating rate of 10 °C/min. The melting temperature and enthalpy of fusion (ΔH_m) were determined from the peak of the endothermic transition during the second heating cycle.

The degree of crystallinity of PCL was calculated using the following formula:

x_e = ∆H_e/∆H_e⁰

where x_e is the degree of crystallinity, ΔH_e was obtained from the area under the thermal transition curve of the soft segment and PCL transition, and ΔH_e⁰ corresponds to the enthalpy of fusion for perfect PCL crystals (135.3 J/g, as reported by Crescenzi [73]).

3.6. Polarized Optical Microscopy (POM)

POM micrographs were acquired using a NIKON optical microscope (MODEL). Photographs were captured using an iPhone 13. Samples were prepared on glass slides as thin films melted at 120 °C using a hot plate, applying manual pressure between two glass slides containing the sample and a coverslip. The samples underwent an isothermal treatment at 50 °C for 24 h and were subsequently cooled to room temperature before analysis. All micrographs were collected at 40× magnification.

4. Results and Discussion

4.1. Preparation and Characterization of α,ω-Hydroxy Telechelic Poly(ε-caprolactone) (HOPCLOH)

The precursors of poly(ester-urethanes) (PEUs) typically consist of a macrodiol and a diisocyanate [23,26]. In this study, the macrodiol used was α,ω-hydroxy telechelic poly(ε-caprolactone) (HOPCLOH), which is generally synthesized via the ring-opening polymerization (ROP) of ε-caprolactone (CL). For this purpose, ammonium decamolybdate was employed as the catalyst, while 1,8-octanediol (HOROH) served as the initiator in the ROP of CL (Scheme S1). This synthetic route, using alcohol and diols as initiators, has been previously reported by our group [25,71,74]. In ROP, the degree of polymerization (DP) is controlled by the CL/HOROH molar ratio, a critical parameter since the starting material (HOPCLOH) in PEU synthesis requires a low number-average molecular weight (M_n), typically in the oligomeric range. Accordingly, the HOPCLOH prepared in this study was designed with a theoretical DP of 10. After 1 h at 150 °C, the reaction reached completion. To confirm the chemical structure of HOPCLOH, the resulting oligomer was analyzed using various analytical techniques. The ¹H NMR spectrum (Figure 1a) of HOPCLOH revealed two distinct and significant signals: one at 3.64 ppm, corresponding to the methylene group attached to hydroxyl terminals (-CH₂-OH), and another at 2.31 ppm, representing the α-methylene group adjacent to the ester moiety [-CH₂-(C=O)-O-]. These signals confirm the presence of α,ω-hydroxy telechelic terminal groups and the repetitive unit within the oligomer, respectively. The thermal properties of HOPCLOH were evaluated using differential scanning calorimetry (DSC). The thermogram (Figure 1b) displayed a prominent endothermic transition attributed to double melting temperatures (T_m) at 39 and 43 °C. This profile is characteristic of crystallites of varying sizes in HOPCLOH [25,26]. Additionally, polarized optical microscopy (POM) confirmed the presence of semicrystalline domains, as evidenced by the formation of spherulites (Figure 1c).

The second reaction in this study involves two components: HOPCLOH and 1,6-hexamethylene diisocyanate (HDI), which serve as the starting materials for PEU synthesis (Scheme 1). The progress of the polymerization reaction between HOPCLOH and HDI was monitored using ¹H NMR spectroscopy (Figure 1d,g). During the reaction, the signal corresponding to the ester repetitive unit [-CH₂-(C=O)-O-] remained unchanged, while the intensity of the hydroxyl signal (-CH₂-OH) decreased. This decrease indicates the consumption of hydroxyl groups (-OH) as they react with diisocyanate groups (-N=C=O) to form urethane linkages [-NH-(C=O)-O-]. The reaction progression was quantitatively analyzed by comparing the integral ratios of the hydroxyl and ester peaks (OH/ESTER response), referred to as the first response.

Figure 1d shows the peak assignments for poly(ester-urethane) (PEU-20, Table S2) with a magnified view of a key region in the ¹H NMR spectrum. PEU-20 was synthesized under the least favorable conditions [50 °C, 1 h, acetonitrile (ε = 38), 0.089 molal concentration]. These conditions were deemed suboptimal based on the presence of unreacted HOPCLOH, identified by the characteristic triplet signal of the hydroxyl end group (-CH₂-OH) at 3.64 ppm, and PEU-20 exhibited the highest integral value for this signal among all 32 samples. In contrast, the ¹H NMR spectrum of the PEU-13 sample (Figure 1g) showed the absence of unreacted HOPCLOH, indicating optimal reaction conditions [61 °C, 8 h, chloroform (ε = 4.8), 0.176 molal concentration]. Additionally, the appearance of a signal at approximately 3.16 ppm (-CH₂-NH-(C=O)-O-) confirmed the formation of the urethane group. The progression of the reaction was assessed via several integral ratios: the ratio of the hydroxyl peak (-CH₂-OH, corresponding to unreacted hydroxyl groups) to the ester peak (-CH₂-COO) was termed the HO/ESTER response, while the ratio of the hydroxyl peak (-CH₂-OH) to the urethane peak (-CH₂-NHCOO-) was designated as the HO/URET response, also called the second response.

Thermal analysis using DSC thermograms for both PEU-20 (Figure 1e) and PEU-13 (Figure 1h) revealed two distinct crystalline domains. For PEU-20, the enthalpy of fusion (ΔH_m) decreased significantly to 31 J/mol (Figure 1e) compared to the starting material HOPCLOH (ΔH_m = 85 J/mol, Figure 1b). This reduction indicated a disruption in the crystalline domain of the PCL soft segment within the PEU, attributed to the formation of urethane groups with intermolecular hydrogen bonding, which promoted the formation of amorphous domains [25]. This disruption was further supported by the polarized optical microscopy (POM) micrograph of PEU-20 (Figure 1f), which showed a significant reduction in spherulite formation, consistent with the DSC results. For PEU-13, DSC thermograms (Figure 1h) displayed a further decrease in ΔH_m to 10 J/mol, while POM analysis (Figure 1i) confirmed the absence of spherulite structures. These results suggest an even greater disruption in the crystalline domains and a predominance of amorphous regions under the optimized reaction conditions.

Complementary to this, the ¹H NMR analysis shows another peak at 4.73 ppm, indicative of the hydrogen attached to the urethane group (N-H). Near the N-H peak, two additional less intense peaks are observed, corresponding to hydrogens from N-H groups. These peaks suggest the presence of hydrogen bonded to nitrogen in at least three distinct chemical environments (Figure 2). The peak at 4.50 ppm is likely attributed to urea hydrogen, as this value closely matches previously reported chemical shifts for N-H hydrogen in N,N’-dihexylurea [75]. The integral values of these hydrogen signals vary depending on the degree of polymerization.

FT-IR analysis was performed to identify the functional groups of three different species previously characterized by ¹H NMR, DSC, and POM (Figure 1). Figure 3a presents the expected bands in the infrared spectrum of HOPCLOH. The primary bands include one at 1723 cm⁻¹, corresponding to the stretching of the ester carbonyl group, and another at 3446 cm⁻¹ attributed to the hydroxyl (–OH) group involved in hydrogen bonding.

In the spectrum of PEU-20 (low M_n; Figure 3b), two prominent bands are observed at 1720 cm⁻¹ and 1625 cm⁻¹. The latter is attributed to the formation of urea (N-H bending) [76]. Notably, the band at 1625 cm⁻¹ was also detected in a sample of HDI intentionally exposed to an excess of water, which promoted the formation of polyurea (Figure S1).

Figure 3c shows the infrared spectrum of PEU-13 (high M_n). In the region of the carbonyl groups, multiple bands are present. The first band, at 1726 cm⁻¹, corresponds to the ester group within the repetitive unit. The second band, at 1683 cm⁻¹, is traditionally attributed to the carbonyl group of urethane involved in hydrogen bonding with N-H. However, recent studies suggest that this band at 1683 cm⁻¹ may also indicate the formation of branching or cross-linking in PEU [77]. The third band, at 1626 cm⁻¹, appears as a slight shoulder, possibly indicating a minor presence of urea in the PEU, consistent with the urea spectrum (Figure S1). Finally, in the region of N-H stretching, two bands are observed at 3390 cm⁻¹ and 3325 cm⁻¹, further confirming the presence of urethane and urea functionalities.

4.2. 2⁴ Experimental Design: Effect of Concentration, Temperature, Solvent, and Reaction Time on the M_n of PEUs

A detailed investigation was conducted to evaluate the effects of four key factors—concentration (c), temperature (T), solvent (s), and reaction time (t)—on the molecular weight (M_n) of poly(ester-urethanes) (PEUs). These factors were selected based on insights from the literature and prior experience, as they are believed to exert the greatest influence on M_n. Each factor was analyzed at two levels: high and low (Table 1). Preliminary testing revealed that the reaction could proceed in the absence of the Sn(Oct)₂ catalyst, which is notable. The exclusion of this catalyst is important because there had been concerns that inaccuracies in measuring the catalyst amount could introduce substantial experimental error, potentially masking real differences between the factor levels.

A 2⁴ factorial design was implemented to evaluate a total of 15 effects (Equation (S1)), including the individual impact of each factor and the interaction effects among the four factors (c, T, s, t). The analysis revealed that all four primary factors had a statistically significant influence on the molecular weight (M_n), as reflected in the M_n response. The detailed findings of these significant effects were examined in the first analysis of variance (ANOVA).

Initially, the statistical model included all 15 effects (Equation (S1)). However, following the first ANOVA, it was determined that only eight of these effects were statistically significant (

Table 2. The significant main factors and interactions considered in the model derived from the original 2⁴ factorial design.

No	Source	DF	SS Adj.	MS Adj.	F Value	p Value
1	Temp (°C)	1	3,942,342,609	3,942,342,609	16.06	0.00055243
2	Molal conc. (molality)	1	3,198,620,149	3,198,620,149	13.03	0.00147501
3	Time (h)	1	697,075,220	697,075,220	28.39	2.0721 × 10−5
4	Dielectric const. (Solvent)	1	1.4474 × 1010	1.4474 × 1010	58.96	8.6 × 10−8
5	Temp (°C) × Time (h)	1	7300760075	7,300,760,075	29.74	1.5261 × 10−5
6	Temp (°C) × Dielectric const. (Solvent)	1	2,920,485,845	2,920,485,845	11.9	0.00218247
7	Time (h) × Dielectric const. (Solvent)	1	4,912,709,345	4,912,709,345	20.01	0.00017298
8	Temp (°C) × Time (h) × Dielectric const. (Solvent)	1	4,217,591,285	4,217,591,285	17.18	0.00039241
	Error	23	5,646,470,439	245,498,715
	Lack of fit	7	1,270,754,470	181,536,353	0.66	0.69928137
	Pure error	16	4,375,715,970	273,482,248
	Total	31	5.3584 × 1010

Notes: DF: Degrees of Freedom. SS Adj.: Adjusted Sum of Squares. MS Adj.: Adjusted Mean Square.

and Equation (S2), vide supra). The analysis confirmed that each of the four main factors had a significant effect on M_n, as supported by the ANOVA results presented in Table 2. Additionally, the presence of three significant two-factor interactions and one significant three-factor interaction indicates that M_n is influenced not only by the individual factors, but also by the specific combinations of factor levels in these interactions.

4.3. Analysis of Main Effects (c, T, s, t) on M_n of PEUs

To examine the main effects of c, T, s, and t on the M_n of PEUs, Figure 4 presents a graph that illustrates the impact of each factor at two levels—high and low (as defined in Table 1)—with M_n values quantified by gel permeation chromatography (GPC). In this graph, the steepness of the slope between the average M_n values at the two levels provides a measure of the magnitude of the effect for each factor.

The first main effect, moving from left to right in Figure 4, is temperature (T). A change from the low level (50 °C) to the high level (61 °C) results in a substantial increase in the average M_n, rising from 31,350 g/mol to 46,940 g/mol. This represents a 50% increase in M_n when the temperature is raised from 50 °C to 61 °C.

The second main effect pertains to the initial molal concentration (c) of HOPCLOH. Increasing the concentration from the low level (0.089 molal) to the high level (0.186 molal) results in a significant improvement in the average M_n, rising from 30,140 g/mol to 48,450 g/mol, which corresponds to a 60% increase.

The third main effect is reaction time (t). Extending the reaction duration from 1 h (low level) to 8 h (high level) leads to an increase in the average M_n from 27,850 g/mol to 51,450 g/mol, representing an 85% improvement.

The fourth main effect is the choice of solvent (s). Two solvents with different dielectric constants were used: chloroform (ε = 4.8) and acetonitrile (ε = 38). The average M_n values for these solvents were 58,725 g/mol and 22,915 g/mol, respectively. This represents a substantial increase of 150% when switching from acetonitrile to chloroform.

Figure 5 provides a clearer perspective on the magnitude of these effects in terms of M_n increases from low to high levels. In Figure 5a, the percentage increase in M_n follows the following order: T (50%) < c (60%) < t (85%) < s (150%). However, when analyzing the absolute growth in M_n (Figure 5b), the ranking changes, with temperature (T) showing the lowest increase, while the effects on M_n follow the following pattern: T > c > s > t.

To aid in the interpretation of Figure 5b, the relative impact of each variable is defined as follows:

$$\mathrm{Relative}\mathrm{Impact}={\displaystyle \frac{∆M\mathrm{n}\%}{∆x\%}}$$

where:

• ΔM_n% represents the percentage change in the response variable (M_n) caused by variations in the variables;
• Δx% corresponds to the percentage change in each variable (T: temperature, c: concentration, s: solvent dielectric constant, and t: time).

The numerical values within each box in Figure 5b indicate the relative impact (RI) of the respective variable. Among these variables, temperature (T) demonstrates the most pronounced influence on the response variable, with an RI of 2.5. This is followed by concentration (c), with an RI of 0.61, the dielectric constant of the solvent (s) with 0.271, and, finally, reaction time (t), which exhibits the lowest RI at 0.121. These results underscore that, while all factors contribute to changes in M_n, temperature has the greatest relative impact when normalized to the percentage change in the variable.

The solvent was the only factor that failed to meet the assumption of homogeneity of variances. This deviation, however, was not deemed significant enough to compromise the validity of the experimental results. Furthermore, certain combinations of factor levels (interaction effects) were found to elevate the average M_n above 60,000 g/mol.

In Figure 6, each dot in the graphic illustrates the average of eight experiments, and Figure 6d depicts the dual interaction effects, specifically the interaction between temperature and solvent (T•s). The data reveal that increasing the temperature from 50 °C to 61 °C while using chloroform as the solvent results in a substantial increase in the average M_n, rising from 45,870 g/mol to 87,170 g/mol. In contrast, the same temperature increase with acetonitrile as the solvent produces only a marginal change in M_n, with values increasing from 22,440 g/mol to 25,530 g/mol. Table S3 confirms that the combination of 61 °C and chloroform (ε = 4.8) generates the highest statistically significant average M_n (87,176 g/mol). Conversely, the two lowest combinations of factor levels involve acetonitrile as the solvent, demonstrating its lower efficacy in achieving high M_n values under the tested conditions. This evidence further validates temperature as a key factor, as illustrated in Figure 5b.

The temperature and time (T•t) interaction plot is shown in Figure 6b. This graph illustrates that, when the reaction time is 1 h, increasing the temperature from 50 to 61 °C results in only a modest increase in M_n from 26,491 to 34,502 g/mol. Detailed comparisons of the means for the temperature and time interaction are provided in the Supplementary Material (Table S4). According to Table S4, the highest statistically significant M_n value (86,220 g/mol) is achieved when the reaction is conducted at 61 °C for 8 h. In contrast, the other level combinations—1 h at 50 °C, 1 h at 61 °C, and 8 h at 50 °C—yield statistically similar M_n values (34,502, 33,811, and 26,491 g/mol, respectively).

The interaction between reaction time and solvent type is depicted in Figure 6f. The data reveal that, when acetonitrile is used as the solvent, increasing the reaction time from 1 h to 8 h produces only a slight change in M_n from 21,620 to 26,350 g/mol. However, when chloroform is used as the solvent, the same increase in reaction time leads to a substantial rise in M_n from 39,370 to 93,670 g/mol, as reported in Table S5. The highest mean M_n value (93,670 g/mol) is achieved with 8 h of reaction time and chloroform as the solvent. In contrast, the other three mean values (39,370, 26,350, and 21,620 g/mol) are statistically equivalent, highlighting the critical role of the combination of chloroform and extended reaction time in significantly increasing M_n.

Table 3. Summary of comparisons of means for the interaction between temperature, time, and solvent type (M_n response by GPC).

Temperature × Time × Type of Solvent (°C, Hours, Dielectric Constant)	N	Mean	Group
61, 8, 4.8	4	140,910	A
50, 8, 4.8	4	46,430	B
50, 1, 4.8	4	45,300	B
61, 1, 4.8	4	33,440	B
61, 8, 38.0	4	31,530	B
50, 1, 38.0	4	23,690	B
50, 8, 38.0	4	21,180	B
61, 1, 38.0	4	19,540	B

Means that do not share a letter are significantly different.

summarizes the results of the mean comparisons for the three-way interaction between temperature, time, and solvent type. The analysis reveals that most combinations of these factors produce statistically similar M_n values. However, one combination stands out: a reaction temperature of 61 °C, a reaction time of 8 h, and chloroform (dielectric constant 4.8) as the solvent. This specific combination yields a significantly higher M_n value of 140,910 g/mol.

This analysis confirms that only the specific combination of high temperature, extended reaction time, and chloroform as the solvent results in a substantially higher M_n, while the other combinations do not lead to significant variations in M_n.

Based on the results from the 2⁴ factorial design, the optimal conditions for synthesizing high-M_n PEUs were identified as follows: a temperature of 61 °C, a reaction time of 8 h, a 0.1876 molal concentration of HOPCLOH, and chloroform (ε = 4.8) as the solvent. These conditions produced the highest M_n values observed in this study.

Additionally, it was noted that the molal concentration of HOPCLOH is the only factor that does not exhibit any interaction effects. This indicates that changes in M_n due to concentration are independent of the levels of the other factors. In other words, increasing the concentration level will either significantly or nominally increase M_n, regardless of temperature, reaction time, or solvent type (within the studied reaction space). This behavior is visually supported by the three gray-background graphs in Figure 6a,c,e, where the nearly parallel lines demonstrate that concentration changes proportionally affect the M_n of PEUs. In contrast, the other factors—temperature, reaction time, and solvent—exhibit various interaction effects, meaning their influence on M_n depends on the levels of other factors.

The choice of solvent significantly affects the polymerization of HOPCLOH with HDI. Acetonitrile, a polar solvent with a high dielectric constant (ε = 38) and low vapor pressure, leads to low conversions of HOPCLOH. Its high polarity likely impedes polymerization by forming strong interactions with hydroxyl (OH) groups, reducing their availability for reaction with HDI. Additionally, during film formation on a Teflon surface, the slow evaporation of acetonitrile facilitates the gradual crystallization of unreacted HOPCLOH, which was detected by a relatively high enthalpy value (ΔH_m). Furthermore, the hygroscopic nature of acetonitrile promotes side reactions between HDI and water, further decreasing polymerization efficiency. However, this side reaction is minimal and only occurs during the evaporation step at room temperature to produce the PEU films. As a result, molecular weight (M_n) values remain consistently low with minimal variation.

In contrast, chloroform, a less polar solvent with higher vapor pressure, improves polymerization efficiency. In a closed system (reflux), it facilitates the interaction between HDI and OH groups, promoting polymerization. In an open system, the rapid evaporation of chloroform inhibits some PCL crystallization, enabling continued polymer growth, including branching and cross-linking. The filtration of PEU samples prior to GPC analysis was notably difficult due to a partially insoluble fraction, likely caused by cross-linking and branching. The insoluble fraction has been previously reported for theoretically linear PUs using an excess of diisocyanate [48,78]. Experimentally, the signal of cross-linking attributed to allophanate is detected at around 1680 cm⁻¹, and, usually, at the same wavenumber (cm⁻¹), the signal of the urethane group overlaps [77,79]. This result yields higher M_n values and greater variability compared to acetonitrile.

Polydispersity (M_n/M_n) was analyzed as a complementary response variable in the 2⁴ experimental design. Levene’s test confirmed that chloroform produced significantly greater variability compared to acetonitrile. The primary factors influencing polydispersity were reaction time and solvent choice, with significant three-way interactions also observed. Longer reaction durations, higher temperatures, and the use of chloroform led to increased cross-linking and branching, which broadened the molecular weight distribution (as shown in Table S6). Consequently, while chloroform facilitates higher molecular weights, it also results in increased polydispersity due to enhanced branching and cross-linking during polymerization.

On the other hand, the analysis of the frequency vs. M_n plot, which ideally should resemble a Gaussian distribution, reveals a right skew toward higher M_n values (Figure 7). The Ryan–Joiner normality test confirmed that the data do not follow a normal distribution, indicating a lack of normality in the M_n values. This skewness suggests the presence of non-normal behavior in the distribution of M_n, likely influenced by the interaction of the experimental factors.

In Figure 7, it is clear that the highest M_n values correspond to the last five PEU samples, all synthesized using chloroform as the solvent. The pronounced spacing between these data points indicates that, in addition to yielding higher M_n values, the use of chloroform introduces greater variability in the M_n data. This observation is statistically supported by Bartlett’s test for solvent type, which confirms that the variability in M_n associated with chloroform is significantly greater than that observed with acetonitrile.

5. Contrasting M_n (GPC) of PEUs with Other Response Variables

5.1. OH/ESTER Response by ¹H NMR

The number-average molecular weight (M_n) of poly(ester-urethanes) (PEUs) can also be estimated using ¹H NMR spectroscopy by analyzing the OH/ESTER response. This metric reflects the ratio of signal intensities corresponding to hydroxyl (OH) and ester groups, providing insights into the conversion of unreacted HOPCLOH in the final PEU product (see Supporting Information Table S7). By combining conversion data from the OH/ESTER response with the known M_n values of 1,6-hexamethylene diisocyanate (HDI) and HOPCLOH, the M_n of the synthesized PEUs can be calculated (Table S7).

However, as the proportion of unreacted HOPCLOH decreases with increasing polymerization, the precision of M_n determined via ¹H NMR diminishes. This is due to integration errors associated with low-intensity signals in the NMR spectrum, particularly when M_n values are high. Therefore, caution is required when interpreting M_n values for PEUs with high degrees of polymerization, as these estimates are inherently less reliable.

Figure 8 demonstrates the relationship between M_n of PEUs, as determined by GPC, and HOPCLOH conversion calculated from the OH/ESTER response. The data exhibit a typical step-growth polymerization behavior, where M_n remains low for conversions below 0.95, but rises sharply once conversion exceeds this threshold. This aligns with the characteristic mechanism of step-growth polymerization, where high molecular weights are achieved only at near-complete monomer conversion. It is important to note that the OH/ESTER response is not the only way to contrast M_n values obtained via GPC. Other NMR-based metrics, such as the OH/URET response, demonstrate similar behavior and trends (see Section S1 of the Supporting Information).

5.2. Enthalpy of Fusion (ΔH_m) Response by DSC

All PEU samples were analyzed via differential scanning calorimetry (DSC). In a typical DSC thermogram, the primary thermal transition observed was the melting temperature (T_m) and its associated enthalpy of fusion (ΔH_m). Since all PEU samples exhibited a T_m, the entire series of PEUs can be classified as semicrystalline polymers. The ΔH_m was attributed to the polycaprolactone (PCL) soft segment within the PEUs. An inverse correlation was observed between M_n(GPC) and ΔH_m. The 2⁴ factorial design revealed that all main factors, except temperature, significantly influenced ΔH_m and T_m, while no significant interaction effects were detected (Figure 9). Conditions that reduced ΔH_m correlated with those that maximized M_n. At high M_n, the increased concentration of urethane groups promotes hydrogen bonding, which inhibits the crystallization of some PCL segments. Furthermore, chemical cross-linking at high M_n further suppresses crystallinity. The optimal conditions for minimizing crystallinity and melting temperature were identified as a reaction time of 8 h, the use of chloroform as the solvent (ε = 4.8), and a 0.176 molal concentration of HOPCLOH. These conditions align with those that produce the highest M_n, further supporting the inverse relationship between M_n and ΔH_m.

6. Characterization of PEUs by Mechanical Properties

Mechanical testing was performed on a subset of PEUs synthesized as part of the 2⁴ factorial design. However, many films were excluded from testing due to their fragility. Notably, all PEUs with M_n values above 64,000 g/mol, exclusively synthesized using chloroform as the solvent, exhibited elongations exceeding 1000%. In contrast, samples with lower M_n values and those synthesized using acetonitrile exhibited intermediate-to-low elongations. Figure 10 presents the stress–strain curve for a representative PEU-22 (similar to PEU-13, Figure 1) synthesized with chloroform. This sample displayed a high M_n (≈153,000 g/mol), an elastic modulus of 121 MPa, a ΔH_m of 11 J/g, and a significantly high elongation at break (≈1200%). The curve demonstrated classic plastic behavior, consistent with findings in previous publications [23,25,37,71]. In contrast, a typical sample synthesized using acetonitrile as the solvent (PEU-20) exhibited poor mechanical properties due to its low molecular weight and fragile physical appearance, indicative of a relatively low M_n. These results underscore the critical role of solvent choice in determining the mechanical and structural properties of PEUs. Specifically, chloroform facilitates the synthesis of higher-molecular-weight polymers, resulting in improved elongation at break and enhanced mechanical performance compared to acetonitrile.

The mechanical properties of PEU-30 (M_n ≈ 38,000 g/mol) and PEU-22 (M_n ≈ 153,000 g/mol) are compared in Figure 10 (stress–strain curves), where the influence of M_n on the mechanical behavior of PEUs is evident. Both samples were synthesized using chloroform as the solvent. PEU-30 exhibited a high modulus (221 MPa) compared to PEU-22. This is attributed to the relatively high enthalpy of the fusion (ΔH_m = 20 J/g) of the PCL soft segment in PEU-30, which contributes to increased stiffness but results in limited elongation at break (approximately 10%), leading to poor mechanical performance.

In contrast, PEU-22 demonstrated a significantly higher elongation at break, consistent with its high M_n and the presence of repetitive urethane units that promote intermolecular hydrogen bonding. Additionally, covalent cross-linking, likely involving allophanate groups, may be present in PEU-22. This cross-linking enhances cohesion between polymer chains, allowing the material to withstand greater elongation before fracturing. These findings highlight the critical role of molecular weight and cross-linking density in governing the mechanical properties of PEUs. While higher M_n and cross-linking contribute to improved elongation and toughness, in contrast, increased crystallinity, as observed in PEU-30, leads to enhanced stiffness but reduced ductility.

7. Conclusions

α,ω-Hydroxy telechelic poly(ε-caprolactone) (HOPCLOH) was synthesized through the ring-opening polymerization (ROP) of ε-caprolactone (CL). HOPCLOH was obtained with a low degree of polymerization (DP = 10) as it served as the starting material for the synthesis of poly(ester-urethanes) (PEUs) in the presence of 1,6-hexamethylene diisocyanate (HDI). The chemical structures of both HOPCLOH and PEUs were validated using nuclear magnetic resonance (NMR), differential scanning calorimetry (DSC), and polarized optical microscopy (POM).

A 2⁴ statistical factorial design was systematically employed to prepare 32 PEU samples, where four main factors—concentration (c), temperature (T), solvent (s), and reaction time (t)—were investigated to optimize the number-average molecular weight (M_n), as determined by gel permeation chromatography (GPC), as the primary response. The results indicated significant double and triple interactions between the main factors. The optimal conditions for maximizing M_n were identified as a concentration of 0.176 molal, a temperature of 61 °C, a reaction time of 8 h, and chloroform as the solvent (dielectric constant: 4.8). Among the factors, temperature exhibited the most significant influence on M_n compared to concentration, solvent, and reaction time.

The choice of solvent in a polyaddition mechanism, such as PEU synthesis, was shown to be critical. Acetonitrile yielded the lowest M_n values, while chloroform provided the most favorable environment for chain propagation, resulting in significantly higher M_n values. Additionally, NMR analysis revealed that the OH/ESTER response was inversely proportional to M_n (GPC).

The M_n of PEUs was found to have a pronounced impact on their thermal and mechanical properties, with most samples exhibiting a semicrystalline structure and plastic mechanical behavior. These findings suggest that future research could focus on exploring a broader range of solvents to identify additional options for optimizing PEU synthesis. A more comprehensive study of solvent effects could provide valuable insights into improving the efficiency and scalability of PEU production.