Succinic acid (99+%), azelaic acid (98%), glutaric acid (99%), reagent grade glycerol (99.9%), anhydrous tetrahydrofuran (99.9%), and HPLC grade toluene (99.8%) were purchased from Sigma Aldrich (St. Louis, MO, USA). Deuterated NMR solvent, dimethylsulfoxide-d₆, was ordered from Cambridge Isotope Laboratories (Andover, MA, USA). HPLC grades of acetone, chloroform, and methanol were purchased from J.T. Baker (Phillipsburg, NJ, USA). Sodium carbonate (anhydrous, granular) was obtained from Mallinckrodt-Baker, Inc. (Paris, KY, USA).

Poly(diacid-glycerol)s were synthesized as previously described [16]. A 2:1 molar ratio of diacid (0.02 mol) and glycerol (0.0105 mol) or a 1:1 molar ratio of diacid (0.015 mol) and glycerol (0.0155 mol) were reacted in the presence of 0.15% w/w (catalyst/reactants) dibutyltin(IV)oxide in a single-neck 50 mL round bottom flask with 28 mL of toluene. Experiments were performed at oil bath temperatures of 110 °C, 135 °C and 155 °C for 10 h, 24 h, or 72 h. A reflux condenser was connected to the top of a Dean-Stark apparatus used to remove water over the course of the esterifications. Following reaction, most of the solvent was decanted from the crude reaction products and the rest was removed by rotary evaporation. The diacids were extracted from their polymers by three centrifugations in water at 4,000 rpm for 10 min at 21 °C. The water was decanted off, the polymer was dissolved in THF, and then allowed to stand overnight in sodium carbonate. After vacuum filtration, the THF was removed by rotary evaporation.

Poly(diacid-glycerol)s were synthesized as previously described [16]. The diacid (0.20 mol), glycerol (0.105 mol) and 0.15% w/w dibutyltin(IV)oxide (catalyst/reactants), were placed in a 100 mL two-neck round bottom flask and heated to 60 °C under reduced pressure (~150 Pa) for one hour. The reaction mixture subsequently was allowed to react for 2 h at 100 °C, then 2 h at 120 °C, and finally at 150 °C under reduced pressure (~150 Pa), for either 10 h or 24 h.

Solution-state NMR spectra were recorded at 9.4 Tesla on a Varian INOVA NMR Spectrometer at 27 °C, using a 5 mm indirect-detect probe with Z-axis pulsed field gradient. All samples were dissolved in d₆-DMSO with TSP added for referencing. The 1D proton (¹H) spectra (400 MHz) were acquired with a spectral width of 6,000 Hz, a 90-degree pulse angle and a 2.5 s relaxation delay, and were referenced to the TSP peak. The ¹³C spectra (100 MHz) were acquired with a spectral width of 25–30 kHz, a pulse angle of 45°, a relaxation delay of 20 s, 128 K data points, and 6,000–18,000 transients. These spectra were referenced to the DMSO methyl carbon (39.5 ppm). To allow for accurate integration of ¹³C signals, these 1D–¹³C spectra were recorded with proton decoupling only during the acquisition periods (“inverse-gating”), to avoid non-uniform enhancement of carbon signals from proton NOE effects. No attempt was made to measure the T1 relaxation of the ¹³C resonances, however, the relaxation delay of 20 s, combined with the 45° excitation pulse, helped to minimize any distortions due to incomplete relaxation.

Resonance assignments utilized the DEPT (Distortionless Enhancement Polarization Transfer) spectra, as well as 2D-NMR. A DEPT experiment was run using the standard 135° flip angle to distinguish amongst CH, CH₂ and CH₃ ¹³C resonances. The 2D-NMR studies included gradient enhanced versions of COSY (Correlation Spectroscopy), HSQC (Heteronuclear Single Quantum Correlation) and HMBC (Heteronuclear Multiple Bond Correlation) (8 and 16 Hz coupling) experiments, and non-gradient versions of the HMQC (Heteronuclear Multiple Quantum Correlation) and TOCSY (Total Correlation Spectroscopy) (80 ms mixing time) experiments. The proton homonuclear COSY and TOCSY (80 ms mixing time) 2D experiments were recorded with spectral widths of 6 or 8 kHz in both dimensions, using 4,096 points in the directly-detected dimension, and 512 increments in the second dimension; 16 transients per fid were collected with a 2 s delay between scans.

The ¹H-¹³C heteronuclear experiments, HSQC, HMQC and HMBC (8 Hz and 16 Hz coupling), were recorded using using 4,096 data points and spectral widths of 6 kHz in the proton dimension (directly-detected). For the carbon (indirectly-detected) dimension, 512 increments were acquired with a spectral width of 25 or 30 kHz, a 2 s delay between scans, and 32 or 64 transients per fid.

¹H NMR of white powder after vacuum filtration of azelaic acid-glycerol polymer (DMSO-d₆, 200 MHz; R = H or Ester)): δ 1.25 (m, –CH₂–CH₂–CH₂–), δ 1.48 (m, –CH₂–), δ 2.19 (t, –CH₂–COOH).

The synthesis and analytical charaterization of these polymers have been previously reported [16]. Therefore, information regarding yields, solubilities, and molecular weights is available. Similar NMR peak assignments have also been published by ourselves and others [2,3,17].

In this study, ¹H and ¹³C NMR have been employed to determine how many glycerol units have been esterified at the secondary alcohol to form branched polymers. The glycerol backbone of each hyperbranched structure can be composed of trisubstitued dendritic (D), disubstituted linear (L), and terminal (T) units as shown in Figure 1. Determining the degree of branching (D.B.%) by NMR relies upon the ability to distinguish between these units and the ability to thereby assign the carbons at the branch points and the terminal units as shown in Figure 1. The ¹H and ¹³C NMR resonance peaks associated with these units can then be integrated and used to calculate the degree of branching according to Equation (1) [2,3,6,13,17,22,23,24]. This equation is more appropriate for A₂ + B₃ hyperbranched polymer systems because, unlike the equation introduced by Hawker [25] and modified by Kim [26], it is valid for both low and high molecular weight hyperbranched polymers and oligomers. It is also more reliable when monomer feed compositions are varied [6] such as in the experiments reported here.

In this work, we have performed DEPT and 2D NMR to assign the NMR resonances using through-bond connectivity, rather than depend on chemical shift analyses, which are less reliable and can be misleading. The proton resonances were thus assigned, and compared favorably with published data [2,3]. A review of the literature reveals that the exact assignment of the carbon resonances (especially the central carbon in the glycerol subunit in the T_G and L(1,2) branching structures) may be dependent upon the chemical composition of the branched chains. The HMBC experiment was of particular importance, as it enabled the definitive determination of the chemical connectivity from the carbonyl carbons of the diacid to the glycerol carbons, through the ester linkage. The resulting assignments are largely consistent with those of Kulshrestha et al. [3] but differed from those of Stumbe and Bruchmann [2], presumably because of slight differences in chemical environments in the different polymers. Whereas the ¹³C spectra generally produced sharper, and more resolvable peaks, the ¹H resonances were broader and required careful baseline subtraction to obtain useful integrations. The ¹³C integrations and degree of branching analysis should be therefore considered more accurate and reliable, but comparison with the ¹H values is useful for confirmation of the analyses.

The ¹H and ¹³C assignments for the glycerol region are depicted in the HMQC spectra (Figure 2). A complete listing of the NMR assignments for the glycerol region is provided as supplementary material and a condensed version of the average resonance assignments appears in Table 1. Representative 1D- ¹³C spectra of our oligomers are shown in Figure 3. Some of the resonances listed in Table 1 were assigned from 2D analyses that may not be visible on the scale depicted in the 1D spectra. As expected the resonance frequencies of the glycerol carbon atoms (positions a–c. Figure 1) are independent of the A₂:B₃ monomer ratio or the reaction temperature, but are more dependent upon the substitution pattern of the glycerol unit (Table 1). Although the chemical shift values of a, b and c of the different subunits very similar for each of the diacid derivatives, slight variations arise from the different diacids that have be incorporated.

The ¹³C NMR spectra of most of the dilute-solution samples revealed the presence of two clearly distinguishable peaks associated with the central glycerol carbon (Cb) for linear polymerization (especially L_1,2, but also to a lesser extent L_1,3 and T_G, see supplementary material). The only samples in which this was not observed were the two neat samples (Table 2, lines 13 and 15), the 72 h azelaic:glycerol (2:1 molar ratio) polymer (Table 2, line 11) and the glutaric:glycerol (2:1 molar ratio) polymer made at 135 °C (Table 2, line 8). These two peaks were most frequently observed in those samples which had medium-to-low dendritic branching (D.B. < ~33%). The relative intensities of these peaks vary amongst the samples and may be somewhat dependent upon preparation method, although no clear pattern could be discerned. The most likely explanation is that these samples consist of a mixture of long and short-chain linear polymers. It was also observed that some samples had multiple ¹³C peaks associated with dendritic branching. These peaks were different from the L_1,2 peaks just mentioned in that in most cases they appear as a splitting of the main “D” peak and are not well resolved. This was observed in all of the glutaric acid:glycerol (2:1 molar ratio) products and the succinic acid:glycerol (2:1 molar ratio) polymer prepared at 135 °C (Table 1, line 6). All of these samples have higher levels of dendritic branching (>~20%). While these might also arise from a mixture of long and short-chains, their presence in the neat samples suggests that they arise from structures that are more likely to be found in higher concentrations. Hence we postulate that these arise from cyclic polymer structures, which are not possible in structures consisting of linear branching.

The assignments and integrations of both the ¹³C and ¹H spectra (Table 1) were used for the calculation and comparison of their respective degree of branching ratios (Table 2(a,b)). As previously mentioned, the ¹³C integrations in this study are considered to be more accurate and reliable than the ¹H values. Therefore, while the D.B.% values obtained from the assignment and integration of the ¹H spectra are available for comparison in Table 2(a), the ¹³C data in Table 2(b) will be the primary focus of the following discussion.

General observations of the degree of branching results reveal that the 2:1 (diacid:glycerol) formulations gave products with the highest D.B.%. The polymers co-polymerized with glutaric acid at temperatures at or above 135 °C produced materials with D.B.% that ranged from 70.5% for a 10 h reaction to 87.8% for a 24 h reaction. Under similar conditions, the analoguous products made from succinic acid and azelaic acid gave considerably lower degrees of branching (Table 2, lines 7 and 9). Even increasing the reaction time for the synthesis of the poly(glycerol-azelaic acid) to 72 h (Table 2, line 11) only gave a product with a D.B.% of 48.5%. Allowing the neat, glutaric acid:glycerol (2:1) reaction to proceed for 24 h, yielded a clear, colorless, flexible material with a high degree of branching (Table 2, line 15) rather than a thick viscous gel as observed for the complimentary reaction performed in toluene which resulted in a lower degree of branching (Table 2, line 14). Despite this observation, there seems to be no correlation between D.B.% and reaction medium. In fact, when comparing the glutaric-acid derived polymers, temperature seems to play a role in how much the polymers branch and, surprisingly, it appears that product synthesized in toluene at 135 °C (Table 2, line 8) branch to a higher degree than those synthesized at 155 °C (Table 2, line 14). Even when a neat reaction was performed at 155 °C for 10 h (Table 2 line 13), the D.B.% was comparable to that of a reaction performed in toluene at 135 °C (Table 2, line 12) for the same amount of time. It may be of interest to further investigate a larger set of diacids to determine if this observation for the glutaric acid-derived polymer is a unique occurrence or if its chemical or physical properties, such as solubility, polarity, and the spatial arrangement of its atoms, play a role in increasing its degree of branching. When using 1:1 molar ratios of glycerol and diacid, polymers with D.B.% lower than 40% resulted even when reacted for 24 h at 155 °C (Table 2, lines 4–6, 10). For the 1:1 formulation, the difference in D.B.% for the succinic acid and glutaric acid-derived materials may not be significant. However, as observed for the 2:1 forumation, the azelaic acid derived polymer continues to branch less frequently than the succinic acid and glutaric acid analogues. While keeping all other reaction conditions the same for the esterification of glycerol with glutaric acid (1:1 molar ratio), increasing the oil bath temperature from 135 °C to 155 °C resulted in crosslinked hydrogels that were solid and insoluble in all solvents. However, the degree of branching only increased by 2.1% (Table 2, lines 5 and 10) suggesting that the degree of branching here represents intermolecularly crosslinked polymers that are more energetically favored at higher temperatures and can therefore be controlled. It was previously observed and discussed in reference 16 that water was not transferred into the Dean-Stark apparatus unless the oil bath temperature was heated to at least 135 °C. Therefore, performing the reaction at any temperature lower than 135 °C was the equivalent to performing the reaction without the Dean-Stark apparatus. Removing the Dean-Stark apparatus resulted in a ~47% decrease in degree of branching for both the succinic acid-derived polymers and the glutaric acid-derived polymers, indicating either that hydrolysis of the ester bond was faster than esterification of the secondary alcohol on glycerol or that the energy required to esterify the secondary alcohol on the glycerol was not sufficient at reflux.