Jean-Baptiste Lena
email: jean-baptiste.lena@pg.canterbury.ac.nz

Alexander K Goroncy

Joel J Thevarajah

Alison R Maniego

Gregory T Russell
email: greg.russell@canterbury.ac.nz

Patrice Castignolles
email: p.castignolles@westernsydney.edu.au

Marianne Gaborieau
email: m.gaborieau@westernsydney.edu.au

Effect of transfer agent, temperature and initial monomer concentration on branching in poly(acrylic acid): A study by 13 C NMR spectroscopy and capillary electrophoresis

Keywords:

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Poly(acrylic acid) (PAA) is a water-soluble polymer with a wide range of applications, for example as superabsorbent [1], water purification aid [2], drug carrier [3,4] and scale control agent [5]. Even if it is not always acknowledged, PAA is branched when produced by radical polymerization [6][7][8]. The branching strongly influences the properties of the polymer. Short branches influence physical properties such as melting point and glass transition temperature whilst long branches affect rheology [9]. One consequence of the branching can be inaccurate determination of the propagation rate coefficient, k p , by pulse-laser polymerization (PLP) coupled with size exclusion chromatography (SEC) [10]. Long-chain branching (LCB) was detected even at low conversion and it was shown that it can decrease the accuracy of the molar mass determined by SEC, and hence the k p obtained is less accurate (up to 100 % error) [11]. The molar masses of PAAs determined by SEC showed low accuracy [12] potentially due to long-chain branching. In terms of kinetics, LCB results from intermolecular chain transfer to polymer (or random intramolecular transfer to polymer) and short-chain branching (SCB) results from intramolecular transfer to polymer such as backbiting [13]. In both cases, the secondary propagating radical (SPR) is transformed into a mid-chain radical (MCR) (see Figure S1). The MCR can propagate but with a rate coefficient, k p tert , much lower than k p . Intramolecular transfer to polymer thus influences the polymerization rate and can lead to inaccurate k p values determined by PLP if not at low enough polymerization temperature [10,14,15] or high enough pulse frequency [16]. Studying the branching in PAA obtained by radical polymerization thus gives important information regarding its kinetics.

The only method to determine the average degree of branching (DB) in PAA is quantitative 13 C NMR spectroscopy. DB is expressed in percents of monomer units and is determined from the integration of the signal of the quaternary carbons (C q ) characteristic of a branched polymer and of a signal of a carbon whose characteristics remain unchanged in the branched and unbranched monomer units. This method has been utilized several times in order to determine DB in PAA [6,8,18] and poly(alkyl acrylate)s [17,[19][20][START_REF] Ballard | The role of chain transfer agent in reducing branching content in radical polymerization of acrylates[END_REF][START_REF] Wenn | Photoinduced acrylate polymerization: Unexpected reduction in chain branching[END_REF][START_REF] Ahmad | Chain transfer to polymer and branching in controlled radical polymerizations of n-butyl acrylate[END_REF][START_REF] Hamzehlou | Analyzing the discrepancies in the activation energies of the backbiting and beta-scission reactions in the radical polymerization of n-butyl acrylate[END_REF]. Both resolution and sensitivity are required for reliable quantification of DB. Various NMR methods (solution-state, solid-state and melt-state) were previously compared for poly(n-alkyl acrylate)s [20]. However, optimal analyses were by melt-state NMR spectroscopy obtained at 150 °C above the glass transition temperature (T g ) [20]. As the T g of PAA is relatively high (between 90 and 150 °C) and PAAs degrade between 250 and 400 °C [START_REF] Caykara | Effect of preparation methods on thermal properties of poly(acrylic acid) silica composites[END_REF], the branching in PAA was determined in this work by solution-state NMR spectroscopy.

In 2010, Gaborieau et al. studied the influence of the polymerization temperature and presence of 1octanethiol on the branching in poly(n-butyl acrylate) [17]. They confirmed that DB increases with temperature and showed that DB is considerably reduced when 1-octanethiol (as a chain transfer agent, CTA) is present amongst the reactants. The temperature increases the frequency of the reaction which leads to formation of MCRs. MCR species can then take 4 different pathways: propagation of the tertiary radical, which leads to a branched polymer; β-scission, which does not lead to a branched polymer (at least not directly); a "patching" reaction, in which a hydrogen radical is transferred from the 1octanethiol to an MCR; and radical-radical termination (Figure S1). DB is measurably reduced when 1octanethiol is present; this has been attributed to "patching". Ballard et al. [START_REF] Ballard | The role of chain transfer agent in reducing branching content in radical polymerization of acrylates[END_REF] showed that there is another possible explanation for the decrease of DB. The presence of CTA may reduce the number of backbiting events in comparison to the number of propagation events as the macroradical polymerizes for a shorter time when the reaction is carried out with a CTA and the chains formed after only a few propagation events are too short to undergo backbiting.

The development of electrospray-ionization mass spectrometry (ESI-MS) has been useful to determine the product spectrum of a polymer sample and its changes within the chain length distribution [START_REF] Barner-Kowollik | Probing mechanistic features of conventional, catalytic and living free radical polymerizations using soft ionization mass spectrometric techniques[END_REF]. A higher level of polymer characterization has become available, in that polymer chains can be 'visualized' precisely according to their end groups and chain length. The influence of temperature and of chaintransfer-agent (CTA) concentration on the structure of poly(n-alkyl acrylate)s has been studied by ESI-MS [START_REF] Junkers | Mapping poly(butyl acrylate) product distributions by mass spectrometry in a wide temperature range: Suppression of midchain radical side reactions[END_REF][START_REF] Koo | Quantitative product spectrum analysis of poly(butyl acrylate) via electrospray ionization mass spectrometry[END_REF]. The amount of β-scission increased with temperature and decreased with CTA concentration. However, linear and branched species cannot be distinguished by ESI-MS, which gives molar masses but no information related to branching. It is however challenging to obtain consistent ionization of different macromolecules within a sample. Different end-groups [START_REF] Gaborieau | Molecular weight and tacticty of oligoacrylates by capillary electrophoresis -mass spectrometry[END_REF] or molar masses [START_REF] Guttman | Quantitative mass spectrometry and polydisperse materials: Creation of an absolute molecular mass distribution polymer standard[END_REF] can for example affect the ionization efficiency. This can thus limit the accuracy of the average molar mass values and of molar mass distributions determined by MS. ESI-MS analysis gives complementary information to other methods of analysis, such as SEC and NMR spectroscopy. SEC is the most widely used method to determine molar mass [START_REF] Berek | Size exclusion chromatography -A blessing and a curse of science and technology of synthetic polymers[END_REF]. It separates polymers according to their hydrodynamic volume, V h [START_REF] Grubisic | A universal calibration for gel permeation chromatography[END_REF][START_REF] Grubisic | A universal calibration for gel permeation chromatography[END_REF], which depends on both molar mass and branching [START_REF] Gaborieau | Size-exclusion chromatography (SEC) of branched polymers and polysaccharides[END_REF]. This may lead to incomplete SEC separation in terms of molar mass due to branching [START_REF] Kostanski | Size-exclusion chromatography -a review of calibration methodologies[END_REF][START_REF] Gaborieau | Theory of multiple detection size exclusion chromatography of complex branched polymers[END_REF][START_REF] Gaborieau | Separation of complex branched polymers by size-exclusion chromatography probed with multiple detection[END_REF]. Multiple-detection SEC can be used to detect LCBs [20]. This method allows determination of the local number-and weight-average molar mass as well as the local dispersity of molar mass at each elution volume Ð(V h ) [START_REF] Gaborieau | Size-exclusion chromatography (SEC) of branched polymers and polysaccharides[END_REF]. The local dispersity assesses the accuracy of the determined molar mass [11] but it provides only an indirect assessment of the heterogeneity of the macromolecular structure due to branching. In the case of PAA, aqueous and organic SEC provide different molar mass values [12] due to the presence of branches.

In further work, poly(sodium acrylate)s (PNaAs) were separated by free-solution capillary electrophoresis (CE) according to their branching topology with limited influence of the molar mass [7].

Indeed, for homopolyelectrolytes, such as poly(sodium acrylate) [START_REF] Gaborieau | Molecular weight and tacticty of oligoacrylates by capillary electrophoresis -mass spectrometry[END_REF][START_REF] Castignolles | High-resolution separation of oligo(acrylic acid) by capillary zone electrophoresis[END_REF] above around 10 monomer units, the analysis is undertaken in the critical conditions. This does not refer to a separation mode but to the conditions sought in liquid chromatography in which polymers are not separated according to their molar mass [START_REF] Thevarajah | Separation and characterization of synthetic polyelectrolytes and polysaccharides with capillary electrophoresis[END_REF]40]. The electrophoretic mobility increases as DB decreases [7,[START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF]. Capillary electrophoresis in the critical conditions (CE-CC) can thus separate polyelectrolytes according to their microstructure and allow characterization of the heterogeneity of branching. By heterogeneity, we mean that different macromolecules within the same samples can differ by their branching, namely number of branches per macromolecule, but also position of the respective branching points along the polymer chain, distribution of molar masses of the branches etc. CE-CC was used in this work to determine the dispersity of the electrophoretic mobility distributions. As different branching topologies lead to different electrophoretic mobilities in the case of poly(sodium acrylate), the obtained values of dispersity are representative of the heterogeneity of branching [START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF].

The aim of this study was to characterize the structure of PAA (synthesized by conventional radical polymerization) by ESI-MS, solution-state NMR spectroscopy and CE-CC. From these three methods, the influence of different parameters -temperature, initial monomer concentration and presence of CTA -on the chemical structure of PAA was determined in order to better understand the mechanism and kinetics of polymerization.

Experimental section 2.1. Materials

Acrylic acid (AA, 99%), 4,4'-azobis(4-cyanovaleric acid) (75%+) and thioglycolic acid (98%) were supplied by Sigma-Aldrich. Deuterium oxide (99.9% D), NaOD (40% in D 2 O) and DCl (35% in D 2 O) were supplied by Cambridge Isotope Laboratory Inc. Traces of PAA were found in the deuterium oxide at the last stage of the experimental work. The effect of the contamination on this study was tested and results are available in the supplementary data (Figures S15 andS16). Methanol (analytical grade) was supplied by Merck. Tetrahydrofuran (THF, HPLC grade) was passed through a solvent purification system [START_REF] Pangborn | Safe and convenient procedure for solvent purification[END_REF].

Acetonitrile and methanoic acid (analytical grade) were provided by Fluka. Water was of Milli-Q quality.

Boric acid (≥ 98%) was purchased from BDH AnalaR, Merck Pty Ltd. Sodium hydroxide pellets and dimethyl sulfoxide, DMSO, were supplied by Sigma Chemical Company. One PAA sample was received from Sigma-Aldrich (catalog number: 026C; lot number: 100416003). The linear PNaA was obtained from PSS (Mainz, Germany), as described in [7].

4,4'-azobis(4-cyanovaleric acid) was used as received. Thioglycolic acid and acrylic acid were distilled under reduced pressure.

2.2.

Synthesis Into a 50 mL Schlenk round-bottom flask were added 12.4 mg of 4,4'-azobis(4-cyanovaleric acid) (to give a concentration of 2.00  10 -3 mol L -1 for polymerization), 3.00 mL of acrylic acid (1.99 mol L -1 for polymerization), 0.0 or 0.3 mL of thioglycolic acid (0.0 or 0.2 mol L -1 for polymerization) and 22 mL of solvent (H 2 O/THF 8/2 v/v). This solvent mixture was chosen because it has been found to be efficient for chain transfer to thioglycolic acid [START_REF] Loubat | Telomerization of acrylic acid with thioglycolic acid -Effect of the solvent on the C-T value[END_REF]. The amount of CTA was chosen in order to obtain a DP n close to 10, and thus facilitate analysis of these (short) polymers by ESI-MS. The Schlenk round bottom flask was degassed by bubbling nitrogen through the solution for 30 min. The mixture was left under stirring at 50, 70 or 90 °C for 24 h, 6 h or 1 h, respectively. After these reactions times, the samples were quenched in ice water. THF was evaporated using a rotary evaporator and the remaining aqueous solution was freeze-dried for 48 h. Then, a white powder was collected. Polymerization at 90 °C without CTA was repeated with different amounts of solvent (14.6 mL and 44 mL, corresponding to 3.00 mol L -1 and 0.99 mol L -1 , respectively, of acrylic acid) in order to study the influence of the initial monomer concentration on the structure of the polymer. Reaction times were chosen to give high conversion (see Table S1). The monomer conversions were shown to be higher than 88 % by both 1 H NMR spectroscopy and CE (see Figure S2 and Table S2). The samples for ESI-MS analysis were prepared as follows: 1 mg of PAA was dissolved in 1 mL of water/methanol (1/1 v/v). The samples were injected into a Thermo Fisher Scientific Dionex UltiMate 3000 liquid chromatography (LC) system (without a column) comprised of an Ultimate 3000 RS Pump, 3000 RS Autosampler, 3000 RS Column Compartment, 3000 Diode Array Detector. The LC system was attached to a Bruker maXis 3G Ultra High Resolution Time of Flight tandem mass spectrometer (Bruker Daltonics). The isocratic mobile phase comprised 0.1% (v/v) formic acid and 50% (v/v) acetonitrile in water at a flow rate of 300 µL min -1 (operator a) and 200 µL min -1 (operator b). Ions were generated by electrospray ionization (ESI) and cleaned of solvent by a nitrogen flow of 8.0 L min -1 , temperature of 200 °C, nebulizer at 1 bar, end plate offset at 500 V, capillary voltage at 4000 V, and analysis in positiveion mode. The intensity of positive ions was recorded in the range of 30-2414 m/z (operator a) and 100-3000 m/z (operator b), at a rate of 2 s -1 and analysed using Bruker Compass HyStar 3.2 -SR 2 (Build 44).

Mass spectrometry

The voltage peak to peak was 3000 Vpp (operator a) and 1200 Vpp (operator b).

NMR spectroscopy

Spectra of PAAs synthesized by conventional radical polymerization with and without CTA were acquired in D 2 O at 26 °C ( 1 H NMR spectra) or 49 °C ( 13 C NMR spectra) on an Agilent 400 MR with Varian 7600-AS auto-sampler, equipped with a OneNMR probe and variable temperature capabilities, operating at Larmor frequencies of 399.84 MHz for 1 H and 100.55 MHz for 13 C. The presence of thioglycolic acid during the synthesis is expected to influence the chain length and DB. The solubility of the PAAs in D 2 O and the signal to noise ratios (SNRs) of the peak of the quaternary carbon thus vary, and so some conditions of analysis (number of scans, concentration of PAA in D 2 O) were adjusted for each sample.

The polymer concentrations for 13 C NMR analyses are given in Table S5. For the 1 H NMR analyses, a few mg of PAA were dissolved in a few tenths of mL of D 2 O. The volume of D 2 O was measured with a plastic syringe. One-dimensional 1 H NMR spectra were acquired with 16,384 data points, 128 scans, 16 ppm spectral width (6,410.3 Hz), 40 s relaxation delay, 2.556 s acquisition time and a 90° flip angle. Onedimensional 13 C NMR spectra were recorded with 32,768 data points, 16,500 to 19,000 scans, 246.8 ppm spectral width (25,000 Hz), 10.0 s relaxation delay and a 90° flip angle with inverse-gated decoupling.

The chemical shift scales were calibrated for 1 H and 13 C NMR spectra by measuring spectra of acrylic acid with methanol in D 2 O. The 1 H and 13 C NMR signal assignments are provided in Tables S7 andS8, and examples of the NMR spectra are shown in Figures S3 to S6. In order to assign each peak, 2D COSY and HSQC NMR experiments were carried out (see Figure S7).

One-dimensional T 1 -relaxation time experiments have determined that a relaxation delay of 10.0 s with an acquisition time of 1.311 s is sufficient to ensure quantitative results (acquisition time + relaxation delay > 5  T 1 ) (see Figure S8). The inversion recovery experiment was carried out with one value of τ between the two pulses. Another inversion recovery experiment established that a 6.5 s relaxation delay with a 1.311 s acquisition time is insufficient for a full recovery of these signals (see Figure S9). The inversion recovery experiments are described in detail in the supplementary data. Estimations of the T 1 of the C q signal are given in table S9.

DB was quantified in percentage of monomer units by comparing the integrals, I, of C q at 48 ppm and of the main chain CH at 39-42 ppm as follows:

𝐷𝐵(%) = 100 • 𝐼(C q ) 𝐼(C q ) + 𝐼(CH) (1)
For thiol-containing PAA, the carbon called C thiol , meaning the carbon of the CH adjacent to the thioglycolic acid end group-residue (i.e. adjacent to the sulfur atom), exhibited a signal at 44 ppm. This is overlapping with the main-chain CH signal (see Figure S6). An over-and underestimation of DB were calculated as follows for thiol-containing PAA. For the overestimation, the integral of the CH signal excluded the contribution of the overlapping C thiol signal by setting the left integration limit to the valley between the C thiol and CH signals (Eq. ( 2)). For the underestimation, the integral of the CH signal included the contribution of the overlapping C thiol signal by setting the left integration limit to the left of the C thiol signal (Eq. ( 3)).

𝐷𝐵 𝑜𝑣𝑒𝑟𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 (%) = 100 • 𝐼(C q ) 𝐼(C q ) + 𝐼(CH) excluding overlapping C thiol (2) 𝐷𝐵 𝑢𝑛𝑑𝑒𝑟𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 (%) = 100 • 𝐼(C q ) 𝐼(C q ) + 𝐼(CH) including overlapping C thiol

The signal of C q of in the 13 C NMR spectrum of PAA synthesized at 50 °C without CTA was observed with a SNR < 3, which is the limit of detection (LOD). To have an estimate of a "potential" maximum degree of branching, the SNR of the main chain CH signal and the one of the C q signal were compared (see Eq. ( S2) and (S3)).

The PAA from Sigma Aldrich was analyzed at room temperature on a Bruker DRX300 spectrometer (Bruker, Biospin Ltd, Sydney) equipped with a 5 mm dual 1 H/ 13 C probe at Larmor frequencies of 300.13

MHz for 1 H and 75 MHz for 13

𝐷𝐵(%) = 100 • 𝐼(𝐶 𝑞 ) 𝐼(𝐶𝑂𝑂𝐻) (4)
This equation was also used to obtain another estimate of DB for all samples of this work (Table S9).

The relative standard deviation (RSD) of DB (in percent of DB values) was calculated from the signal-tonoise ratio (SNR) of the quaternary carbon C q using Eq. ( 5), which was established for branching measurements in polyethylene by combination of both derivation from calculation error and empirical results [START_REF] Klimke | Optimisation and application of polyolefin branch quantification by melt-state 13C NMR spectroscopy[END_REF] and assessed to be accurate also for branching measurements in hydrophobic polyacrylates [20].

𝑅𝑆𝐷 =

238 𝑆𝑁𝑅 1.28 (5)

Capillary electrophoresis

The instrument and conditions were as in [7]. The preparation of a 110 mM sodium borate buffer at pH 9.2 was as in [7]. For each sample, 10 mg of PAA were dissolved in 1.5 mL of Milli-Q water with a small volume of sodium hydroxide solution (15 μL, 1 mol L -1 in Milli-Q water). 500 µL of dissolved PNaA were mixed with 10 μL of 10 wt. % aqueous DMSO (added as an electroosmotic flow marker). Each sample was diluted several times with Milli-Q water until repeatable normalized electrophoretic mobility distributions at two successive concentrations were obtained (see Table S11 as well as Figures S18 andS19). The separations were performed with a high sensitivity, 50 μm internal diameter fused-silica capillary (Agilent, Australia) with a total length of 62.2 cm and an effective length of 53.7 cm at 30 kV and 25 °C. The electrophoretic mobility distributions and their dispersities were calculated from the raw electropherograms, as in [START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF] (see also Eq. (S10) to (S13)). Electrophoretic mobility is preferred to migration time because it is more repeatable and it characterizes the topology of polymers [START_REF] Thevarajah | Separation and characterization of synthetic polyelectrolytes and polysaccharides with capillary electrophoresis[END_REF]. The pH of each PNaA sample before injection was measured to be between 4 and 5 (using a pH meter). In order to check if incomplete dissolution due to low pH influences the electropherograms, the samples were titrated until pH > 8 and CE experiments were repeated in similar conditions. Electrophoretic mobility distributions of PNaA dissolved at acidic and basic pH are reproducible in terms of shape and electrophoretic mobility (Figure S20). However, an effect on the peak area of the electropherogram exists. This issue will not be discussed at this stage. Data was treated with the Origin 9.0 software. The pH meter was a SevenCompact™ pH/Ion meter S220 (Mettler Toledo), calibrated with internal standards with pH values of 4, 7 and 9.2 or 4, 7 and 10.

3.

Results and discussion

The PAAs synthesized in the presence and in the absence of thiol were characterized in terms of end groups, chain length and branching. They were compared to other PAAs (or PNaAs). Table 1 summarizes all polymers used to carry out this study and how they were synthesized. Hyperbranched PAA [7] Nitroxide mediated Alkoxyamine/SG1/acrylic acid/1,4-dioxane 50 % 12,300 g.mol -1 polymerization *: the monomer conversion of AA was estimated using 1 H NMR spectroscopy and CE (See Table S2 and Figure S1.

#: from the supplier, determination method not given.

End groups by ESI-MS

Figure 1 shows the mass spectra of PAAs synthesized with thiol at 50, 70 and 90 °C. When synthesized without CTA, no peaks were observed, as high molar mass components tend to ionize poorly [START_REF] Leenheer | Molecular resolution and fragmentation of fulvic acid by electrospray ionization/multistage tandem mass spectrometry[END_REF]. When the PAA is synthesized at 70 °C with CTA, the number-average degree of polymerization, DP n , is expected to be about 10 [START_REF] Loubat | Telomerization of acrylic acid with thioglycolic acid -Effect of the solvent on the C-T value[END_REF] (i.e. number-average molar mass, M n , of about 813 g.mol -1 , this being the molar mass of 10 acrylic acid units inserted into a thioglycolic acid molecule).

According to the ESI-MS spectra, the majority of the species have the same end groups (HOOC-CH 2 -S of CTA at one end and H at the other). The different families of peaks observed for the PAA obtained at 50, ). [START_REF] Strohalm | mMass -Open Source Mass Spectrometry Tool[END_REF] The average size of the polymer is, of course, reduced by transfer from propagating radicals to a CTA. No terminal double bond was detected in the polymers obtained at any of the three polymerization temperatures, which is a similar trend to the the results of Junkers et al., who found that the presence of a CTA reduces the amount of β-scission in poly(alkyl acrylates) [START_REF] Junkers | Mapping poly(butyl acrylate) product distributions by mass spectrometry in a wide temperature range: Suppression of midchain radical side reactions[END_REF]. This should also apply to PAA.

Determination of the average degree of branching

As the PAAs synthesized by conventional radical polymerization and the PAA provided by Sigma were analyzed in different conditions (temperature and pH), the influence of these physical parameters on the required time for precise, quantitative measurement of DB by 13 C NMR spectroscopy was studied.

The temperature and magnetic field of the NMR spectroscopy analysis, as well as the electronic configuration of the analyzed molecule -the PAA provided by Sigma was analyzed as PNaA -influence the relaxation delay, T 1 , of its nuclei. When the molecule is charged and the temperature is lower, T 1 decreases. A repetition delay of 6 s was sufficient to have quantitative results when PAA was analyzed at room temperature and with NaOD, whilst a repetition delay of 7.811 s was insufficient to obtain a quantitative 13 C NMR spectrum of PAA when analyzed at 49 °C in D 2 O without NaOD. At room temperature and with 27,411 scans, a higher SNR is observed than at 49 °C with 17,500 scans, but the resolution is lower (see Figures S11 andS12). Table S6 sums up all the conditions for analyses of branching in PAA or PNaA by 13 C NMR spectroscopy that have been reported in the literature. The SNR of the C q peak is never given in the literature and the time of analysis is not always mentioned.

Moreover, even when it is claimed that the analyses are quantitative, the T 1 measurement experiment is not always mentioned, while it is the only way to know whether or not the conditions for quantitative analysis are met. Consequently, it was not possible to determine the optimal conditions of analyses based on literature. Figure 2 shows the partial 13 C NMR spectra of PAAs synthesized at 90 °C with and without CTA.

The different values obtained for DB (with Eq. ( 1), ( 2), ( 3) and ( 4)) are similar (and in the same range if the RSD is taken into account). The dissolution of polymers is a process whose complexity is regularly underestimated. [START_REF] Miller-Chou | A review of polymer dissolution[END_REF][START_REF] Thevarajah | Towards a less biased dissolution of chitosan[END_REF] For example in the case of starch, transparent liquids resisting to centrifugation were shown by NMR spectroscopy to still be incompletely dissolved. [START_REF] Schmitz | Assessment of the extent of starch dissolution in dimethyl sulfoxide by 1H NMR spectroscopy[END_REF] Some inaccuracies of DB measurement could be due to incomplete dissolution of PAA in D 2 O (especially for the CTA-containing PAAs). The solubility of PAA in D 2 O was tested by comparing the 13 C NMR spectra of different PAAs using the normalized peak area to noise ratio, defined as follows.

The "peak area to noise ratio" (PNR) of a NMR signal is defined as the absolute peak area divided by the Results are presented in Figure S13. Similar calculations were carried out using the SNR instead of the PNR. Results are presented in Figure S14. However, PNR is preferred to SNR as it is not demonstrated that the height of the signal is proportional to the amount of sample.

In the case of PAAs synthesized with CTA, a significantly lower normalized PNR than in the case of the linear PNaA is observed for both COOH and CH backbone signals, which suggests that they are less dissolved in D 2 O. This could be due to the presence of sulfur in the end group. Consequently, DB values obtained for these two samples may be less accurate than the ones measured in the other PAAs.

Values of the average DB

DBs obtained for CTA-containing polymers are significantly lower than the ones obtained in conventional systems at 70 °C and 90 °C (Figure 3b). Thus the CTA reduces not only the average chain length of the polymer but also DB. Of course reduction of average chain length also reduces the number of branches per chain, as observed in PLP [START_REF] Junkers | Mapping poly(butyl acrylate) product distributions by mass spectrometry in a wide temperature range: Suppression of midchain radical side reactions[END_REF]. However, DB is expressed per monomer unit and not per chain, and so the reduction of DB is a different phenomenon, as conventional transfer to CTA does not change the macroradical concentration and consequently should not change the frequency of transfer to polymer reactions. One likely explanation is the patching effect of tertiary MCRs by CTA, as postulated for poly(n-butyl acrylates) [17]. Another possible explanation for the reduction of DB due to the presence of a CTA is the lowering of the number of backbiting events in comparison to propagation of SPRs [START_REF] Ballard | The role of chain transfer agent in reducing branching content in radical polymerization of acrylates[END_REF][START_REF] Ballard | Reevaluation of the formation and reactivity of midchain radicals in nitroxide-mediated polymerization of acrylic monomers[END_REF], since the time of polymerization is shorter for the PAA synthesized in the presence of the CTA. This difference might also be exacerbated by unintended temperature increase. Although in laboratory experiments like these one strives to maintain constant temperature, the polymerizations were performed in round-bottom flasks with magnetic stirring and the fast rates of acrylate polymerizations sometimes give rise to an exotherm, even in relatively dilute solution. In the absence of CTA, chains will be longer, and hence solutions more viscous. This makes heat transfer more difficult, and hence exotherm effects more likely. Such would give an enhancement of DB, as observed. DB increases with the temperature. This can be explained by the increase of frequencies of the reactions that lead to MCRs, viz. inter-and intramolecular (chain) transfer. Typical activation energies of these transfer reactions are between 20 and 25 kJ mol -1 higher than that of chain-end (as opposed to midchain) propagation in the case of alkyl acrylates [13]. Wittenberg et al. tabulated the activation energy of backbiting and chain-end propagation steps for polymerization of non-ionized acrylic acid as being 38 and 13 kJ mol -1 respectively [18]. These values were calculated for batch radical polymerization of 5 to 40% non-ionized acrylic acid in aqueous solution between 40 °C and 90 °C. In this study, the temperatures and monomer concentration are within the same range but acrylic acid was polymerized in water/THF (8/2 v/v)), also in batch. Thus conditions were essentially the same, apart from having 20% THF as solvent rather than 100% water.

Figure 3b shows that as temperature is increased, the effect of CTA on DB becomes stronger, i.e. there is a bigger gap between DB with and without CTA: at 50 °C there is no difference within the limit of detection, but at 90 °C the value with 0.2 mol L -1 CTA is about one third of what it is without. An obvious explanation for this is that the patching reaction becomes more prominent as the temperature increases.

Wittenberg et al. [18] also quantified DB of PAA produced by radical polymerization in water without CTA at high conversion (> 95 %) in a similar range of temperatures (40 °C to 90 °C). Their results (DB from 0.48 % to 1.60 %) are close to the ones in this study (and are in the same range taking the error bars into account). Figure 4 The present DBs -for PAA synthesized in water/THF (8/2 v/v) -are lower than for poly(n-butyl acrylate) (PnBA) synthesized in bulk by Gaborieau et al. between 60 and 140 °C. To be precise, these PnBAs have DBs of 2 to 5 % when synthesized without CTA and 0.7 to 2 % when synthesized with CTA. [17] Both these minimum values are lower than those obtained at 90 °C in this work (see Figure 3b). This could possibly be explained by a lower rate of intermolecular chain transfer when polymers are in dilute solution: polymers do not overlap and consequently DB is reduced. Dilution by water also favors the propagation through an entropic effect: the strong hydrogen bonding between the water and the propagating radicals creates disorder (thus lowering the pre-exponential factor of the propagation rate coefficient) [START_REF] Degirmenci | Origins of the solvent effect on the propagation kinetics of acrylic acid and methacrylic acid[END_REF]. The propagation rate coefficient of AA was observed both experimentally and theoretically to strongly increase with dilution by water. Dilution and H-bonding may also reduce the formation of branching points (by intramolecular transfer to polymer). As water forms H-bonding with the carboxylic group of the acrylic acid unit, the dilution by water could explain the discrepancy between this work and results from Gaborieau et al.. However, the most likely explanation for the lower DB is simply that backbiting relative to propagation is slower in AA than in n-butyl acrylate.

The initial monomer concentration does not seem to have any influence on DB (Figure 3a). Indeed, DBs at initial [AA] = 1 mol L -1 , 2 mol L -1 and 3 mol L -1 (which correspond to 7.3 to 18.1 wt.%) are comparable.

As explained previously, the chain length, which depends on the monomer concentration, does not directly influence DB. Rather, it confirms the assumption that DB does not decrease with the chain length. The initial monomer concentration may influence the number of branches per chain but not the number of branches per monomer unit. The monomer conversion could also play a role here, as the rates of polymerization and of branch formation depend on the monomer conversion: the cumulative DB is expected to increase significantly when above 90 % monomer conversion [18,[START_REF] Nikitin | The Effect of Intramolecular Transfer to Polymer on Stationary Free-Radical Polymerization of Alkyl Acrylates, 3-Consideration of Solution Polymerization up to[END_REF]. The syntheses at initial monomer concentrations of 1, 2 and 3 mol L -1 may not have led to exactly the same monomer conversion. According to Wittenberg et al.'s simulations, even a small difference of conversion above 90 °C would lead to different DBs. As the syntheses of PAAs at 3 different monomer concentrations were carried out using the same reaction time, this is quite possible. Another issue that could lead to these results is an exotherm. As explained previously, this issue becomes more important in viscous solutions, and could explain the results observed at different monomer concentrations (the increase in monomer content leads to more viscous solutions). Another explanation can be based on observations by Lovell et al. at high conversion (on n-butyl acrylate) [19] and Loiseau et al. for the RAFT polymerization of acrylic acid [6]: branches can result from intermolecular chain transfer to polymer reactions, whose rate does not depend on the initial monomer concentration as soon as the polymer concentration is above the critical overlapping concentration, c*. Since all the syntheses of PAA without CTA have been done mostly above c*, there is thus the possibility of intermolecular chain transfer, leading to DB roughly independent of initial monomer concentration. Of course backbiting is assumed to dominate in most cases, especially in PLP ( even if LCB was detected for poly(alkyl acrylates) obtained by PLP [11]). It cannot be affirmed that the branching is mostly due to intermolecular transfer to polymer. Finally, as the relative standard deviation of DB of PAAs synthesized at 90 °C without CTA is quite large (up to 20 %), the precision of these results is relatively limited. Some variations of DB, lower than 20%, may exist.

Wittenberg et al. observed potentially different results. When the polymerization occurs at 40 °C and 70

°C, a potential decrease in DB is observed when the initial monomer concentration is increased from 10 to 20 wt.% [18]. This is in line with expectation: as monomer concentration is increased, the frequency of propagation (a bimolecular process) is increased whereas the frequency of backbiting (a unimolecular process) remains unchanged, and thus the fraction of branches decreases. This has been observed in most other works, and thus doubt is cast on the present results for DB as a function of initial [AA].

However, as the standard deviation is not given by Wittenberg at al., it is impossible to know whether or not their observed differences are significant. Moreover, it is not proven that their 13 C NMR analyses are quantitative (it was not shown that the repetition delay was greater than 5T 1 ).. The presence of a nonsoluble fraction, whose branching would not be detected and quantified by solution-state NMR, could also play a role.

The present results were compared with DB of a PAA provided by Sigma Aldrich. This PAA has an expected number average molar mass M n = 240 000 g mol -1 (it is however to be noted that determination of PAA molar mass suffers from a poor accuracy [12,[START_REF] Berek | Size exclusion chromatography -A blessing and a curse of science and technology of synthetic polymers[END_REF]). A DB was measured in this work as 1.13 ± 0.07 %. This value is in the same range as DBs of PAAs synthesized by conventional radical polymerization without CTA, which suggests that it may have been synthesized using similar experimental conditions.

Backbiting rates coefficients

Assuming, reasonably, that the loss of MCRs by transfer (in the absence of transfer agent), β-scission and termination by disproportionation is negligible, then every backbiting event leads to a branching point, and thus the fraction of branching points is given by the ratio of the rate of backbiting to the rate of propagation. The rate of propagation is not constant during a polymerization but Nikitin et al. were able to link the DB to the ratio of the backbiting to the propagation rate coefficients as in Eq. ( 6):

𝐷𝐵 (%) = 𝑘 bb 100 (ln ([M] 0 /([M] e ) 𝑘 p ([M] 0 -([M] e ) (6)
Where [M] 0 is the initial monomer concentration and [M] e is the final monomer concentration. Thus from a measurement of DB one can very easily obtain k bb /k p , where this k p refers to chain-end (secondary-radical) propagation. Wittenberg et al. [18] were able to use an even simpler expression since they used low-conversion conditions in their particular experiments to determine k bb /k p from DB.

In the present case our results are from batch polymerization in which conversion traversed from 0 % to nearly 100 % and equation ( 6) is thus used instead. If one uses DB values of similar precision and accuracy, then Wittenberg et al.'s expression should lead to more accurate values since it is not impacted by the uncertainty on the determination of the conversion.

To obtain individual values of k bb , the value of k p was needed. This was calculated using Eq. (S6) given in [18], which is re-estimated from an earlier PLP-SEC study on non-ionized AA [START_REF] Lacik | Aqueous phase size-exclusion-chromatography used for PLP-SEC studies into free-radical propagation rate of acrylic acid in aqueous solution[END_REF] Figure 5 is an Arrhenius plot for k bb obtained in both the presence and absence of CTA in water/THF (8/2 v/v) compared with the Arrhenius equation tabulated by Wittenberg et al. [18] and Barth et al. [START_REF] Barth | SP-PLP-EPR study into termination and transfer kinetics of nonionized acrylic acid polymerized in aqueous[END_REF].

Wittenberg et al.'s equation was obtained by combining their k bb from a handful of low-conversion DB

(from polymerization in pure water) with a larger data set from Barth et al. [START_REF] Barth | SP-PLP-EPR study into termination and transfer kinetics of nonionized acrylic acid polymerized in aqueous[END_REF], who used single pulsepulsed laser polymerization -electron paramagnetic resonance (SP-PLP-EPR) spectroscopy experiments to determine k bb , also at low-conversion conditions. These experiments involve monitoring of EPR signals on a microsecond timescale over which the conversion of chain-end radicals into MCRs can be observed. Eqs. ( 8), ( 9) and (S8) represent, respectively, the Arrhenius fits for k bb calculated from DBs of this study in both the absence and presence of CTA; and from Wittenberg et al. at low conversion [START_REF] Barth | SP-PLP-EPR study into termination and transfer kinetics of nonionized acrylic acid polymerized in aqueous[END_REF].

The linear fits parameters are presented in table S11. The linear fit for the PAA obtained in this work in the absence of CTA gave a Pearson's R 2 coefficient of 0.56 only with the point for the polymerization at 90 °C and 1 M monomer concentration looking like an outlier. This point was removed and the Pearson's R 2 coefficient increased to 0.996. The parameters for both fits are given in Table S11, but only the fit excluding 1 M monomer concentration is given on figure 5. The RSD of ln k bb was calculated based on the RSD of DB, according to Eq. (S9), which assumes that the error on k bb only depends on the error on DB. The error is not visible on the graph as it is negligible (between 4  10 -7 and 4  10 -4 ). This high precision is distinct from the accuracy of these measurements, which is likely lower than in previous works due to the high monomer conversion. 𝑘 𝑏𝑏 (𝑠 -1 ) = 2.99 × 10 9 (𝑠 -1 ) 𝑒 -5066 𝑇/𝐾 (8) 𝑘 𝑏𝑏 (𝑠 -1 ) = 5.20 × 10 8 (𝑠 -1 ) 𝑒 -4777 𝑇 /𝐾 (9) In Figure 5 the (apparent) activation energy of k bb is similar in the presence of CTA. The pre-exponential factor is, however, lower in the presence of CTA. As previously explained, the presence of CTA might reduce the number of backbiting steps as the macroradical polymerizes for a shorter time [START_REF] Ballard | The role of chain transfer agent in reducing branching content in radical polymerization of acrylates[END_REF]. Another hypothesis is the invalidity of Eq. ( 6) in the presence of CTA. Given that a patching effect is possible some MCRs could not lead to a branched chain, thus DB would not be directly related to k bb . In effect this is a breakdown of the assumption that all MCRs undergo propagation rather than any other reaction (see above).

The k bb values observed in this study in the absence of CTA are a bit more than 170 % lower than the ones determined by Wittenberg et al. Several explanations are possible. First, the observed differences could just be due to different systematic error (for example due to incomplete dissolution in some cases). Second, the high conversion in this work leads to a lower accuracy of the determined k bb values for at least three potential reasons: (i) the uncertainty on the value of the monomer conversion, (ii) the non-validity of the assumption that k p is constant, (iii) intermolecular chain transfer to polymer may not be negligible. . In the case of Wittenberg et al., the conditions to obtain quantitative DB values were not checked and the RSD of DB was not provided at all.

On Figure S17 no proportionality between DB and 1/[M] 0 is observed.

Heterogeneity of branching

While the average DB has been determined for PAAs obtained in a number of different polymerization conditions in this work and in the literature, the variation of DB from macromolecule to macromolecule within a given sample has not been examined. CE-CC provides important information related to the heterogeneity of branching. This heterogeneity is not just due to different DBs within a sample but also different positions of the branching points or a distribution of molar masses of the branches. As polymers are separated according to their topology and not according to their size in CE-CC, the dispersity of the distribution of electrophoretic mobilities is related to the heterogeneity of branching [START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF]. It is in contrast with SEC with which polymers are separated according to their hydrodynamic volume [START_REF] Grubisic | A universal calibration for gel permeation chromatography[END_REF] (which depends on both the molar mass and the branching). Multiple-detection SEC allows measurement of local weight-and local number-average molar mass as well as their ratio Ð(V h ). Values of the local dispersity Ð(V h ) (of the local molar mass distribution) primarily inform the accuracy of the determined molar mass but also provide indirect information on the heterogeneity of branching. In the case of poly(alkyl acrylates), the most heterogeneous samples (in terms of branching) were shown to be obtained for low DBs [11,20]. Multiple-detection SEC is however not only an indirect characterization method for the branching, but also a tedious method. Free-solution CE allows much higher throughput and simple characterization of the branching [7,[START_REF] Thevarajah | Separation and characterization of synthetic polyelectrolytes and polysaccharides with capillary electrophoresis[END_REF]. The dispersity of the electrophoretic mobility distributions was calculated in this work as a standard deviation [START_REF] Chamieh | Quantitative analysis in capillary electrophoresis: Transformation of raw electropherograms into continuous distributions[END_REF], and as a ratio of four moments of the mobility distribution [START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF]. The dispersities of the distributions of electrophoretic mobilities D(W(µ),1,0), D(W(µ),2,0), D(W(µ),3,0) and D σ were calculated according to Eq. (S10) to (S13) [START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF].

D(W(µ),1,0) is calculated as the ratio of the first and zeroth order moments divided by the ratio of the zeroth and -1 st order moments. It is in analogy with M w /M n where M w is the weight-average molar mass.

D(W(µ),2,0) is calculated as the ratio of the second and first order moments divided by the ratio of the first and zeroth order moments. It is in analogy with M z /M w where M z is the z-average molar mass.

D(W(µ),3,0) is calculated as the ratio of the third and second order moments divided by the ratio of the second and first order moments. The last dispersity Dσ is calculated as a standard deviation of the weight distribution of electrophoretic mobilities. The weight-average electrophoretic mobility µ W is the equivalent of the weight-average molar mass in term of electrophoretic mobility. µ W is determined as the ratio of the first and zeroth order moments of the mobility distributions and is given by Eq. (S14) [START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF]. The values of the different dispersities and of the µ W of the different PNaAs are given in Table S13.

The electrophoretic mobility distributions of branched PNaA exhibit two peaks (see Figure 6) that are not resolved. This is not the case for the linear PNaA, whose electropherogram exhibits only one peak.

The bimodal shape of branched PNaA was already observed in previous work [7,[START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF]. The relation between the polymer structure and it electrophoretic mobility can be undertaken using a "slope plot" [START_REF] Ibrahim | Extracting Information from the Ionic Strength Dependence of Electrophoretic Mobility by Use of the Slope Plot[END_REF] but this beyond the scope of this work. The dispersities of electrophoretic mobility distributions were calculated on the whole distributions of electrophoretic mobilities in order to assess the heterogeneity due to branching in each individual PNaA sample. As a DP n around 10 is expected for the PAAs synthesized at 50 °C, 70 °C and 90 °C with CTA [START_REF] Loubat | Telomerization of acrylic acid with thioglycolic acid -Effect of the solvent on the C-T value[END_REF], their separation and analysis by capillary electrophoresis are not expected to be in the critical conditions and are thus not considered in this study of the heterogeneity of branching (the distributions are broader in the case of CTA-containing polymers than non-CTA containing polymer, as observed in figures S18 and S19 due to the combined influences of molar mass and branching). The evolution of the dispersity of electrophoretic mobility distributions with DB is shown on Figure 8.

The dispersity of electrophoretic mobility distributions of the PNaAs produced by conventional radical polymerization is compared with those of the linear PNaA and of a hyperbranched PNaA [START_REF] Thevarajah | Quantifying the heterogeneity of chemical structures in complex charged polymers through the dispersity of their distributions of electrophoretic mobilities or of compositions[END_REF] produced by nitroxide-mediated polymerization in the presence of an alkoxyamine inimer, leading to a DB estimated at 3.9 ± 0.1 %. The synthesis of the hyperbranched PNaA is described elsewhere in detail [7].

The linear PNaA has the lowest heterogeneity of branching as all chains are unbranched (the dispersity should be equal to unity, the lowest value possible, as no heterogeneity from branching is expected).

The heterogeneity of branching of the hyperbranched PNaA (produced by controlled polymerization and with a DB of 3.9 ± 0.1 %) is higher than the ones observed for the PNaAs produced by conventional radical polymerization. When PNaAs are produced by conventional radical polymerization, branching results only from inter and intramolecular (chain) transfer to polymer. Only LCB and SCB are expected.

Branching initiated by the inimer is also expected in the case of the hyperbranched PNaA, which may explain the higher heterogeneity. A higher Ð(V h ) was also observed for poly(alkyl acrylates) produced by controlled radical polymerization than by conventional radical polymerization [START_REF] Gaborieau | Separation of complex branched polymers by size-exclusion chromatography probed with multiple detection[END_REF]. The dispersities determined in this work should relate to the local dispersities Ð(V h ) which could also be determined by multiple-detection SEC but have not been reported in the literature for PAA or PNaA. The lowest dispersity of the electrophoretic mobility distribution should correspond to the lowest Ð(V h ) and thus the most accurate determined molar mass. The higher dispersities observed for PNaAs produced by radical polymerization can be explained by branching and is one likely cause of the low accuracy of the molar mass of PNaA (or PAA, or equivalent) determined by SEC [12]. Figure 9 shows the evolution of the dispersity with µ W , and confirms that the more a polyelectrolyte is branched, the lower the mobility is.

The same phenomenon as in Figure 7 is observed. The hyperbranched PNaA produced by controlled radical polymerization has the highest dispersity of the electrophoretic mobility distributions and, as the highest DB, the lowest mobility and the linear PNaA which has no branches has the highest mobility (as expected).

Conclusion

In this paper, DB was measured with quantitative 13 C solution-state NMR spectroscopy and the heterogeneity of branching was measured by CE-CC. These were both done for PAA synthesized in both the presence and absence of thioglycolic acid at various temperatures and initial monomer concentrations. The presence of thiol decreases DB, the so-called "patching effect" is observed for PAA, exactly as it has been for other acrylic monomers. However, the reduction in DB may also be due to a decrease of the number of backbiting steps in comparison to propagation steps. DB was observed to increase with the temperature. This is due to an acceleration of the reactions which lead to the formation of branching points (transfer to polymer). When PAA is synthesized at 90 °C without a CTA, the initial monomer concentration (1, 2 and 3 mol L -1 ) does not appear to influence the degree or the heterogeneity of branching, although this observation for DB is not commensurate with other observations, both in this work and in the literature. This might be due to unintended temperature increase over the polymerization process, slight differences in monomer conversion, or the limited precision of the analyses. PAA produced by conventional radical polymerization is not only branched, but different macromolecules within a sample are branched differently. The heterogeneity of branching observed for a linear PNaA is negligible, as it should, and lower than the one of the PNaAs synthesized by conventional radical polymerization, which is in turn lower than the one of the hyperbranched PNaA (synthesized by nitroxide-mediated polymerization). The heterogeneity increases with the diversity of branching structures. Moreover, it is confirmed that the electrophoretic mobility decreases with the increase of branching. This work provides relevant information for a systematic variation of reaction conditions that can be used for future kinetic and mechanistic studies, which will help to optimize conditions for poly(acrylic acid) synthesis in numerous applications. 24.9 mn * Calculated using a frequency factor of 6.21  10 15 s -1 and an activation energy of 132.9 kJ mol -1 [2]

5.

Synthesis of poly(acrylic acid)

Determination of the monomer conversion

Monomer conversion in acrylic acid polymerization is commonly determined in the literature using 1 H NMR spectroscopy [3,4] and gravimetry [5][6][7][8][9] but also by HPLC [10], UV absorbance at 260 nm, Near-Infrared (NIR) spectroscopy [8,11] (or NIR checked by 1 H NMR [12]) and calorimetry [13].

In the case of PAA synthesized at 50 °C with CTA and [AA]0 = 2 M, the gravimetry indicated an average conversion of 66 % only, but with a standard deviation of 20 % (n=3). The low precision of this gravimetric measurement may add to a low accuracy because of the presence of both THF and water to evaporate in the gravimetry. The monomer conversion was thus also measured by solutionstate 1 H NMR and the conversion was found to be high (Table S-2). The discrepancy between the values determined by gravimetry and 1 H NMR is large with values of 66 % (gravimetry, large error) and 98 % by 1 H NMR on the same sample. The large conversion observed by NMR spectroscopy was thus confirmed by a completely different method, namely free solution capillary electrophoresis (CE). CE of pure acrylic acid monomer leads to 3 full resolved peaks (dashed line on figure S-2). The sodium acrylate is likely the peak at 2.5  10 -8 m 2 V -1 s -1 . The peak at 3.30  10 -8 m 2 V -1 s -1 is likely from poly(sodium acrylate) generated by autopolymerization. It is to be noted that the bottle of acrylic acid used for this experiment was different from the one used for the polymerization (it was provided by Aldrich and the purity was superior to 99%). The small peak at 2.05  10 -8 m 2 V -1 s -1 could be either a dimer or an inhibitor. The preliminary study to determine the monomer conversion was performed with a fused-silica capillary of about 60 cm total length and with sodium borate at pH = 9.2 as buffer at a concentration close to 100 mmol L -1 . The conversion was determined as the ratio of the polymer peak area to the polymer, monomer and dimer peak areas. The UV absorption (Beer-Lambert) coefficient of the monomer is expected to be higher than the one of the carboxylate (chromophore) moiety of the polymer. The peak attributed to the dimer may be another species such as the inhibitor. For both these reasons, we expect these conversion values to be an underestimate of the monomer conversion. The monomer conversion determined by CE is higher than 88 % in the presence of thiol and consistent with the one determined by NMR spectroscopy. The monomer conversion is expected to be at least higher fo the polymerization in the absence of thiol since the rate of polymerization is generally observed to be higher in the absence of transfer agent. S-5

S-3

S-4

Mass spectrometry

Mexp is the experimental molar mass obtained for an adduct, Mth is the theoretical molar mass of the same adduct calculated with the mMass software, and hpeak is the peak height.

NMR spectroscopy

Concentration of PAA for NMR analyses and previous work for assessment of branching in PAA by 13 C NMR spectroscopy:

Table S5: [PAA] in

S-10

S-11

Two-dimensional NMR of PAA In order to identify the signals and to check if some signals of impurities were overlapping with the quantified signals, the COSY and HSQC NMR analyses of PAA were carried out (see Figure S7).

It was shown that nothing is overlapping with the main-chain CH signal (42 ppm) and the branching signal (48 ppm).

S-12

Estimation of the longitudinal relaxation time

In order to obtain quantitative results, it is necessary to have an estimation of the longitudinal relaxation time, T1, of each signal that will be quantified.

The most common experiment used to determine T1 is a so-called inversion recovery experiment [18].

This experiment consists of a 2-pulse sequence. In a first step, the spin population is inverted through the application of a 180° pulse. The magnetization vector will first shrink back toward the X-Y plane and then make a full recovery along the Z-axis at a rate dictated by the relaxation time T1. As the magnetization along the Z-axis is not observable, the vector will be placed back in the X-Y plane with a 90° pulse after a suitable waiting time τ.

For a short τ, the magnetization vector will be located along the negative Y axis, and a negative signal will be observed. For a long τ, the magnetization vector will be recovered and a positive signal will be observed.

The intensity of the detected magnetization Mτ follows Eq. (S1):

𝑀 τ = 𝑀 0 (1 -2𝑒 -𝜏 𝑇 1 ⁄ ) (S1)
So the experiment is repeated for several values of τ, and when extinction of the signal is observed, the waiting time corresponds to 𝜏 null = 𝑇 1 𝑙𝑛2.

The branching was observable with a SNR > 5 only after 53 h (except for the PAA synthesized at 50 °C without CTA). So, it would unpractical and very expensive to perform a full inversion recovery experiment with many values of τ. However it is possible to check if the repetition time between 2 pulses (acquisition time + relaxation delay) used when the branching was detected is greater than 5T1.

In that case, these parameters are valid for quantitative NMR spectroscopy analysis.

The spectra were recorded with 10 s relaxation delay and 1.311 s acquisition time. So, if 11.311 s > 5T1, i.e., if τnull < 1.568 s for Cq and main-chain CH signals, the analysis is quantitative. An inversion recovery experiment with τ = 1.568 s was completed. It was found that the Cq signal and the signals of the main chain CH and the CH adjacent to a branch are positive (see Figure S8). Consequently, the condition for quantitative analysis is fulfilled.

Another experiment was performed to check if a relaxation delay of 6.5 s with an acquisition time of 1.311 s was enough to be quantitative (which means if τnull < 1.082 s). However, Figure S9 shows that the quaternary carbon signal is in its extinction zone (not observable in the spectrum). It may be exactly absent, slightly positive, or slightly negative (below the noise level). Thus it is unsure if a 13 C NMR signal recorded with the corresponding repetition time is quantitative. Sigma-Aldrich ---1.13 16.75 6.45 * For the PAA synthesized at 50 °C without CTA, the SNR was below 3, which means below the limit of detection (LOD). It is thus not possible to confirm whether this polymer is branched or not. To estimate a maximum possible degree of branching, the SNR of the main chain CH signal and the one of the Cq signal were compared as follows (Eq. S3). This equation was used for this one particular case.

S-13

S-14

𝐷𝐵(%) =

S-16

S-17

S-18

Probing the dissolution of PAA in D2O: Dissolution of analytes can be analyzed by NMR spectroscopy [19].

𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑃𝑁𝑅 = 𝑃𝑁𝑅

[𝑎𝑛𝑎𝑙𝑦𝑡𝑒]√𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑎𝑛𝑠 (S4)

The noise was measured in 2 steps. First, the SNR was measured using the ACD/Lab software and then, the height of the signals was measured with the Origin 9.0 software. The peak area was also measured with the Origin 9.0 software by integration of the signal.

The uncertainty of the normalized PNR was calculated based on the uncertainty of the concentration of analyte neglecting the error on the number of scans and the peak area (Eq. S5). The error on the mass was based on the last digit appearing on the scale (mg) and the error on the measured volume was calculated by weighting 5 times 1 mL of MilliQ water taken with 5 different 1 mL plastic syringes (SD1 mL syringes = 0.016936 mL). In the case of the thiol-containing PAA synthesized at 70 °C, there is also an uncertainty on the peak area of main chain CH and Cthiol signals are overlapping. Effect of the contamination of the deuterium oxide:

𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑃𝑁𝑅) = |𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑃𝑁𝑅 𝑚𝑎𝑥 -𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑃𝑁𝑅 𝑚𝑖𝑛 | (S5)

S-19

A 1 H NMR analysis of the D2O used to run the different analyses showed that this solvent has been contaminated with PAA (see Figure S15). In order to test the effect of the contamination on the study, a 13 C NMR analysis was run in same conditions as the quantitative analyses of PAA. Figure S16 shows that the contamination has a negligible impact on a regular spectrum. On the 13 C NMR spectrum of the contaminated D2O, the main chain CH and main chain COOH signals have respectively SNR around 4 and 6, which is less than 1 % of the SNR of the same signals on regular spectra. So, the error potentially induced by the contamination on the DB is much lower than the calculated error bar of DB. S-21

S-20

Kinetics of polymerization: Backbiting rate coefficients and degree of branching

Parameters used for the linear fits:

The values of the backbiting rate coefficients were estimated using equation ( 6) as well as the values of the propagation rate coefficient estimated from equation (S6). The final monomer conversion [M]e was calculated based on the monomer conversion estimated using CE for the polymer synthesized in the presence of CTA and using 1 H NMR spectroscopy for the polymer synthesized in the absence of CTA.

𝑘 𝑝 (𝐿. 𝑚𝑜𝑙 -1 . 𝑠 -1 ) = 3.2 10 7 𝑒 -1564 𝑇 (0.11 + (1 -0.11)𝑒 -3𝑤 ′ 𝐴𝐴 ) (S6)

In Eq. (S6), w'AA is the wt. fraction of AA solution on a polymer-free basis. The average value of w'AA over the polymerization process was used in order to calculate kp.

Arrhenius equation:

ln (𝑘) = ln(𝐴) - 𝐸 𝐴 𝑅𝑇 (S7)
Where k is the kinetic rate coefficient, A is the frequency factor (same unit as k), EA is the activation energy (J.mol -1 ), R is the ideal gas constant (J.K -1 .mol -1 ), T is the temperature (K).

The slope and intercepts were calculated with the Origin 9.0 software.

𝑘 𝑏𝑏 (𝑠 -1 ) = 9.94 × 10 S-23

Capillary electrophoresis

Determination of the optimal injection concentrations

Preliminaries studies to determine the optimal injection concentrations were performed with a fusedsilica capillary of about 60 cm total length and with sodium borate as buffer at a concentration close to 100 mmol.L -1 . For each sample, the concentrations of PAA and NaOH decreased by the same factor for their initial values through the sample dilution with water.

S-24

S-27

Reproducibility of the electrophoretic mobility distributions obtained from injections of PNaA at different pHs

2

  different operators performed the ESI MS analyses: one run the PAA samples synthesized at 70 and 90 °C (operator a) and the second one the PAA sample synthesized at 50 °C (operator b).

  70 and 90 °C correspond to different adducts. The main observed adducts are HOOC-CH 2 -S-(AA) n -H H + , HOOC-CH 2 -S-(AA) n -H NH 4 + , and HOOC-CH 2 -S-(AA) n -H Na + . Doubly charged adducts were observed in the spectrum of thiol-containing PAA synthesized at 70 °C and 90 °C. Tables S2, S3 and S4 detail the different adducts and compare their observed m/z with the theoretical value calculated with the mMass software (version 3.1.0

Figure 1 :

 1 Figure 1: ESI mass spectra of thiol-containing PAAs synthesized at (a) 50 °C, (b) 70 °C, and (c) 90 °C.

  noise. It is relevant to study the dissolution of a sample in the deuterated solvent as the peak area is used as the quantity proportional to the amount of sample and the noise as the scaling factor to put all spectra on the same scale. The normalized PNR corresponds to the PNR of a signal divided by the PAA label concentration used for the NMR measurement and by the square root of the number of scans (Eq. (S4) was used). Both main chain CH and COOH signals were used in this instance. The normalized PNR of COOH and CH signals in all PAAs synthesized by conventional radical polymerization were compared to the normalized PNR of the same signals in the linear PNaA (which is assumed to be fully soluble in D 2 O).

Figure 2 : Partial 13 C

 213 Figure 2: Partial 13 C solution-state NMR spectra in D 2 O at 49 °C of PAA synthesized at 90 °C (a) without CTA and (b) with CTA.

Figure 3 :

 3 Figure 3: Average degree of branching, DB, in percent of monomer units, as a function of: (a) initial monomer concentration: results from Wittenberg are represented by semi-filled squares and results from this study by semi-filled circles; and (b) synthesis temperature for PAA synthesized in solution without (blue diamonds) or with (red crosses) 0.2 mol L -1 CTA. DBs of CTA-containing polymers presented in this graph were calculated with Eq. (2). DBs of non-CTA containing PAAs were calculated with Eq. (1) (except for the PAA synthesized at 50 °C without CTA, where Eq. (S2) was used).

  provides a comparison between DB obtained for PAA synthesized without CTA in this study and in the study by Wittenberg et al. The DBs are of the same magnitude between both sets of work, for polymer obtained under similar conditions and analysed with the same solvent, D 2 O, in 13 C NMR. It is important to note that, although Wittenberg et al. carried out AA polymerizations in the presence of 2-mercaptoethanol, they do not appear to have measured DB in such experiments, rather just the molar mass distributions (by size exclusion chromatography) and conversion as a function of time (by infrared spectroscopy). Nevertheless, the fact that our DBs from PAAs synthesized without CTA are in such good agreement gives confidence that DBs given by Wittenberg et al. are obtained without CTA.

Figure 4 :

 4 Figure 4: DB of PAAs synthesized by conventional radical polymerization in aqueous solution without CTA: comparison between the results obtained in this study (semi-filled circles) and results obtained by Wittenberg et al. (semi-filled squares) [18]. In both studies DB is from the whole polymer present near the end of a batch polymerization.

Figure 5 :

 5 Figure 5: Arrhenius plot of k bb in absence of CTA (blue line and points), presence of CTA (red line and points) and from Wittenberg et al.[18] (full green line) and Barth et al [54](dashed green line).

Figure 6 :

 6 Figure 6: Electropherograms of PAAs synthesized without CTA at 70 °C (red line,) 90 °C (blue line) and a linear PNaA (green line). All samples are analyzed as PNaAs at high pH.

Figure 7

 7 Figure7shows that neither the temperature nor the initial monomer concentration influences significantly the heterogeneity of branching of the 3 PNaAs obtained by conventional radical polymerization at different temperatures and monomer concentrations. When the PNaA is synthesized without CTA, high enough DBs may be obtained for the branching to be relatively homogeneous which would explain the similar heterogeneity of branching with the temperature and the initial monomer concentration.

Figure 7 : 1 )

 71 Figure 7: Dispersities D(W(μ), x, 0) of electrophoretic mobility distributions of PNaAs as a function of (a) synthesis temperature (all PAAs synthesized without CTA at [M] 0 = 2 mol L -1 ), (b) initial monomer concentration (all PAAs synthesized at 90 °C). x = 1: ; x = 2: ; x = 3: ; D σ : .

Figure 8 :

 8 Figure 8: Dispersity D(W(μ),1,0) of the electrophoretic mobility distributions of PNaAs as a function of their average DB.

Figure 9 :

 9 Figure 9: Dispersity D(W(μ),1,0) of the electrophoretic mobility distributions of PNaAs as a function of the weight-average electrophoretic mobility µ W .

Figure S1 :

 S1 Figure S1: Reaction pathways for mid-chain radicals (MCRs) in the presence of chain transfer agent (CTA) (adapted from [1])

Figure S2 :

 S2 Figure S2: Separation of sodium acrylate and poly(sodium acrylate) by capillary electrophoresis (CE) shown as raw electropherogram (top) and distribution of electrophoretic mobility (bottom). Acrylic acid (black dashed line) was prepared at 2 g/L in 1 mM aqueous NaOH spiked with DMSO. PAAs synthesized at 50 °C, 70 °C and 90 °C with CTA (red, green and blue lines, respectively) were injected as crude medium diluted by a factor of 100 with water.

  D2O for each13 C NMR experiment Samples Concentration in D2O PAA synthesized at 50 °C with CTA at [AA]0 = 2 M 750 mg mL -1 PAA synthesized at 50 °C without CTA at [AA]0 = 2 M 100 mg mL -1 PAA synthesized at 70 °C with CTA at [AA]0 = 2 M 750 mg mL -1 PAA synthesized at 70 °C without CTA at [AA]0 = 2 M 190 mg mL -1 PAA synthesized at 90 °C with CTA at [AA]0 = 2 M 750 mg mL -1 PAA synthesized at 90 °C without CTA at [AA]0 = 2 M 190 mg mL -1 PAA synthesized at 90 °C without CTA at [AA]0 = 1 M 190 mg mL -1 PAA synthesized at 90 °C without CTA at [AA]0 = 3 M 190 mg mL -1 PAA supplied by Sigma-Aldrich 27 mg mL -1

Figure S3 :

 S3 Figure S3: Full 1 H solution-state NMR spectra in D2O at 26 °C of PAA synthesized at 50 °C (a) without CTA and (b) with CTA.

Figure S4 :

 S4 Figure S4: Full 13 C solution-state NMR spectra in D2O at 49 °C of PAA synthesized at 90 °C (a) without CTA and (b) with CTA.

Figure S5 :

 S5 Figure S5: Partial 13 C solution-state NMR spectra in D2O at 49 °C of PAA synthesized at 90 °C (a) without CTA and (b) with CTA.

Figure S6: Partial 13 C

 13 Figure S6: Partial 13 C NMR spectrum of PAA synthesized at 70 °C with CTA, analyzed at 750 g L -1 in D2O. The signals of C adjacent to the sulfur and of main-chain CH are overlapping.

  COSY and HSQC spectra were acquired at 26 o C in D2O on an Agilent 400 MR with Varian 7600-AS auto-sampler, equipped with OneNMR probe and variable temperature capabilities, operating at a Larmor frequency of 399.84 MHz for 1 H and 100.55 MHz for 13 C. 2D HSQC ( 1 H, 13 C) spectra were acquired with (1024, 1024) data points, 32 scans, (6,404.0 Hz, 20,090.97 Hz) spectral width, (0.1501 s, 0.0048 s) acquisition time, 4.5 s relaxation delay, and with the pulse program bsHSQCAD. 2D COSY ( 1 H, 1 H) spectra were acquired with (1150, 128) data points, 1 scan, (7,662.04 Hz, 7,608.80 Hz) spectral width, (0.1501 s, 0.0048 s) acquisition time, 1.0 s relaxation delay, and with the pulse program gCOSY.

Figure S7 :

 S7 Figure S7: Two-dimensional NMR of CTA-containing PAA synthesized at 70 °C, analyzed in D2O: (a) COSY; (b) HSQC, white shapes represent CH2 and black shapes represent CH and CH3.

Figure S8 :

 S8 Figure S8: Partial 13 C NMR spectra of PAA synthesized at 70 °C without CTA: top -obtained from an inversion recovery experiment with τ = 1.568 s; bottom -regular conditions.

Figure S9 :

 S9 Figure S9: Partial 13 C NMR spectrum of PAA synthesized at 70 °C without CTA obtained from an inversion recovery experiment with τ = 1.082 s.

Figure

  FigureS10shows that SNR(CH) / SNR(Cq) ≈ I(CH) / I(Cq), meaning that equation (S3) provides an estimation for a maximum potential DB:

Figure S10 :

 S10 Figure S10: Ratio of the SNRs of the backbone CH and Cq signals as a function of the ratio of their integrals for the experiments of this work.

Figure S11: 13 C

 13 Figure S11: 13 C NMR spectrum of PAA provided by Sigma-Aldrich, analyzed at 27 g L -1 in D2O (with 1 mol eq. of NaOD and 0.5 mol eq. of DCl) at room temperature.

Figure S12 :

 S12 Figure S12: Partial 13 C NMR spectra of (a) PAA supplied by Sigma-Aldrich, analyzed at room temperature at 27 g L -1 in D2O (with 1 mol eq. of NaOD and 0.5 mol eq. of DCl) with 27,411 scans, and (b) PAA synthesized at 90 °C without CTA, analyzed at 190 g L -1 in D2O at 49 °C with 17,500 scans.

Figure S13 :

 S13 Figure S13: Normalized PNR of the different PAAs synthesized by conventional radical polymerization. Green bars represents the PAAs synthesized at 90 °C without CTA at different initial minomer concentrations, red and blue bars represent the PAAs synthesized at [AA]0=2 M at different temperatures, with and without CTA, respectively. Graphs a and c represents the results obtained with the backbone COOH signal, b and d graphs represents the results obtained with the backbone CH signal. Magenta lines represent the PNR values obtained for the linear PNaA.

Figure S14 :

 S14 Figure S14: Normalized SNR of the different PAAs synthesized by conventional radical polymerization. Green bars represents the PAAs synthesized at 90 °C without CTA at different initial minomer concentrations, red and blue bars represent the PAAs synthesized at [AA]0=2 M at different temperatures, with and without CTA, respectively. Graphs a and b represents the results obtained with the backbone COOH signal, c and d graphs represents the results obtained with the backbone CH signal. Magenta lines represent the SNR values obtained for the linear PNaA.

Figure S15: 1 H

 1 Figure S15: 1 H NMR spectrum of the contaminated D2O

Figure S17 :

 S17 Figure S17: Average DB as a function of the inverse of the initial monomer concentration, where all experiments were at 90 °C and without CTA.

  Figure S18: PAA synthesized at (a) 90 °C with CTA and [AA]0 = 2 mol L -1 , (b) 90 °C without CTA and [AA]0=1 mol L -1 , (c) 90 °C without CTA and [AA]0 = 2 mol L -1 , (d) 90 °C without CTA and [AA]0=3 mol L -1 . In all raw electropherograms, all PAA are injected at 2 different concentrations: the concentration at which no overloading occurs (see table S11) (blue line) and half of it (red line).

Figure S19 :

 S19 Figure S19: PAA synthesized at (a) 50 °C with CTA and [AA]0=2 mol.L -1 , (b) 70 °C with CTA and [AA]0=2 mol. L -1 , (c) 50 °C without CTA and [AA]0=2 mol•L -1 , (d) 70 °C without CTA and [AA]0=2 mol•L -1 . In all raw electropherograms, all PAA are injected at 2 different concentrations: the concentration at which no overloading occurs (see table S9) (blue line) and half of it (red line).

Figure S20 :

 S20 Figure S20: Electrophoretic mobility distributions of PNaA synthesized at 70 °C without CTA and [AA]0=2 M (a), PNaA synthesized at 90 °C without CTA and [AA]0=1 M (b), PNaA synthesized at 90 °C without CTA and [AA]0=2 M (c). The PNaA were injected at pH between 4 and 5 (blue line) or between 8 and 9 (red line).

Table 1 : Summary of all polymerizations used to carry out this study

 1

	Polymer		Synthesis	Reactants		Conversion	M n
			method	(Initiator/CTA/monomer/solvent)
	PAAs specifically	Conventional	ACVA/No CTA/Acrylic acid/water	> 94 %*	unknown
	synthesized for	radical	THF (v/v 8/2)
	this	study	polymerization
	(without CTA)
	PAAs specifically	Conventional	ACVA/thioglycolic	acid/Acrylic	> 88 %*	Unknown
	synthesized for	radical	acid/water THF (v/v 8/2)		(but	the
	this study (with	polymerization				DP n s	are
	CTA)						expected to
							be close to
							10 at 65 °C)
	PAA provided	unknown	unknown		unknown	240,000
	by sigma Aldrich					g.mol -1 #
	Linear PNaA[7]	Anionic	t-butyl acrylate		unknown	39,300
			polymerization				g.mol -1

Table S1 : Reaction times Temperature Reaction time Half-time for decomposition of

 S1

			4,4'-azobis(4-cyanovaleric acid) *
	50 °C	24 h	96.6 h
	70 °C	6 h	5.40 h
	90 °C	1 h

Table S2 : Monomer conversion determined by 1 H NMR spectroscopy

 S2

	Polymer (PAA) synthesis conditions	Conversion by NMR (%)	SNR (residual monomer) NMR	SD (%) of in NMR the residual monomer	Conversion by CE (%)	SD (%) of the conversion by CE (%, n=3)
	50 °C with a
	CTA and at	98.0	38	0.04	99.3	0.2
	[AA]0 = 2M
	50 °C without a
	CTA and at	93.8	240	0.1
	[AA]0 = 2M
	70 °C with a
	CTA and at	98.8	24	0.05	99.0	0.6
	[AA]0 = 2M
	70 °C without a
	CTA and at	97.4	58	0.05
	[AA]0 = 2M
	90 °C with a
	CTA and at	>99.9 *			88.4	4.0
	[AA]0 = 2M
	90 °C without a
	CTA and at	97.6	61	0.05
	[AA]0 = 2M
	90 °C without a
	CTA and at	99.9	5.2	0.03
	[AA]0 = 1M
	90 °C without a
	CTA and at	98.9	25	0.04
	[AA]0 = 3M
	* no residual monomer detected.

Table S2 : Species detected by ESI-MS for PAA synthesized at 50 °C

 S2

	Formula	Mexp (amu) Mth (amu)	hpeak (arbitrary units)
	C2H3O2S(C3H4O2)15H H +	1173.3175	1173.3174	1067
	C2H3O2S(C3H4O2)15H Na +	1195.2949	1195.2994	298

Table S3 : Species detected by ESI-MS for PAA synthesized at 70 °C

 S3

	Formula	Mexp (amu)	Mth (amu)	hpeak (arbitrary units)
	C2H3O2S(C3H4O2)7H H +	1173.3048	1173.3174	1828
	C2H3O2S(C3H4O2)7H Na +	1195.2858	1195.2994	782
	C2H3O2S(C3H4O2)32H 2 H +	1199.3287	1199.3419	564
	C2H3O2S(C3H4O2)32H Na + H +	1210.3189	1210.3329	358
	C2H3O2S(C3H4O2)32H 2 Na +	1221.3129	1221.3239	281

Table S4 : Species detected by ESI-MS for PAA synthesized at 90 °C

 S4

	Formula	Mexp (amu) Mth (amu)	hpeak (arbitrary units)
	C2H3O2S(C3H4O2)7H H +	1173.3038	1173.3174	4680
	C2H3O2S(C3H4O2)7H NH4 +	1190.3295	1190.3440	324
	C2H3O2S(C3H4O2)7H Na +	1195.2846	1195.2994	1754
	C2H3O2S(C3H4O2)32H 2 H +	1199.328	1199.3419	690
	C2H3O2S(C3H4O2)32H Na + NH4 + 1246.83	1218.8462	479
	C2H3O2S(C3H4O2)32H 2 Na +	1221.309	1221.3239	361
				S-6

Table S6 : Conditions for 13 C NMR analyses of branching in PAA and PNaA in the literature.

 S6 NMR of PAA and signal assignment:All PAAs were analyzed by 1 H and 13 C NMR spectroscopy. All thiol and non thiol-containing PAAs had similar spectra. Examples of 1 H and13 C NMR spectra are given in Figures S3 to S6.

	Sample	Solvent	Concentr ation	Temper ature	Repetition delay	Pulse angle	Larmor frequency	Type of study	Ref.
								Detection
	Linear PNaA	D2O	150 g L -1	RT*	20 s	90°	75 MHz	of	[14]
								branching
	Hyperbranched PNaA	1,4--d8 Dioxane	50 g L -1	RT	20 s	90°	75 MHz	Detection branching of	[14]
	3-arm star PNaA (synthesized by NMP, trifonctional initiator)	D2O with NaOH 428 nM	50 g L -1	RT	20 s	90°	75 MHz	Detection branching of	[14]
	PNaAs synthesized by RAFT	D2O	30 % (w/w)	60 °C	4.5 s	70°	100.6 MHz	Quantific branching ation of	[10]
	PNaAs							Quantific
	synthesized by	D2O	Not given	RT	20 s	20°	125.7 MHz	ation of	[15]
	NMP							branching
	PAAs produced by batch radical polymerization	D2O	Not given	Not given	Not given	Not given	Not given	Quantific branching ation of	[12]
	* RT stands for room temperature
								S-7

Table S7 : Signal assignment for 1 H NMR spectra of PAA in D2O at 26 °C

 S7

	δ (ppm)	δ (ppm)	δ (ppm)	δ (ppm)	δ (ppm)	δ (ppm)	Assignment
	for thiol-	for non	Literature	Literature	Literature	ChemNMR
	containing	thiol-	[14]	[10]	[16]	calculations
	PAA	containing	(analyses	(analyses	(analyses	and solvent
		PAA	done in	done in	done in	table[17] in
			D2O with	D2O at 60	dioxane-	the case of
			NaOH at	°C)	d8 at RT)	residual
			RT)			water
	1.65-1.95	1.65-1.95	1.3-1.8	1.3-1.8	1.0-1.8	1.75	CH2 (main
							chain)
	2.3-2.5	2.3-2.5	2-2.3	1.9-2.3	1.8-2.3	2.35	CH (main
							chain)
	2.75		-	-	2.60	2.33	CH2-CH2-
							COOH (end
							group)
	2.88		-	-	2.87	1.79	CH2-CH2-
							COOH (end
							group)
	3.4	-	-	-	-	3.38	S-CH2-COOH
							(end group)
	4.76	4.7	-	4.7	-	4.79	Residual
							solvent
	6	6	5.8-5.9	-	-	5.75	monomer (H in
							cis to COOH)
	6.2	6.2	5.9-6	-	-	6.22	monomer (H on
							same C as
							COOH)
	6.4	6.4	6.7	-	-	6.50	monomer (H in
							trans to COOH)

Table S9 : overestimated values of the longitudinal relaxation time T1 measured for the signals of interest for DB quantification of PAA in different conditions.

 S9

	Degree of branching (DB): equations and results
	Samples	Conditions of NMR	T1 of signals of interest for DB quantification
		analyses
	PAAs synthesized	D2O, 49 °C	1.56 s < T1 < 2.26 s for the Cq signal
	in this work		T1 < 1.56 s for CH and CH2 signals (main chain)
			1.56 s < T1 < 2.26 s for COOH signal (main chain)
	PAA from Sigma	D2O/NaOD, RT	T1 < 1.2 s the Cq signal,
			T1 < 1.2 s for the CH and CH2 signals (main chain)
			T1 < 1.2 s for COOH signal (main chain)
			S-15

Table S10 : DB of PAAs calculated with different equations and its relative standard deviation (RSD) based on the signal to noise ratio (SNR) of the Cq (calculated using Eq. (5) of the main text).

 S10

	PAA synthesis	DB (%) from	DB (%) from	DB (%) from	DB (%)	SNR RSD
		Eq. (1) or	Eq. (3)	Eq. (2)	from		(%)
		Eq. (S3)*	(underestimate)	(overestimate)	Eq. (4)
	90 °C with CTA and at	-	0.36	0.37	0.37	9.22	13.9
	[AA]0 = 2 M
	70 °C with CTA and at	-	0.31	0.33	0.32	8.16	16.4
	[AA]0 = 2 M
	50 °C with CTA and at	-	0.21	0.25	0.23	5.85	24.8
	[AA]0 = 2 M
	90 °C without CTA and	1.32	-	-	1.28	7.15	19.2
	at [AA]0 = 2 M
	70 °C without CTA and	0.83	-	-	0.83	7.55	17.9
	at [AA]0 = 2 M
	50 °C without CTA and	Below 0.61*	-	-	-	2.62	-
	at [AA]0 = 2 M*
	90 °C without CTA and	1.36	-	-	1.37	9.28	13.8
	at [AA]0 = 1 M
	90 °C without CTA and	1.16	-	-	1.17	6.94	20.0
	at [AA]0 = 3 M

  8 (𝑠 -1 ) 𝑒

		4576 -𝑇/𝐾	(𝑆8)
	𝑅𝑆𝐷 (ln 𝑘 𝑏𝑏 ) =	𝑅𝑆𝐷 (𝐷𝐵) 𝑘 𝑏𝑏	(𝑆9)

Table S11 : Linear fit parameters for the different Arrhenius plots of kbb, where the slope refers to the activation energy and the intercept to the ln (A) where A is the frequency factor. kbb (s -1 ) from this study in the absence of CTA kbb (s -1 ) from this study in the absence of CTA excluding the polymerization at 90 °C and 1 M monomer kbb (s -1 ) from this study in the presence of CTA kbb (s -1 ) of Wittenberg et al. study [8, 12]

 S11

	slope ( -Ea/R	-3737	-5066	-4777	-4576
	(J.mol -1 ))
	Standard error	1933	244	86
	(slope)
	Intercept (ln	17.8	21.8	20.1	20.7
	(A (s -1 ))
	Standard error	5.5	0.7	2.4
	(intercept)
	Correlation	0.56	0.996	0.97
	coefficient R 2
					S-22

Table S12 : Concentrations of injected PAAs without overloading

 S12

Table S13 : Values of the dispersities and weight-average of the electrophoretic mobility distributions of PNaAs, with their average and standard deviation SD Sample synthesis

 S13 𝑫(𝑾(𝝁), 𝟏, 𝟎) 𝑫(𝑾(𝝁), 𝟐, 𝟎) 𝑫(𝑾(𝝁), 𝟑, 𝟎) 𝑫 𝝈 𝝁 𝒘 (m 2 V -1 s -1 )

			1.00011	1.00011	1.00011	3.94  10 -10	3.76  10 -8
	50 °C without CTA and [AA]0 = 2 M	average	1.00012 1.00012 1.000116667	1.00012 1.00012 1.000117	1.00012 1.00013 1.00012	4.07  10 -10 4.14  10 -10 4.05  10 -10	3.72  10 -8 3.73  10 -8 3.73515  10 -8
		SD	4.71405  10 -6	4.71  10 -6	8.16  10 -6	8.64  10 -12	1.6631  10 -10
			1.00013	1.00013	1.00013	4.36  10 -10	3.77  10 -8
	70 °C without CTA and [AA]0 = 2 M	average	1.00012 1.00013 1.000126667	1.00012 1.00013 1.000127	1.00012 1.00013 1.000127	4.21  10 -10 4.25  10 -10 4.27  10 -10	3.79  10 -8 3.75  10 -8 3.77  10 -8
		SD	4.71405  10 -6	4.71  10 -6	4.71  10 -6	6.07  10 -12 1.69056  10 -10
			1.00013	1.00013	1.00013	4.30  10 -10	3.72  10 -8
	90 °C without CTA and [AA]0 = 2 M	average	1.00012 1.0001 1.000116667	1.00012 1.0001 1.000117	1.00012 1.0001 1.000117	4.05  10 -10 3.82  10 -10 4.06  10 -10	3.74  10 -8 3.76  10 -8 3.74123  10 -8
		SD	1.24722  10 -5	1.25  10 -5	1.25  10 -5	1.96  10 -11	1.6696  10 -10
			1.00014	1.00014	1.00014 4.43 × 10 -10	3.72 × 10 -8
	90 °C without CTA and [AA]0 = 1 M	average	1.00012 1.00011 1.000123333	1.00012 1.00011 1.000123	1.00012 4.07 × 10 -10 1.00011 3.95 × 10 -10 1.000123 4.15 × 10 -10	3.72 × 10 -8 3.74 × 10 -8 3.72857 × 10 -8
		SD	1.24722 × 10 -5	1.25 × 10 -5	1.25 × 10 -5 2.02 × 10 -11	8.3467 × 10 -11
			1.00012	1.00012	1.00012 4.16 × 10 -10	3.79 × 10 -8
	90 °C without CTA and [AA]0 = 3 M	average	1.0001 1.00012 1.000113333	1.0001 1.00012 1.000113	1.0001 3.81 × 10 -10 1.00012 4.22 × 10 -10 1.000113 4.07 × 10 -10	3.78 × 10 -8 3.79 × 10 -8 3.78657 × 10 -8
		SD	9.42809 × 10 -6	9.43 × 10 -6	9.43 × 10 -6 1.79 × 10 -11 8.06687 × 10 -11
			1.00001	1.00001	1.00001 1.40 × 10 -10	3.86 × 10 -8
	Linear PNaA [14]	average	1.00001 1.00001 1.00001	1.00001 1.00001 1.00001	1.00001 1.48 × 10 -10 1.00001 1.42 × 10 -10 1.00001 1.44 × 10 -10	3.86 × 10 -8 3.88 × 10 -8 3.86489 × 10 -8
		SD	0	0	0 3.43 × 10 -12 1.33498 × 10 -10

Acknowledgements

We thank Dr Chris Fellows (University of New England), Adam Sutton (University of South Australia) and Cedric Loubat (Specific Polymer Ltd) for their feedback related to this research. We thank the Macromolecular Characterization Team (WSU) for their help in the lab with CE, Dr Ghislain David (Ecole Nationale Superieure de Chimie de Montpellier) for providing very useful information related to the synthesis of PAA, Dr Matthew Polson (UC) for assistance in the laboratory, Dr Marie Squire (UC) for help with NMR spectroscopy and ESI-MS and Dr Sarah Masters (UC) for help with proof-reading. JBL thanks the University of Canterbury for a UC Doctoral Scholarship and general research support from the Evans Fund.

Graphical abstract

S-1

Effect of transfer agent, temperature and initial monomer concentration branching in poly(acrylic acid): a study by 13 C NMR spectroscopy and capillary electrophoresis

Supplementary data

Jean-Baptiste Lena a,b,c , Alexander K. Goroncy a , Gregory T. Russell a, *, Joel J. Thevarajah b,c , Alison R.

Dispersities of the distributions of electrophoretic mobilities

The dispersities of the distributions of electrophoretic mobilities, which are related to the heterogeneity of branching, are given by Eq. (S10) to (S13) [20]. They are all ratios of moments of different orders of the weight distribution of electrophoretic mobilities W(µ). Eq. (S14) gives the weight average electrophoretic mobility [20].