How Does the Branching Effect of Macromonomer Influence the

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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How Does the Branching Effect of Macromonomer Influence the Polymerization, Structural Features, and Solution Properties of Long-Subchain Hyperbranched Polymers? Nairong Hao,† Xiaozheng Duan,*,‡ Hongjun Yang,*,§ Ahmad Umair,† Mo Zhu,† Muhammad Zaheer,† Jinxian Yang,† and Lianwei Li*,† Macromolecules Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 01/29/19. For personal use only.

†

Department of Chemical Physics, University of Science and Technology of China, Hefei, China 230026 State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin, China 130022 § Jiangsu Key Laboratory of Environmentally Friendly Polymeric Materials, School of Materials Science and Engineering, Jiangsu Collaborative Innovation Centre of Photovoltaic Science and Engineering, Changzhou University, Changzhou, Jiangsu, China 213164 ‡

S Supporting Information *

ABSTRACT: This work aims to elucidate how the branching effect of macromonomer influences the polymerization, structural features, and solution properties of ABn long-subchain hyperbranched polymers (LHPs). Our result reveals that compared with linear AB2 macromonomers, star AB3 macromonomers result in the suppression of chain extension, and the enhancement of macromonomer self-cyclization during the preparation of LHPs by “click” polymerization, due to the branching-enhanced steric hindrance effect. The combined triple-detection SEC and stand-alone LLS studies of unfractionated and fractionated AB3 LHPs unambiguously demonstrate their statistically fractal nature. Namely, the intrinsic viscosity ([η]) and radius of gyration (Rg) are scaled to the macromonomer molar mass (M macro ) and the total molar mass (M hyper ) as [η] = Kη,AB3MhyperνMmacroμ (ν ≃ 0.39, μ ≃ 0, and Kη,AB3 ≃ 0.29 mL/g) and Rg = HR,AB3MhyperαMmacroβ (α ≃ 0.47, β ≃ 0, and HR,AB3 ≃ 3.6 × 10−2 nm). Surprisingly, [η] and Rg are both almost independent of Mmacro (μ ≃ 0 ≃ β), indicating a similar draining property and local segment density for LHPs with different subchain lengths, which is different from the classic AB2 systems (μ ≃ 0.3 and β ≃ 0.1). A comparison of results for ABn LHPs (n = 2, 3) and short-subchain hyperbranched systems indicates that the fractal dimensions (f) for LHPs are generally smaller than shortsubchain systems, whereas f is not sensitive to the local segment density or branching pattern. A combination of experimental observation and Langevin dynamics simulation of ABn dendrimers and LHPs further reveals (i) the segment back-folding phenomenon is prominent only for ABn (n ≥ 3) LHPs systems because it is mainly dominated by the macromonomer branching effect, rather than the internal subchain length, and (ii) the trend for segment interpenetration increases remarkably as Mmacro increases for both dendrimers and LHPs. The result also indicates that the unique synergistic effect of segment backfolding and segment interpenetration in AB3 system is the most probable reason for the observed Mmacro independent solution properties. Specifically, because of the unique synergistic effect, small macromonomer/oligomer chains can interpenetrate more easily into hyperbranched oligomer chains composed of longer subchains and subsequently “click” couple with the back-folded segments in the interior space of LHPs, which eventually could lead to a similar draining property and local segment density for AB3 LHPs with different subchain lengths.

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INTRODUCTION Hyperbranched polymers (HPs) have received considerable attention in the past two decades due to their unique properties such as high solubility, high number of terminal functional groups, intramolecular topological cavity and low intrinsic viscosity.1−3 According to the relative length of internal branching subchains, all reported HPs could be classified into two categories, i.e., short-subchain hyperbranched polymers (SHPs) and long-subchain hyperbranched polymers (LHPs).2 SHPs refer to the type of HPs with single © XXXX American Chemical Society

or several repeating units between two neighboring branching points; LHPs are analogues of SHPs, but with long linear segments dispersed between branching points. The existence of long branching subchains endows LHPs with a sparsely branched framework and unique properties compared with SHPs, such as weaker steric hindrance effect, diverse terminal Received: November 5, 2018 Revised: December 24, 2018

A

DOI: 10.1021/acs.macromol.8b02364 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

Scheme 1. Schematic Illustration of the Topological Structures of Long-Subchain Hyperbranched Polymers (LHPs) Prepared from (a) Linear AB3 Macromonomer, (b) 4-Arm Star AB3 Macromonomer, (c) 3-Arm Star AB3 Macromonomer, and (d) VType AB2 Macromonomer, Where the Highlighted Regions with Different Colors Represent Branching Subchains with Different Lengths (Ls)

(Scheme 1a), the three B groups are located at the same chain end (correlated), i.e., A∼∼B3; for 4-arm star structure (Scheme 1b), the reactive A group is located at one arm end, and the three B groups are located at the other three arm ends (noncorrelated), i.e., (A∼∼)(∼∼B)3; while for 3-arm star structure (Scheme 1c), the reactive A group is located in the star center, but the three B groups are located at different arm ends (noncorrelated), i.e., A(∼∼B)3. It is worth noting that the chain configuration of macromonomer and the spatial location of functional end-group have a tremendous impact on the branching pattern of prepared LHPs. In principle, linear AB3 and 4-arm star macromonomers (Scheme 1a,b) can only realize partial control over parameters Ls and DL; namely, for linear AB3 macromonomer, the unreacted B groups can easily lead to the extension of branching subchain by one macromonomer length (Lm) repeatedly, resulting in the variability of average subchain length (Ls = kLm, k ≥ 1). Moreover, for the linear AB3 structure, the spatially strong correlation among three B groups inevitably results in unequal reactivity for the three B groups, further leading to the nonideal branching patterns for LHPs. In contrast, the use of star AB3 macromonomer can guarantee that each branching subchain of LHPs is exactly composed of one-third of macromonomer (one arm, Ls = Larm), accordingly, leading to a narrower subchain length distribution and a more uniform segment density distribution. More recently, we have, for the f irst time, elucidated the structural difference for LHPs prepared by Y-type and V-type AB2 macromonomer strategies. Namely, the average subchain length of Y-type AB2 LHPs is much longer than the initial macromonomer chain length, i.e., Ls = 5/2Lm, while Ls = 1/2Lm for V-type AB2 LHPs (Scheme 1d).49 This finding clarifies the difference between Ls and Lm for nonideal AB2 LHPs systems and simultaneously demonstrates that the preparation of model samples with controlled

group functionalization, better mechanical property, and unique phase behavior.1−3 Therefore, LHPs have been of particular interest and receiving increasing attention over the past few years. The controllable synthesis of LHPs with predesigned branching parameters remains significantly challenging. Among various synthetic approaches, polymerization using ABn (n ≥ 2) macromonomer has been proved to be one of the most effective strategies to control the structural parameters of LHPs, such as the average length of branching subchains (Ls, the average segment length between two branching points) and the subchain length distribution (DL),4−10 which play an important role in determining the relevant properties. Originally, the classic ABn monomer strategy (n ≥ 2) could be traced back to Flory’s pioneering work on the discussion of ABn monomer strategy for the preparation of SHPs,11 which was later extended to the case of ABn macromonomer strategy in the 1990s.4 So far, a variety of SHPs have been synthesized via this strategy; for example, AB2,1−3 AB3,12−20 AB4,21−24 and even AB621 monomers have been previously reported in the literature for the exploration of structure−property correlation for SHPs. In contrast, though there are numerous studies reporting the preparation of LHPs by AB2 macromonomer strategy,4−10,25−40 including our contributions,41−48 the study of LHPs prepared from ABn macromonomers (n ≥ 3) is lacking, which greatly hinders the understanding of structure− property relationship for LHPs. To the best of our knowledge, no one has tried to use ABn macromonomers (n ≥ 3) to prepare ABn LHPs and study how the macromonomer branching affects the polymerization and fundamental properties of LHPs. Contrary to the uniqueness in structure of small-molecule AB3 monomer, there exist three possible topological structures for AB3 macromonomer system, i.e., linear, 4-arm, and 3-arm star structures (Schemes 1a−c). For the linear structure B


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Macromolecules

(TD-SEC) system in Changzhou University. The TD-SEC system is equipped with refractive index detector (RI), the multiangle light scattering detector (MALS), and the viscosity detector. The instrumentation consists of a Waters 1515 isocratic HPLC pump with 5 mm Waters Styragel columns (guard, HR6, HR4, and HR2; the efficient exclusion limits for the HR columns are 2 × 105−1 × 107 g/mol, 5 × 103−6 × 105 g/mol, and 5 × 102−3 × 104 g/mol, respectively), a Waters 717 PLUS autosampler, a Waters 2414 RI detector, a MALS detector (Wyatt mini-DAWN HELEOS-II) with a scattering volume of 0.07 μL and an 18-angle light scattering detector at a wavelength of 690 nm and 220 W power, a Wyatt Visco Star viscometer detector, and a Waters Breeze data manager. The eluent was HPLC-grade THF with a flow rate of 1.0 mL/min. Prior to injection, the sample solutions were filtered through PTFE membranes (0.45 μm pore size). The TD-SEC system was carefully calibrated with two polystyrene standards: (1) a polystyrene standard with peak molar mass (Mp) of 3.01 × 104 g/mol was used to calibrate the normalization coefficients of the 18 detectors; (2) toluene and polystyrene standard with Mp of 2.21 × 106 g/mol were used to calibrate the voltage calibration constant, and the calibrated constant of 7.9 × 10−6 V−1cm−1 was obtained and used in this study. For quantitative study, 50 μL of polymer solution was injected, and the polymer concentration was fixed at 15 mg/mL for all samples. The dn/dC values for HPS1−5 samples in THF at 25 °C are determined by a precise refractometer.41−46 During the analysis of light scattering data, the Zimm plot was found to produce negative molar masses in some cases, and some curves appeared to curve upward due to the branching effect. Considering the large size (>50 nm) and high molar mass (>106 g/ mol) of polymer samples in this study, the “qRg > 1” is not valid for Zimm plot analysis, where q is the scattering vector. The Berry model is used for the molar mass and size plotting for all samples. Calculations were performed with the Berry method, which is a fit to [KC/R(θ)]1/2 vs q2 according to the following equation:

branching parameters is the prerequisite for further structure− property investigation. It is generally accepted that the use of ABn monomers (n ≥ 3) endows SHPs with higher branching densities and varied branching patterns.50−52 However, such a structure−property relationship has never been experimentally explored for LHPs, even for the simplest case n = 3. It is still unclear how the macromonomer structure and branching pattern affect the structural features and fundamental properties for a specific ABn LHPs system (n ≥ 3). In this work, on the basis of our previous study of the AB2 system,49 we further extend to study the AB3 LHPs system, synthesized by using 3-arm star polystyrenes as macromonomers. By combining experimental characterization and computational simulation, we not only investigated the effect of macromonomer branching on the polymerization and intrachain self-cyclization process of AB3 LHPs but also elucidated how the macromonomer branching influences the structural features and solution properties of AB3 LHPs, such as the chain size, the intrinsic viscosity, the chain configuration parameter, the draining and interpenetration factors, and the segment back-folding property. For comparison, the result for AB2 system was also presented. The results reveal that due to the unique branching pattern, the AB3 LHPs system presents unique features which are not held by AB2 LHPs system, such as the subchain length-independent solution properties as well as the synergistic effect of segment interpenetration and segment back-folding. This study aims to provide a deep insight into the effect of macromonomer branching on the structural feature and solution property of LHPs, from a perspective of experimental observation and computational simulation.

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KC = Rθ

EXPERIMENTAL SECTION

Materials. Unless stated otherwise, all chemicals were obtained from commercial suppliers and were used as received. Styrene (Sinopharm, 97%) was passed through a basic alumina column to remove inhibitor, distilled under vacuum, and stored at −20 °C. Dimethylformamide (DMF, Sinopharm, AR) was dried with anhydrous magnesium sulfate and then distilled under reduced pressure prior to use. Dichloromethane (DCM), tetrahydrofuran (THF), anisole, and triethylamine (TEA) from Sinopharm were distilled over CaH2 just prior to use. Copper(I) bromide (CuBr, Alfa, 98%) was washed with glacial acetic acid to remove soluble oxidized species, filtrated, washed with ethanol, and dried under vacuum. Sodium azide (NaN3, Aldrich, 99%), tin(II) 2-ethylhexanoate (Sn(EH)2, Aladdin, 95%), 2-bromoisobutyryl bromide (Aladdin, 98%), PMDETA (Aldrich, 99%), Tris(2-(dimethylamino)ethyl)amine (Me6TREN, Aladdin, 98%), p-toluenesulfonic acid monohydrate (Aladdin, 98%), and methanol (Sinopharm, 99.8%) were used as received. Compounds I53 and II54 (AB3-type ATRP initiator) were prepared according to the published procedures. Analytical Methods. NMR spectra were recorded at 300 K on a Bruker Avance III Ascend 500 (500 MHz) spectrometer with a delay time (d1) set to 8 s by using deuterated chloroform (CDCl3) as the solvent and tetramethylsilane (TMS) as the insternal standard. FTIR spectra were recorded on a Bruker Tensor 27 Fourier transform spectrometer. Size Exclusion Chromatography. The relative number- and weight-average molar masses (Mn and Mw) of macromonomer and hyperbranched polystyrene samples were first characterized by a normal size-exclusion chromatography (SEC) system in our own lab,46 and the molar masses were determined by a conventional polystyrene calibration method (six polystyrene standards ranging from 7.65 × 102 to 2.21 × 106 g/mol). The absolute number- and weight-average molar masses of hyperbranched polystyrene samples were measured by a triple-detection size-exclusion chromatography

2 1 (1 + R g q2 /6) Mw 2

(1)

/(NAλ04)

2

and q = (4π/λ0) sin(θ/2) with C, where K = 4π (dn/dC) dn/dC, NA, and λ0 being concentration of the polymer solution, the specific refractive index increment, Avogadro’s number, and the wavelength of light in a vacuum, respectively. Preparative Size Exclusion Chromatography. The LC98II high performance liquid chromatograph (Beijing Wenfen Analytical Instrument) consisted of a P98II Isocratic HPLC pump with three Waters Styragel columns at 35 °C (guard, HR6, HR5, and HR3; the efficient exclusion limits are 2 × 105−1 × 107, 5 × 104−4 × 106, and 5 × 102−3 × 104 g/mol, respectively), a Z98 autosampler, a Shodex RI201H detector, a UV98II variable wavelength UV−vis spectrophotometer (wavelength range: 190−700 nm), and a UC-3265 component collector. The eluent was HPLC-grade THF with a flow rate of 1.0 mL/min. Stand-Alone Laser Light Scattering. A commercial LLS spectrometer (ALV/DLS/SLS-5022F) equipped with a multi-τ digital time correlator (ALV5000) and a cylindrical 22 mW UNIPHASE He−Ne laser (λ0 = 632.8 nm) as the light source was used. In static LLS,55 the angular dependence of the absolute excess time-average scattering intensity, known as the Rayleigh ratio R(θ), can lead to the weight-average molar mass (Mw), the root-mean-square gyration radius ⟨Rg2⟩1/2 (or simply written as ⟨Rg⟩), and the second virial coefficient A2 by using 2 KC 1 = (1 + R g q2 /3) + 2A 2 C R(θ) Mw

(2)

The extrapolation of R(θ) to q → 0 and C → 0 leads to Mw. The plots of [KC/R(θ)]C→0 vs q2 and [KC/R(θ)]q→0 vs C lead to ⟨Rg⟩ and A2, respectively. For long hyperbranched polymers in this study, q⟨Rg⟩ ≫ 1, the Berry plot is used. In static LLS, the scattering intensity was recorded at each angle three times, and each time was averaged over 10 s. The scattering angle ranges from 13° to 120°. C


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Macromolecules

Azidation Substitution Reaction. A 25 mL round-bottom flask was charged with PS1 (0.4 g, 0.2 mmol), DMF (2.0 mL), and NaN3 (177.3 mg, 2.7 mmol). The mixture was allowed to stir under nitrogen at room temperature for 24 h. The mixture was diluted with CH2Cl2 (0.4 mL), and the insoluble inorganic salt was removed by filtration. The filtrate was precipitated into an excess of cold methanol. The sediments were redissolved in CH2Cl2, passed through a neutral alumina column to remove residual sodium salts, and then precipitated into an excess of methanol. After being dried in a vacuum oven overnight at 45 °C, the macromonomer PS 1 functionalized with one alkyne group, and three azide groups was obtained (yield ∼0.35 g). Following the similar protocol, five star AB3 polystyrene macromonomers with different molar masses were synthesized (PS1−5). Preparation of Hyperbranched Samples from AB3 Macromonomers via Azide−Alkyne Cycloaddition Reaction. Compared with our previous protocol,41 a slightly modified procedure was employed. Into a 5 mL dry glass tube with a magnetic stirring bar, PS1 (50 mg, 0.02 mmol), PMDETA (5.2 μL, 0.02 mmol), and DMF (0.2 mL) were added successively. After mixing thoroughly, the polymerization tube was degassed by two freeze−vacuum−thaw cycles, and CuBr (3.6 mg, 0.02 mmol) was added into the frozen solution. The polymerization tube was degassed by one more freeze−vacuum−thaw cycle before sealed under vacuum. The sealed tube was immersed into an oil bath at 35 °C for 24 h. The mixture was then diluted with THF and quickly passed through a neutral alumina column. The CuBr and PMDETA were further removed from resultant hyperbranched polystyrene by the repeating precipitation with THF and methanol. Finally, the pure precipitate of hyperbranched polystyrene HPS1 was collected by filtration and then dried in under vacuum overnight at 45 °C (yield ∼40 mg). Following the similar protocol, five HPS samples were synthesized. Hydrolysis of Star AB3 Polystyrenes. PS1 (5.0 mg, 2.3 mmol) was first dissolved in THF (1.0 mL), and then a saturated solution of NaOH in water (1.0 mL) was added. The layered solution was sealed in a glass vial and stirred vigorously in an oil bath at 60 °C for 48 h. At different time intervals, 0.1 mL of solution in organic phase was withdrawn and dried with anhydrous Na2SO4 for SEC characterization. Atom Transfer Radical Coupling (ATRC) Model Reaction of Linear Polystyrene with Bromine End-Group. Linear polystyrene with bromine end-group (PS-Br, Mn = 5800 g/mol, 0.20 g, 34.0 mmol), Me6tren (3.90 mg, 17.0 mmol), Sn(EH)2 (6.98 mg, 17.0 mmol), and anisole (0.4 mL) were added to glass tube; after three freeze−vacuum−thaw cycles, CuBr (0.50 mg, 3.4 μ mol) was added into the frozen solution. The tube was sealed under vacuum and immersed into an oil bath at T = 80 °C for 24 h. The polymer solution was then filtered through neutral alumina and precipitated in methanol. The product was obtained after being dried under vacuum at overnight and denoted as PS-b-PS. The linear PS-b-PS was further treated by hydrolysis process similar to that of star AB3 polystyrenes. Fractionation of HPS4 by the Preparative SEC Technique. HPS4 sample was dissolved in THF at room temperature with a concentration of ∼10 g/L, and then the polymer solution was filtered into a glass vial through a PTFE filter (0.22 μm pore size). The injection into SEC system was accomplished by an autosampler, where 0.1 mL of solution was injected into the SEC system at a time interval of 40 min. The SEC fractionation was repeated 40−80 times for a given sample, and 10−20 fractions were typically collected. Finally, 0.5−2.0 mg of sample was obtained for each polymer fraction after concentration. Langevin Dynamics Simulation. In our simulations, the chemical heterogeneity was ignored for simplicity, and the bead−spring model was employed to coarse-grain the hyperbranched polymers. We modeled each macromonomer as a connection of several spherical segments and used the Weeks−Chandler−Andersen (WCA) potential to account for the repulsive excluded volume interactions between segments i and j separated with a distance rij:

In dynamic LLS,56 the Laplace inversion of each measured intensity−intensity time correlation function G(2)(q,t) in the selfbeating mode can lead to a line-width distribution G(Γ), where q is the scattering vector. For dilute solutions, Γ is related to the translational diffusion coefficient D by (Γ/q2)q→0,C→0 → D, so that G(Γ) can be converted into a transitional diffusion coefficient distribution G(D) or further a hydrodynamic radius distribution f(Rh) via the Stokes−Einstein equation Rh = (kBT/6πη0)/D, where kB, T, and η0 are the Boltzmann constant, the absolute temperature, and the solvent viscosity, respectively. The polydispersity index Mw/Mn was estimated from Mw/Mn ≈ (1 + 4μ2/⟨D⟩2), where ∞ μ2 = ∫ G(D)(D − ⟨D⟩)2 dD. In dynamic LLS experiments, we 0 used a fixed small-angle (13°) to ensure that the effect of extrapolating to the zero angle is minimum. The time correlation functions were analyzed by both the cumulants and CONTIN analysis. Synthesis of Monopropargyl Pentaerythritol. Pentaerythritol (4.0 g, 29.4 mmol) and p-toluenesulfonic acid monohydrate (56 mg, 0.30 mmol) were suspended in 60 mL of dry toluene and heated to reflux. Triethyl orthoacetate (5.4 mL, 29.4 mmol) was added to the flask, and the resulting suspension was refluxed for 3 days. The milk-white solution was filtered and concentrated under reduced pressure, yielding a white solid (yield ∼4.2 g). The resulting orthoacetate protected product (4.0 g, 25.0 mmol) was then dissolved in anhydrous DMF (50 mL) and cooled to 0 °C under nitrogen. Sodium hydride (0.75 g, 80 wt %, 25.0 mmol) was added to the cooled solution, which was stirred for 30 min; propargyl bromide was then added, followed by an additional 24 h of stirring. Finally, brine (200 mL) was added to the reaction mixture, which was extracted with ethyl acetate (350 mL); the organic phase was then dried. The crude product was redissolved in 100 mL of methanol; a catalytic amount of hydrochloric acid was then added, and the mixture was stirred at T = 40 °C for 3 h. Next, the pH was increased with 0.1 N NaOH solution before the solution was filtered, concentrated, and purified by silica gel chromatography with methanol/dichlomethane as eluent (yield ∼2.0 g). Synthesis of Tetrafunctional AB3 ATRP Initiator. Monopropargyl pentaerythritol (3.0 g, 17.2 mmol) was first dissolved in CH2Cl2 (100 mL), and then triethylamine (8.0 mL, 57.5 mmol) was added. After the mixture was cooled to 0 °C, 2-bromoisobutryl bromide (6.05 g, 26.0 mmol) in CH2Cl2 (40 mL) was added dropwise within 30 min. The reaction mixture was stirred overnight. After filtration, the mixture was extracted with CH2Cl2 (200 mL) and saturated aqueous NaHCO3 (50 mL). The aqueous phase was again extracted with CH2Cl2 (100 mL), and the combined organic phase was dried with anhydrous Na2SO4. The solution was concentrated, and the crude product was purified by column chromatography over silica gel eluting with hexane/ethyl acetate (4:1, v/v) to give white crystal (yield ∼6.5 g). 1H NMR (CDCl 3, ppm): δ 4.28 (s, 6H, −CH2OOC−), 4.16 (d, 2H, CHCCH2O−), 3.65 (s, 2H, CH CCH2OCH2−), 2.43 (t, 1H, CHCCH2O−), 1.94 (s, 18H, −CBr(CH3)2). Preparation of Star AB3 Polystyrene Macromonomers. Into a 100 mL dry glass tube with a magnetic stirring bar, AB3 initiator (62.0 mg, 0.1 mmol), Me6tren (34.4 mg, 0.15 mmol), anisole (1.9 g), and styrene (1.9 g, 15.0 mmol) were added successively. After mixing thoroughly, the polymerization tube was degassed by two freeze− vacuum−thaw cycles, and CuBr (4.4 mg, 0.03 mmol) was added into the frozen solution. The polymerization tube was degassed by one more freeze−vacuum−thaw cycle before sealed under vacuum. The sealed tube was immersed into an oil bath at T = 80 °C. After the polymerization was performed for 0.5 h, the tube was rapidly stopped in liquid nitrogen. The polymer solution was then diluted with THF and passed through a short column of neutral alumina to remove metal salt. After twice precipitation by the addition of polymer solution into methanol, star AB3 polystyrene macromonomer was obtained after being dried under vacuum at T = 45 °C overnight (yield ∼0.5 g, PS1, Mn = 2200 g/mol). Following the similar protocol, five star AB3 polystyrenes with different molar masses were synthesized (PS1−5). D


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Macromolecules

ÄÅ É l ÅÅi y12 i y6ÑÑÑ o o Å ÑÑ o j z j z Å σ σ o o o 4εLJÅÅÅÅjjjj zzzz − jjjj zzzz ÑÑÑÑ + εLJ , rij ≤ rc o o WCA j z j z Å r Ñ Uij (rij) = m ÅÅk rij { o k ij { ÑÑÑÖ ÅÇ o o o o o o 0, rij > rc o n

U with different random angles to fully explore the different orientations for every particular pair of conformations. We defined the LJ parameters εLJ and σ and the monomer mass m as the LJ units and fixed the size of the simulation box to be L = 100 LJ units. To avoid the bond crossing, the parameters for the FENE potential were taken as k = 30 LJ units and R0 = 1.5 LJ units. We set the temperature to be 1 LJ unit. The damp factor (m/ζ) was chosen as 100 LJ units, and the time step of the simulation was set to be t = 0.005 LJ units. Our simulations were performed with the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).59 The results were obtained by averaging 103−104 statistically independent samples after the system equilibration.

(3)

where εLJ and σ denote the energy and the length parameters, respectively. We set the cutoff rc to be 1.12246σ. In addition, we adopted the finite extensible nonlinear elastic (FENE) potential to account for the chain connection between consecutive segments: É ÅÄÅ 2Ñ Ñ Å 1 jij rb zyz ÑÑÑÑ 2 Å Å Å UFENE(rb) = − kR 0 lnÅÅ1 − jj zz ÑÑ j R 0 z ÑÑ ÅÅ 2 k { ÑÖÑ ÅÇÅ (4)

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RESULTS AND DISCUSSION Preparation and Characterization of Star AB3 Macromonomers. Scheme 2 shows our strategy for the synthesis of

where rb denotes the distance between connected segments. The Langevin equation for the simulation can be cast into mi

d2rik dt 2

= − ζi

d2rik dt 2

− ∇k Ui + fik

Scheme 2. Schematic Synthesis of the Star AB3 Polystyrene Macromonomer and the Long-Subchain Hyperbranched Polystyrene (HPS)

(5)

where i denotes the ith segment in the simulation, k is the component of the position vector, t is the time, and mi and ζi represent the mass and the friction coefficient of the ith segments, respectively. Ui and f i are the potential and the random force acting on the ith segments, where f i satisfies the fluctuation−dissipation theorem with its magnitude given by kBTζi/dt . We constructed the simulation models for ABn LHPs (n = 2 and 3) with random conformations according to the chain structures illustrated in Scheme 3. Two different subchain lengths (Ls = 5 and Ls = 10) were used in the simulations for LHPs model chains. The molecular information including the molecular size ⟨Rg⟩ and the interpenetration factor (Ψ) were analyzed. To better understand the segment back-folding property for irregular AB3 LHPs, the simulation was also performed for symmetric dendrimer models composed of ABn macromonomers (n = 2, 3, and 4), where the degrees of polymerization (DP) for AB2, AB3, and AB4 macromonomers were set to be 931, 4841, and 17051, respectively. In this way, the radial density function of chain segments could be analyzed. The modeling of the dendrimers started from the growth of n + 1 branches of subchains with the chain length of Ls segments on a central segment [denoted as the first generation (G1)]. In addition, the ith generation (Gi, 2 ≤ i ≤ 5) was constructed by generating n branches of subchains from each subchain ending of the (i − 1)th generation. Finally, DP for 5 the dendrimer can be calculated as M = 1 + ∑i = 1 [2i − 1(n + 1)Ls]. For comparison, DP for dendrimers composed of ABn macromonomers were set to be the same as that for ABn LHPs counterpart. In the analysis, we calculated the radial density functions [ρ(r)] of chain segments at different generations only for dendrimers and the interpenetration factors Ψ for both LHPs and dendrimers. In the calculation of Ψ, the second virial coefficient A2, which describes the interactions between pairs of molecules, can be obtained by57,58 ÄÅ ÉÑ ÑÑ 2πNA ∞ 2ÅÅÅÅ ijj U (R ) yzz Ñ z − 1ÑÑÑ dR A2 = − 2 R ÅÅexpjj− z ÅÅ j kBT z ÑÑ 0 M (6) ÅÇ k ÑÖ {

star AB3 polystyrene macromonomers A(∼∼B)3 and the corresponding AB3 long-subchain hyperbranched polymers (LHPs). The tetrafunctional ATRP initiator was first prepared via esterification between monopropargyl pentaerythritol and 2-bromoisobutyryl bromide. The 1H NMR characterization confirms the chemical structures of key intermediate and target molecule (Figure 1 and Figure S1). The activator regenerated by electron transfer (ARGET) ATRP was adopted for the polymerization of styrene to suppress the possible side reactions. The monomer conversion of ATRP process was controlled below 60% to maintain high chain-end functionality. As shown in Figure 2a, all the prepared star polystyrenes show narrow molar mass distributions with polydispersity indexes (Mw/Mn) between 1.07 and 1.15, indicating a good control over polymerization process. Star AB3 macromonomers with different number-average molar masses (Mn) are obtained and denoted as PS1−5, and their molecular parameters are summarized in Table 1.

∫

where U(R) represents the intermolecular interaction between chains whose centers of mass are separated by a distance R. For each pair of generated chain conformations, the chain 2 was put on a certain position (with the distance of R and at the random angles of θ and φ from the center of mass of chain 1) in the polar coordinates. The intermolecular interactions between the two polymers can be obtained through M

U (R , θ , ϕ) =

M

∑ ∑ UijWCA(rij) i , m1 j , m2

(7)

where the summation terms correspond to values of the WCA potential for intermolecular interactions between segments i and j in chain 1 and chain 2. We performed a large amount of calculations for E


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Macromolecules

Figure 1. 1H NMR spectra of the tetrafunctional AB3 initiator and the related intermediate compound.

Figure 3. (a) and (b) SEC curves of star polystyrene macromonomers PS3 and PS5 at different hydrolysis times. (c) Hydrolysis time dependence of the degree of hydrolysis [(APS/(APS + APS,arm)] of ester groups, where APS and APS,arm represent the peak intensity of macromonomer (PS) and hydrolysis product (PSarm) in parts a and b, respectively. Figure 2. SEC curves of (a) star AB3 polystyrene macromonomers (PS1−PS5) and (b) their corresponding arm chains (PS1,arm−PS5,arm).

OH− ions near the backbone much lower. The SEC characterization result of fully hydrolyzed products is summarized in Table 2.

The above obtained molecular parameters for star macromonomers are apparent values if we consider the branching feature of their topological structure. Originally, we tried to characterize these star polystyrenes directly via triple-detection size exclusion chromatography (TD-SEC), but no reliable results were obtained due to the poor signal-to-noise ratio in the low molar mass range (103−104 g/mol). An alternative way is to “cut” the 3-arm star chains into individual linear arms for the facility of conventional SEC characterization. Thus, the hydrolysis of macromonomer in THF/NaOHaq was performed to obtain individual arm chains. Figure 2b shows the SEC curves of individual arm chains after hydrolysis. Figures 3a and 3b further show the evolution of SEC curves for PS3 and PS5 as a function of hydrolysis time. Figure 3c summarizes how the degree of hydrolysis of ester groups changes with hydrolysis time. Apparently, a first-order reaction dynamics was observed for both PS3 and PS5. Compared with PS3, the hydrolysis rate for PS5 is much slower, which could be attributed to the much stronger hydrophobicity of PS5. In principle, the stronger hydrophobicity makes the local concentrations of water and

Table 2. SEC Characterization of the Fully Hydrolyzed Products of 3-Arm Star Polystyrene Macromonomers sample

Mna (g/mol)

Mpa (g/mol)

Mw/Mna

PS1,arm PS2,arm PS3,arm PS4,arm PS5,arm

−b 1200 2600 4600 9700

∼500b 1300 2700 4900 9900

−b 1.11 1.09 1.10 1.04

a

Data were determined based on the conventional linear polystyrene calibration method. bData could not be accurately determined due to the overlap of peaks of PS5,arm and solvent.

In addition, we calculated the absolute number-average molar mass (Mn,cal) and peak molar mass (Mp,cal) for star macromonomers based on the following equations: Mn,cal = 3Mn,arm + Minitiator and Mp,cal = 3Mp,arm + Minitiator, where Mn,arm and Mp,arm represent the determined number-average molar

Table 1. Apparent and Absolute Molecular Parameters of 3-Arm Star Polystyrenes sample PS1 PS2 PS3 PS4 PS5

Mn,appa (g/mol) 2200 3800 8100 14000 30000

Mp,appa (g/mol) 2100 3600 7900 13800 27900

Mw/Mna

Mn,calb (g/mol)

Mp,calb (g/mol)

Mn,cal/Mn,app

Mp,cal/Mp,app

1.07 1.15 1.15 1.08 1.11

− 4200 8400 14400 29700

∼2100c 4500 8700 15300 30300

−c 1.10 1.04 1.03 0.99

−c 1.25 1.10 1.11 1.09

c

a

Data were determined based the conventional linear polystyrene calibration method. bData were calculated based on the following equations: Mn,cal = 3Mn,arm + Minitiator and Mp,cal = 3Mp,arm + Minitiator, where Mn,arm and Mp,arm represent the determined number-average molar mass and peak molar mass of individual arms, and Minitiator represents the molar mass of initiator (Minitiator ≃ 600 g/mol). cData were not able to be determined due to the peak overlap for PS5,arm and solvent. F


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Clearly, Mstar/Mlinear ≃ 1.09 when n = 3. Considering that Mstar/Mlinear is equal to Mcal/Mapp, the theoretical value for Mcal/Mapp should also be ∼1.09 for 3-arm star polymers in good solvents,60 which is pretty close to the Mp,cal/Mp,app ratios experimentally determined for 3-arm star polystyrenes (1.09− 1.25 in Table 1). The above comparison unambiguously confirms the branching feature of the resultant 3-arm star macromonomers. In the following discussion, we prefer to use the peak molar mass Mp,cal, instead of the number-average molar mass Mn,cal, as the feature parameter to represent the molar mass information about macromonomers (Mmacro), i.e., Mmacro = Mp,cal. This is because the peak information is generally more accurate and less affected by the side products in the low or high elution time in SEC characterization, where some polymer impurities such as the dead chains and coupled dimers might exist. The elution peaks in the SEC curves of star macromonomers, indeed, show slightly asymmetric feature (Figure 2a), which reasonably explains why the determined Mn,cal/Mn,app ratios are slightly smaller than the Mp,cal/Mp,app ratios. Overall, the result demonstrates the necessity for careful characterization of star macromonomer before further investigation on the structure− property relation of AB3 LHPs. The azide-functionalized macromonomers can be prepared via efficient bromine/azide substitution reaction. A combination of 1H NMR and FTIR characterization confirms that the substitution reaction is quantitatively controllable (Figures S2 and S3). According to our previous study of AB2 system,46 the signal for protons located at the arm ends (CHN3) should be visible at ∼3.90 ppm (Hh), whereas this feature signal is found to overlap with the signal from initiating site (Hd) for AB3 system, making the estimation for the chain-end functionality (f) not possible in Figure S2. Nevertheless, it is obvious that the signal intensity for peak d + h decreases as macromonomer molar mass increases. The successful installation of azide groups can be also reflected in the appearance of a NNN antisymmetric stretching absorption band near ∼2090 cm−1 in

mass and peak molar mass for individual arms, respectively, and Minitiator represents the molar mass for initiator (Minitiator ≃ 600 g/mol). The branching feature for star macromonomers can be reflected in the calculation results summarized in Table 1. Namely, the Mn,cal/Mn,app and Mp,cal/Mp,app ratios are estimated to be 0.99−1.10 and 1.09−1.25 (Figure 4),

Figure 4. Macromonomer molar mass (Mmacro) dependence of Mcal/ Mapp for 3-arm star macromonomers, where Mcal and Mapp represent the calculated and apparent values in Table 1, and Mmacro = Mp,cal is used as the x-variable in this figure.

respectively, indicating that the previously determined molar masses based on conventional calibration method are significantly underestimated. It is well-known that the radius of gyration for n-arm star and linear chains in good solvents can be respectively expressed as Rg,star = b[(3n − 2)/ n2]1/5Nstar3/5 and Rg,linear = bNlinear3/5, where Nstar and Nlinear represent the degree of polymerization for star and linear polymer, respectively, and b represents the Kuhn monomer size. Thus, for a given chain size (Rg,star = Rg,linear), the Mstar/ Mlinear ratio can be theoretically derived to be ÄÅ É ÅÅ n2 ÑÑÑ1/3 Å ÑÑ Mstar /Mlinear = Nstar /Nlinear = ÅÅÅ Ñ ÅÅÇ 3n − 2 ÑÑÑÖ (8)

Figure 5. SEC curves of the hyperbranched polystyrenes (HPS1−5) and their corresponding macromonomers, where the reaction was conducted at T = 35 °C and C = 0.30 g/mL. G


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Macromolecules Table 3. TD-SEC Characterization of AB3 Hyperbranched Polystyrenes (HPS1−5) SEC-RI sample HPS1 HPS2 HPS3 HPS4 HPS5

Mna (g/mol) 5.50 1.12 2.41 4.56 1.09

× × × × ×

103 104 104 104 105

SEC-MALS

Mwa (g/mol)

Mw/Mna

× × × × ×

3.43 5.62 7.00 6.99 11.74

1.90 6.29 4.60 3.19 1.28

104 104 105 105 106

Mnb (g/mol) 3.97 2.23 2.16 1.08 1.03

× × × × ×

103 104 105 105 106

Mwb (g/mol)

Mw/Mnb

× × × × ×

7.68 8.51 10.03 9.34 5.81

3.05 1.90 2.17 1.01 5.97

104 105 106 106 106

a

Data were determined based on the conventional linear polystyrene calibration method. bData were determined based on triple detection detectors.

Figure 6. Macromonomer molar mass (Mmacro) dependence of (a) the degree of polycondensation of macromonomer (DPw,TD‑SEC and DPw,LPC), (b) DPw,TD‑SEC/DPw,LPC, and (c) the polydispersity indexes [(Mw/Mn)TD‑SEC and (Mw/Mn)LPC] of hyperbranched polystyrenes prepared from AB3 macromonomers. The original FTIR spectra of (d) the hyperbranched polymers and the corresponding AB3 macromonomers and (e) the hyperbranched polymers and the corresponding AB2 macromonomers.49 (f) Calculated macromonomer molar mass (Mmacro) dependence of the ratios (Ahyper/Amacro) of absorbances of azide group of hyperbranched polymers (Ahyper) and macromonomers (Amacro) for AB3 and AB2 systems.

Figure 6a shows that DPw first increases with Mmacro and then roughly decreases with Mmacro. Actually, the phenomenon that DPw decreases as Mmacro increases in the high molar mass range of Mmacro (>∼104 g/mol) was observed in our previous study of the AB2 system,46 in which the interchain distance and the diffusion coefficient were found to be the key factors dominating the interchain coupling process. Apparently, our present result (AB3 system) qualitatively agrees well with our previous result (AB2 system).46 However, it is also worth noting that the DPw of HPS4 is much smaller than those of HPS3 and HPS5, showing a significant deviation from the above-described trend. We notice that the SEC curves for star macromonomers exhibit slightly asymmetric feature (Figure 2a), reflecting the existence of a trace amount of undesirable polymer−polymer coupled product (dimer side product). Theoretically, considering that the coupled product can react as chain-extension reagent in the click reaction, the more the coupled product, the more the mass percentage of the ultrahigh molecular weight fraction in the final HPS. Obviously, compared with PS3 and PS5, the SEC curve of PS4 apparently shows a less asymmetric feature, indicating a smaller mass percentage of the coupled product in the star macromonomer and, accordingly, a smaller mass fraction of the ultrahigh molar mass fraction in HPS4 (Figure

FT-IR spectra (Figure S3), in which the peak intensity decreases with the macromonomer molar mass. Influence of Macromonomer Branching on the Interchain Click Coupling. The azide/alkyne click chemistry was utilized to prepare hyperbranched polystyrenes. The addition of Sn(EH)2 was to suppress the potential Glaser coupling between alkyne groups.61 Figure 5 shows the SEC curves of resultant hyperbranched polystyrenes (HPS1−5) prepared at T = 35 °C. As shown, the elution peaks for these AB3 LHPs significantly shift to higher molar mass region after click coupling reaction, signifying the formation of huge hyperbranched chains. Their absolute molar masses and molar mass distributions were obtained based on TD-SEC measurements; meanwhile, the apparent values were also analyzed based on the linear polystyrene calibration (LPC) method for comparison. The characterization results are summarized in Table 3. Similar to our previous study,46 the degree of polycondensation (DP) is used for the description of interchain “clicking” process of macromonomers, where DP represents how many of the initial macromonomer chains coupled together, i.e., DP = Mhyper/Mmacro. More specifically, we prefer to use DPw (DPw = Mw,hyper/Mmacro) instead of DPn (DPn = Mn,hyper/Mmacro) because it is the weight-average molar mass that could be measured accurately in TD-SEC. H


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Macromolecules 5). In principle, in the triple-detection light scattering measurement, the average molar mass is extremely sensitive to the ultrahigh molar mass fraction existing in HPS; namely, 5% change in the mass percentage of ultrahigh molar mass fraction could probably lead to 50%−100% change of the average molar mass of HPS, which reasonably explains why the DPw of HPS4 is much smaller than those of HPS3 and HPS5. Obviously, based on the above observation and discussion, only a qualitative trend could be obtained based on Figure 6a. The discussion about the nature of the star−star coupling side reaction will be presented in a later section. Overall, the values of DPw,TD‑SEC and DPw,LPC for HPS1−5 samples are calculated to be 14−250 and 9−52, respectively, and the highest DPw,TD‑SEC of ∼250 is obtained for HPS3. The branching feature of these AB3 LHPs can be better observed when the DPw,TD‑SEC/DPw,LPC ratio is plotted as a function of Mmacro in Figure 6b. As shown, the value of DPw,TD‑SEC/DPw,LPC ranges from 3.0 to 4.7, signifying that the conventional LPC method greatly underestimates the determined molar masses. The obtained values of DPw,TD‑SEC/DPw,LPC for AB3 LHPs are even much larger than those for AB2 LHPs reported in our previous study,49 qualitatively reflecting the critical role of macromonomer branching in enhancing the degree of branching of hyperbranched structure. In addition, these hyperbranched samples are highly polydispersed (Figure 6c), and the values for (Mw/Mn)TD‑SEC and (Mw/Mn)LPC are determined to be 5.8−10.0 and 3.4−11.7, respectively. It is important to note that the LPC method even changes the trend for the dependency between Mw/Mn and Mmacro, highlighting the fact that the LPC method is not reliable even for the semiqualitative analysis of highly branched systems. The amount of peripheral azide groups of AB3 LHPs is confirmed by the semiquantitative analysis of the relative intensity of asymmetric vibration (Ihyper/Imacro) of azide group on hyperbranched chains (Ihyper) and the corresponding macromonomers (Imacro) in FTIR spectra (Figures 6d and 6e). Figure 6f shows that the values of Ihyper/Imacro (0.60−0.75) for AB3 system are much higher than those (0.30−0.55) for the AB2 system, indicating a much higher weight fraction of residual azide groups. Influence of Macromonomer Branching on the Intrachain Cyclization of 3-Arm Star Macromonomers. Furthermore, we analyzed how the macromonomer branching affects the macromonomer intrachain cyclization process. The topic related to the intrachain cyclization during the chain extension process has been widely explored for SHPs, whereas only limited experimental studies were reported for LHPs systems.10,62 Namely, Hutchings et al. reported that the intrachain cyclization of Y-type AB2 polystyrene macromonomers is strongly dependent on the chain length and polymer concentration. In addition, some theoretical studies have also been reported; namely, Kong’s group recently proposed a few methodologies including cyclic index, terminal index, and macro-cyclic index for the description of intramolecular cyclization of LHPs.63−65 Generally, the NMR method is not applicable to LHPs systems due to the poor signal-to-noise ratio. Our previous work indicated that monitoring the evolution for macromonomer peak in SEC curve could provide massive information related to the intrachain cyclization process because the change for both hydrodynamic size and percentage of macromonomer before and after cyclization can be determined.49

To quantitatively discuss the degree of intrachain cyclization for star macromonomers, two parameters are preferred: (1) the elution peak ratio (Mp,cyclized/Mp,precursor) of molar masses for cyclized product (Mp,cyclized) and star macromonomer precursor (Mp,precursor, Mp,precursor = Mp,macro) in SEC curves (Figure S4); (2) the ratio of peak areas (Ac/At) for cyclized macromonomer (Ac) and entire hyperbranched chains (At). The simple Gaussian mode was used to fit the peak for cyclized macromonomers in SEC curves, and the fitting curves and fitting parameters are summarized in Figure S5 and Table S1. In our previous work,30 the result already proved that more than ∼95% of the residual AB2 macromonomer is cyclized product, rather than the unreacted linear macromonomer, which means that the relative uncertainty is less than ∼5% in the calculation of macromonomer peak area in Figure 7.

Figure 7. (a) Macromonomer molar mass (Mmacro) dependence of the elution peak ratio (Mp,cyclized/Mp,precursor), where Mp,cyclized and Mp,precursor represent the peak molar mass for cyclized product and star macromonomer (Mp,precursor = Mmacro), respectively. (b) Macromonomer molar mass (Mmacro) dependence of weight fraction (Ac/At) of cyclized product for HPS1−5 samples, where the reaction was conducted at T = 35 °C. The data for hyperbranched samples prepared from V-type AB2 macromonomers are also presented for comparison (red curves).49

Nevertheless, to quantify the true ratio of cyclized product and residual linear macromonomer in the final AB3 HPS, a combination of 1H NMR and SEC was used to characterize the fractionated fractions. For this purpose, by taking HPS2 as a model sample, a preparative SEC system was used to fractionate the polydisperse HPS2. Two fractions of different elution times were obtained (“macromonomer” and “hyperbranched” fractions, Figure S6) and characterized by 1H NMR (Figure S7). As shown in Figure S7, compared with PS2 macromonomer, the chemical shift of characteristic protons for the two fractions totally changes. Namely, the signal for proton Ha shifts from 3.32 to 4.34 ppm, indicating the quantitative consumption (85%−95%) of alkyne groups for the I


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Macromolecules “macromonomer” fraction in the click reaction. Overall, a combination of SEC and 1H NMR characterization unambiguously confirms the high degree of cyclization for macromonomers during the click reaction. The analysis result of the molecular information for cyclized macromonomers shows: (i) the Mp,cyclized/Mp,precursor ratios for AB3 macromomers are typically 0.87−0.98 (Figure 7a), which are much larger than our previous reported values for AB2 macromonomers (0.78−0.88);49 (ii) the values of Ac/At for AB3 macromomers are much larger than those for AB2 macromonomers for a given Mmacro (Figure 7b); and(iii) both Mp,cyclized/Mp,precursor and Ac/At show a strong dependence on macromonomer molar mass. Mathematically, half of the chain segments will undergo intrachain cyclization for a AB2 macromonomer chain, while only one-third of the chain segments will do so for a AB3 macromonomer chain, which reasonably explains why the determined Mp,cyclized/Mp,precursor ratios are much larger for 3arm star macromonomer at a given molar mass (Figure 7a). Second, the larger Ac/At ratios for the AB3 system in Figure 7b indicate that the star chains are more likely to undergo the intrachain cyclization instead of the interchain coupling reaction. In principle, the interchain click coupling process is second-order in concentration, which is sensitive to the steric hindrance effect of macromonomer precursors. Apparently, the alkyne group located at the center of AB3 star macromonomer is expected to suffer stronger steric hindrance (inset in Figure 7b) due to its much higher segment density in the star center, which is not favorable to interchain coupling reaction. On the other hand, Figure 7b shows that the degree of intrachain cyclization first decreases and then increases with Mmacro for both AB2 and AB3 systems. This trend can be rationalized by the competitive effect between intrachain and interchain coupling processes, namely, the ratio (kintra/kinter) of rate constants of intrachain cyclization (kintra) and interchain coupling (kinter) processes. Generally, kintra is roughly inversely proportional to the square of radius of gyration (Rg) for a given polymer coil,66 i.e., kintra ∼ Rg−2, explaining why Ac/At decreases first with the chain length; while for much longer chains, the large coil sizes significantly enhance the intermolecular excluded-volume effect, resulting in a dramatic decrease in kinter, which in turn leads to an increase of kintra/ kinter. It is worth noting that the previous studies on smallmolecule ABn systems have already pointed out that the occurrence of cyclization reactions is strongly dependent on the monomer structure.21,65,67−70 Namely, Hawker et al. found that the bis(methylol)propionic acid AB2-type monomer leads to hyperbranched polymers with up to ∼90% of cyclic product; in contrast, up to 95% of the hyperbranched chains prepared from 4,4′-dihydroxyphenylpropionic acid still contain the acid focal unit.67 Our observation demonstrates a universal rule for ABn LHPs systems that the intrachain cyclization of ABn (n ≥ 2) macromonomers is mainly dominated by the steric hindrance of reactive groups, and the spatial distance between reactive groups, which is different with the small-molecule systems. Structural Defects in the Hyperbranched Structure of AB3LHPs. Note that the star macromonomers synthesized by ATRP exhibit slightly asymmetric feature in SEC curves (Figure 2a); i.e., a trace amount of undesirable polymer− polymer coupled product (dimer side product) is presented in the high molar mass range, indicating the occurrence of some undesirable side reaction, such as the radical−radical coupling

termination or acetylenic Glaser coupling reactions.61 To clarify the nature of structural defects in AB3 LHPs, the atom transfer radical coupling (ATRC) model reaction was carried out by using a bromine end-capped linear polystyrene (PS-Br, Mn = 5800 g/mol, black curve Figure 8a) as precursor polymer.

Figure 8. (a) SEC curves for PS-c-PS coupling product before (blue curve) and after (red curve) hydrolysis treatment, where PS-c-PS was prepared by ATRC process by using PS-Br (black curve) as precursor. (b) Schematic illustration of Glaser coupling process during ATRP process and the possible structural defects in the final hyperbranched structure.

Via ATRC reaction between two PS-Br chains, we obtained the coupled product PS-c-PS dimer, accompanied by ∼30% (w/w) of unreacted PS-Br precursor (blue curve in Figure 8a). It is worth noting that our previous hydrolysis experiments indicate that the conversions for the hydrolysis of star macromonomers into individual arm chains could reach 100% within a couple of hours (Figures 2 and 3), which implies that the coupling site in the dimer side product is liable to alkaline conditions. However, our controllable hydrolysis experiment on the PS-c-PS model dimer shows that the SEC curves for PS-c-PS before and after hydrolysis treatment (THF/NaOHaq) are nearly unchanged, if we consider the uncertainty of SEC measurement. This fact demonstrates that the aliphatic carbon−carbon linkages in the middle of PS-c-PS chains are extremely stable to alkaline conditions. A comparison of results in Figures 2 and 8 unambiguously clarifies that the mechanism for side reaction is attributed to the acetylenic Glaser coupling mechanism rather than the radical−radical coupling mechanism. Figure 8b shows the schematic illustration of Glaser coupling during ATRP, where the 6-arm star polystyrene side product containing an acetylene−acetylene linkage in the star center and six azide groups at each arm end is shown. Theoretically, for the 6-arm star−star coupled side product, it is possible to simultaneously react with 1−6 growing hyperbranched oligomers, which leads to structural defects in the final hyperbranched structure. However, one formed hyperbranched chain could on average contain no more than one such kind of 6-arm star−star defect unit because only the focal alkyne unit is suspected to undergo the interchain click J


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Mhyper, which is consistent with our anticipation. (ii) The MHS plots for AB3 LHPs generally show two different dependency relations of Mhyper in the low and high molar mass regions. Namely, the fitting exponent ν is found to be 0.59 ± 0.01 when 104 g/mol < Mhyper < 105 g/mol, while it decreases to be 0.39 ± 0.01 when 105 g/mol < Mhyper < 107 g/mol. The larger exponent ν ≃ 0.59 could be attributed to the lower branching density for hyperbranched oligomers in the low molar mass region. Moreover, the determined ν ≃ 0.39 for the AB3 system is extremely close to ν ≃ 0.40 for the AB2 system determined in our previous work, implying that the macromonomer branching has little effect on the fractal dimension of LHPs. (iii) The determined [η] for AB3 LHPs is found to be almost independent of Mmacro, which is reflected in the overlap of [η] data for HPS1−5 with different subchain lengths (blue region). In contrast, the [η] data for the AB2 LHPs system show significant dependency of Mmacro (pink region in Figure 9a). Specifically, we previously confirmed that [η] is scaled to variables Mhyper and Mmacro as

coupling with the 6-arm star polymer. In principle, if the 6-arm star product reacts with more than three growing hyperbranched oligomers, it could enhance the degree of coupling during click reaction and further lead to higher mass percentage of high molar mass fractions in the final HPS, which helps explain whya significant mass percentage of high molar mass fraction was observed for HPS3 and HPS5 (Figure 5). It is not difficult to realize that the analysis of detailed structure and spatial distribution of the existing defect units is a challenging task. For this purpose, the computational simulation is undergoing to uncover the formation kinetics of the defect units during the chain extension process as well as their structural details in the final product. Influence of Macromonomer Branching on the Structural Features and Fractal Properties of AB3 LHPs: TD-SEC Study of Unfractionated Samples. First, a well-calibrated TD-SEC system was used to characterize the structural features and fractal properties of resultant LHPs samples, such as the intrinsic viscosity ([η]) and the radius of gyration (Rg). The calibration process is detailed in the Experimental Section and in our previous work.49 The TDSEC cumulative/differential molar mass distribution curves are summarized in Figure S8. It is well-known that the [η]−Mν and Rg−Mα scaling are two fundamental equations describing the fractal feature of topological macromolecules, where ν and α are two scaling exponents. Figures 9a and 9b show the plots of experimentally

[η] = K ηMhyper νM macro μ

(9)

where Kη,AB2 ≃ 3.57 × 10−2 mL/g, ν ≃ 0.40, and μ ≃ 0.25 for the AB2 LHPs system. By using universal eq 9 to fit the [η] data for AB3 system, and assuming μ = 0 and ν = 0.39 ± 0.01, we estimate Kη,AB3 to be 0.29 ± 0.01 mL/g. In addition to viscosity data, useful information related to the structural feature can also be extracted from R g measurement. Based on theoretical prediction,72−74 for randomly hyperbranched polymers with controlled subchain length, Rg should be scaled to Mhyper and Mmacro as R g = HR Mhyper αM macro β

(10)

where α = 1/2 and β = 1/10 for hyperbranched chains in a good solvent. Experimentally, we previously confirmed for AB2 LHPs system that HR,AB2 ≃ 1.75 × 10−2 nm, α ≃ 0.47, and β ≃ 0.083. For AB3 LHPs system, we have Rg ∼ Mhyperα with α = 0.47 ± 0.01 (Figure 9b), which is close to α ≃ 0.47 for the AB2 LHPs system,49 reconfirming the similar fractal dimensions for AB3 and AB2 systems. However, similar to our observation for [η] in Figure 9a, Figure 9b further indicates that Rg is surprisingly almost independent of Mmacro for AB3 LHPs. Mathematically, HR,AB3 = (3.6 ± 0.1) × 10−2 nm if we assume α ≃ 0.47 and β ≃ 0. Honestly, such a Mmacro-independency phenomenon could not be easily rationalized by existing theories.49 Further discussion about the origin for this anomaly will be presented in detail based on a combination of experimental observation and Langevin dynamics simulation in a later section (vide infra). Furthermore, a combined analysis of [η] and Rg data gives a mass of information related to the draining property of AB3 LHPs. Figure 10 shows how the draining factor (Φ) varies with Mhyper, where Φ can be expressed as

Figure 9. (a) Total molar mass (Mhyper) dependence of the intrinsic viscosity ([η]) of HPS1−5 measured by the TD-SEC system in THF at T = 35 °C, where the data for AB2 hyperbranched49 and linear polystyrene71 are also plotted for comparison. (b) Total molar mass (Mhyper) dependence of the radius of gyration (Rg) of HPS1−5 measured by the TD-SEC system.

Φ=

measured [η] and Rg as a function of total molar mass (Mhyper) for HPS1−5 AB3 LHPs. On the basis of the Mark−Houwink− Sakurada (MHS) plot of [η] versus Mhyper in Figure 9a, we have three findings: (i) Compared with the data for AB2 LHPs system reported in our previous work (pink region),49 the macromonomer branching effect, indeed, leads to a significant decrease of [η] for AB3 LHPs system (black region) at a given

[η]Mhyper Rg3

(11)

Physically, the draining property decreases as the branching density increases.75 Theoretically, Φ is predicted to be 0.26 for linear chains under theta conditions.75 By taking [η] = 1.36 × 10−2M0.714 and Rg = 2.45 × 10−2M0.546 for linear polystyrene in THF71 and [η] ≃ 0.29Mhyper0.39 and Rg ≃ 3.6 × 10−2Mhyper0.47 for AB3 LHPs in THF into eq 11, the draining property for K


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Influence of Macromonomer Branching on the Structural Features and Fractal Properties of AB3 LHPs: Stand-Alone LLS Study on Fractionated Samples. Note that the fitted curves of Rg data for AB3 LHPs present partially curved characteristics in Figure 9b, such as the purple and orange curves. Unlike [η], as it is well-known, Rg is more difficult to be accurately determined in TD-SEC measurement because it is inherently limited by the detection limit of light scattering method, especially for polymer samples with high polydispersities.76,77 Thus, the slightly curved feature in Rg plots in Figure 9b might be attributed to the decreased signalto-noise ratio induced by the highly dispersed nature of unfractionated AB3 LHPs samples. To clarify this point, HPS4 was further fractionated into a few narrowly distributed fractions, three of which with high molar masses were further studied by TD-SEC and stand-alone laser light scattering (LLS). Figure 11a shows the hydrodynamic radius distributions [f(Rh)] of HPS4 fractions measured by dynamic LLS in toluene. The determined average hydrodynamic radius (⟨Rh⟩) for fractions 1, 2, and 3 is 38.2, 32.3, and 22.8 nm, respectively. These samples show small polydispersity indexes (PDI) ranging from ∼1.20 to ∼1.40, which were estimated from PDI ≈ (1 + 4 μ2/⟨D⟩2) (see Experimental Section). TD-SEC measurement demonstrates that the fractionated samples present different characteristics in Rg−Mhyper plots compared with the unfractionated sample (Figure 11b). A linear relationship between Rg and Mhyper over the whole molar mass range from 8.0 × 105 to 1.0 × 107 g/mol is presented for each fractionated sample; in contrast, a curved feature is observed when Mhyper is smaller than 3.0 × 106 g/mol for the unfractionated sample (Figure 9b). The comparative study of fractionated and unfractionated samples unambiguously clarifies that it is the high polydispersity that accounts for the partially curved feature observed in Rg−Mhyper plots for highly polydispersed AB3 LHPs. Thus, extra caution should be

Figure 10. (a) Total molar mass (Mhyper) dependence of the draining factors (Φ) for AB3 LHPs and linear polystyrene reference in THF, where the magnitude of relative error depends on the fluctuation of [η] and Rg data in Figure 9, and [η] = 1.36 × 10−2M0.714 and Rg = 2.45 × 10−2M0.546 for linear chains in THF were used.75

linear chains and AB3 LHPs in a good solvent can be compared. As shown in Figure 10, AB3 LHPs show much larger Φ (4 × 1024 < Φ < 5 × 1024), indicating less draining property and more compact structure. In polymer physics, the exponents α and ν are inherently correlated by the Flory−Fox equation [η] ∼ R3/M, i.e., ν = 3α − 1. By inputting the determined ν ≃ 0.39 into the equation, we have the derived value for α ≃ 0.46, which is fairly close to the determined α = 0.47 ± 0.01 for the AB3 system (Figure 9a). The simultaneous measurements of [η] and Rg crossvalidate the reliability of obtained data in TD-SEC measurement. Overall, the characterization of unfractionated samples demonstrates that the macromonomer branching leads to an ignorable influence on the fractal dimension but a significant difference in the independency relation between solution property and subchain length for ABn LHP. This can be attributed to the unique synergistic effect of segment−segment interpenetration and segment back-folding phenomena for highly branched AB3 system (vide infra).

Figure 11. (a) Hydrodynamic radius distributions [f(Rh)] of HPS4 fractions in toluene at T = 25 °C. (b) Total molar mass (Mhyper) dependence of the radius of gyration (Rg) of the unfractionated and fractionated HPS4 measured by TD-SEC in THF. (c) Total molar mass (Mhyper) dependence of the radius of gyration (Rg) of HPS4 fractions measured by TD-SEC and stand-alone LLS. (d) Total molar mass (Mhyper) dependence of the chain configuration parameter ⟨Rg⟩/⟨Rh⟩ of HPS4 fractions measured by dynamic LLS in toluene at T = 25 °C, where the data for AB2 LHPs and linear polystyrene are plotted for comparison. L


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local segment density and branching pattern. Scheme 3 illustrates two possible chain configurations which intuitively explains how AB3 and AB2 LHPs could have a similar fractal dimension but different local segment densities.

paid when dealing with highly branched systems of high polydispersities. In addition, the average radii of gyration (⟨Rg⟩) for these fractions were also determined by stand-alone static LLS. The solution concentrations were well-calibrated by UV−vis spectra (Figure S9). Figure 11c shows that the ⟨Rg⟩s determined by TD-SEC and stand-alone LLS agree well with each other. Overall, the control experiment of fractionated samples reconfirms that AB3 LHPs prepared from star macromonomers still holds the statistically fractal feature with a fractal dimensions similar to those for AB2 LHPs. Figure 11d shows the chain configuration parameter ⟨Rg⟩/ ⟨Rh⟩ for these fractionated samples. It is known that for hard spheres, hyperbranched chains, and coiled linear chains ⟨Rg⟩/ ⟨Rh⟩ is ∼0.774, 1.0−1.4, and 1.5−1.8, respectively.46 The ⟨Rg⟩/⟨Rh⟩ ratios for AB3 system vary between ∼1.10 and ∼1.20, which are much smaller than 1.20−1.40 for the AB2 system (8.7 × 105 g/mol < Mhyper < 1.05 × 107 g/mol),46 revealing the more compact structure for AB3 LHPs, which also provides the first quantitative comparison of ⟨Rg⟩/⟨Rh⟩ values for LHPs with different branching patterns but an identical chemical component. Further Discussion on the Basis of Experimental Result and Langevin Dynamics Simulation. The above thorough characterization of [η] and Rg for unfractionated samples and ⟨Rg⟩, ⟨Rh⟩, and ⟨Rg⟩/⟨Rh⟩ for fractionated samples clearly demonstrates that, compared with AB2 LHPs, the macromonomer branching effect leads to significantly different structural features and solution properties for AB3 LHPs. Particularly, the abnormal independency between Mmacro solution properties ([η] and Rg) remains unclear. Overall, the observed phenomenon could not be fully understood according to the existing theories. To date, two popular theoretical models have been proposed for the description of hyperbranched polymers, including the randomly branched model proposed by Zimm−Stockmayer72 and the cascade theory proposed by Kajiwara.78 These theoretical models were previously applied to long-subchain hyperbranched poly(Llactide)s in the work of Kawaguchi et al., but only very limited satisfactory results were obtained.8 First, the [η] and Rg results indicate that the macromonomer branching effect shows an ignorable influence on the fractal dimensions (f, f = 1/α, and Rg ∼ Mhyperα), which is different with our initial anticipation. Experimentally, we have f ≃ 2.10 for the AB3 system (α = 0.47 ± 0.1) and f = 2.05−2.27 for the previous AB2 system (0.44 < α < 0.49).49 A literature search shows that f generally varies from ∼2.0 to ∼2.5 for SHPs systems. For example, f was determined to be ∼2.38 for polyesters79 and ∼2.30 for poly(β-amino esters),80 and similar results were found for dextrane and starch by Burchard et al.;81,82 for some of highly branched SHPs systems, f was even reported to be 2.6−2.8.83 Overall, the reported f values for LHPs systems are smaller than those for SHPs systems, signifying that the existence of long flexible linear subchains between branching points could endow hyperbranched chains with more open/swollen chain conformations. For instance, f was independently reported to be ∼2.10 by our group49 and ∼2.08 by the group of Perrier39 for AB2 polystyrene LHPs; f was found to be ∼2.27 for AB2 poly(L-lactide) LHPs by Kawaguchi et al. (longest macromonomer).8 Upon a comprehensive comparison of the reported f values for AB2 LHPs, AB3 LHPs, and SHPs systems, the result convincingly reveals that the fractal dimension of hyperbranched structure is more sensitive to the internal subchain length rather than the

Scheme 3. Schematic Illustration of Two Possible Chain Configurations Which Intuitively Explains How AB3 and AB2 LHPs Chains Could Have a Similar Fractal Dimension but Different Local Segment Densities, Where Each Blob Represents the Minimum Statistical Unit Reflecting the Fractal Feature

Second, the [η] and Rg results show that both [η] and ⟨Rg⟩ are independent of Mmacro, which appears odd to us at f irst sight. Physically, for a given total molar mass, the numerical values of [η] and ⟨Rg⟩ are quantitative indexes reflecting the draining property and local segment density for different polymer samples. Intuitively, for a given Mhyper, the increase of Mmacro is supposed to make the branching density sparser and pervaded volume larger, which should lead to the increase of [η] and ⟨Rg⟩. Indeed, we previously confirmed that [η] ∼ Mmacroμ (μ ≃ 0.3) and Rg ∼ Mmacroβ(β ≃ 0.1) for the AB2 system.49 Thus, the observed independency relation between solution properties and Mmacro in AB3 system implies that the local chain segment density of AB3 LHPs is almost a constant and irrelevant with Mmacro (internal subchain length), which is significantly different from the AB2 system. How does one understand such a phenomenon from a perspective of macromolecular physics? We propose that the unique synergistic effect of segment interpenetration and segment back-folding, which existed only in highly branched systems, is responsible for the independency of solution properties from Mmacro for AB3 LHPs. Such a statement can be rationalized based on the following fact: both the segment−segment interpenetration factor (Ψ) and the segment back-folding probability (Pb) are sensitive to the branching pattern and branching density of hyperbranched structure. The interpenetration factor Ψ, or the so-called interpenetration function, is defined as Ψ=

A 2 Mhyper 2 4π 3/2NAR g 3

(12)

where A2 is the second virial coefficient which characterizes the interaction between polymer chain segments and solvent molecules.75 In contrast with small-molecule monomers, M


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subchains (HPS1), the interpenetration might be completely inhibited. Consequently, for a given Mhyper, the overall molecular sizes and local draining properties of hyperbranched chains with different subchain lengths could eventually approach to be similar in the end of click polymerization (Scheme 4). In addition to the occurrence of interchain interpenetration, the local concentration of azide group in the internal space of hyperbranched oligomer structure has to be high enough to facilitate the azide−alkyne interchain coupling process. Physically, this is strongly affected by the chain segment backfolding property. Thus, the difference of the segment backfolding probability (Pb) between AB3 and AB2 systems also needs to be considered. The diffusion process of chain segments from the outer layers into the inner space is a wellknown “back-folding” characteristic in highly branched polymers.85,86 Namely, Muthukumar et al. used “kinetic growth” simulations to predict the molecular conformation of the starburst molecules and found that the extensive backfolding may be expected at the later stages of branching growth for dendritic polymers. 87 More importantly, numerous experimental studies demonstrated that Pb generally increases with branching density for a given system. Namely, previous molecular dynamics simulation study by He et al. found that for a highly branched dendritic polystyrene the chain segments of the highest generation (G4 and G5) could even be found throughout the whole molecule via chain back-folding mechanism.86 In the dendritic structure, five chain segments were simultaneously interconnected by one branching point. Physically, the segment back-folding property is mainly determined by the local segment density around the branching point. In our study, four and three chain segments are interconnected by one branching point for AB3 and AB2 systems, respectively, implying that the local segment density around the branching point for AB3 system is 33% higher than that for AB2 system, which is beneficial for the segment backfolding (higher Pb). Moreover, if we consider the spatial conformation for segments connected by one branching point, the tetrahedral orientation for AB3 system is significantly different with the triangular planar orientation for AB2 system. Mathematically, the average segment−segment dihedral angle is ∼109° for the AB3 system and ∼120° for the AB2 system. Obviously, because of the more open conformation and larger segment−segment dihedral angle, the trend for segment backfolding could be greatly suppressed in the AB2 system. Accordingly, the azide end-groups in hyperbranched oligomer tend to accumulate in the peripheral space during branching growth for the AB2 system. For the AB3 system, however, a significant fraction of azide end-groups tend to penetrate into the inner space of hyperbranched structure through segment back-folding, leading to the increase of local concentration of azide group in the core region, which is beneficial for the further interchain coupling inside the internal cavities. The branching pattern-dependent Pb reasonably explains why the solution properties were observed to be independent of Mmacro only in the AB3 system. Obviously, the unique synergistic effect of segment interpenetration and segment back-folding results in the Mmacro-independent solution properties for AB3 LHPs. To further verify the rationality of our proposed explanation, we performed Langevin dynamics simulation to get insight into the difference of the structural properties of ABn LHPs. We constructed the simulation models for ABn LHPs (n = 2 and 3)

macromonomers are draining and permeable. It is known for star and hyperbranched polymers that Ψ increases rapidly as the branching density increases, indicating the suppression of the trend for segment−segment interpenetration. For hard spheres, multiarm star chains, and coiled linear chains, Ψ is ∼1.62, 0.40−1.30, and ∼0.26, respectively.75 The branching points evidently form obstacles which can no longer be circumvented. Unfortunately, the interpenetration behavior of randomly branched systems has been rarely studied due to the complexity of branched structure and the difficulty of sample preparation.81,84 In our previous study, we showed that the reaction-limited cluster−cluster aggregation mechanism dominates the polymerization kinetics of interchain click coupling process.46 Theoretically, the interchain click coupling for the AB3 system mainly occurs between star macromonomers in the initial stage and then between hyperbranched oligomers in the later stage. It is not difficult to realize that hyperbranched oligomers composed of longer subchains are more interpermeable in the initial stage due to the larger free volume inside their cavities (smaller Ψ in Scheme 4). Quantitatively, the segment density Scheme 4. Schematic Illustration of How the Macromonomer Molar Mass (Mmacro) Potentially Influences the Click Interchain Coupling and Segment−Segment Interpenetration Factors (Ψ) of AB3 LHPs Oligomer Chains during Different Stages of Polymerization

of star macromonomer (ρmacro) can be used to roughly estimate the local segment density of hyperbranched oligomer structure, where ρmacro = 3Mmacro/(4NAπ⟨Rg⟩3). Namely, ρmacro decreases from ∼0.20 to ∼0.04 g/cm3 when Mmacro increases from 2.2 × 103 to 3.0 × 104 g/mol. This difference makes one hyperbranched oligomer chain composed of longer internal subchains easier to undergo interpenetration with other small macromonomers/oligomers, facilitating the occurrence of interchain coupling reaction in its interior space (Scheme 4). In the case of hyperbranched oligomers composed of shortest N


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quasi-plateau region in ρ(r) curve starts from r = 5 to r = 20 for the AB3 system and from r = 5 to r = 25 for the AB4 system, indicating the significantly enhanced back-folding of the peripheral segments into the inner space. A similar trend was also observed for the ρ(r) curves of G4 segments (Figure S10). Moreover, the simulation results of ABn systems with different subchain lengths show similar trends. The above result unambiguously reveals that the back-folding property is dominated by the macromonomer branching effect and is not sensitive to the internal subchain length. Theoretically, the segment back-folding phenomenon is significant only in highly branched ABn systems with n ≥ 3, which reasonably explains why the abnormal independency relation between solution properties and Mmacro was observed only in the AB3 system. Table 4 further shows the simulation result of Ψ for different types of long-subchain dendrimers and hyperbranched polymers. The results illustrate that for a given macromonomer type and subchain length the Ψ values for dendrimers are significantly larger than ABn LHPs, which is reasonable and can be attributed to the more condensed molecular structure of dendrimers and stronger steric hindrance effect. As expected, AB2 systems present a stronger trend for segment interpenetration compared with AB3 systems, reflected in the smaller Ψ values. Quantitatively, Ψ = 1.64 for AB3 dendrimer (Ls = 10), signifying a hard-sphere-like structure. For AB3 LHPs, Ψ decreases from 1.21 to 1.15 as Ls increases from 5 to 10, indicating that the trend for segment interpenetration increases with the subchain length. Note that the subchain lengths of experimentally used HPS4 and HPS5 (∼50 and ∼100 monomer units for each arm) are much longer than the lengths used in simulations, implying that the real AB3 LHPs composed of long subchains are still interpenetrable (smaller Ψ). Overall, a combination of experimental observation and Langevin dynamics simulation uncovers the origin for the different dependency relations between solution properties and Mmacro for AB2 and AB3 systems. The macromonomer branching effect plays an important role. For AB3 hyperbranched oligomers, the increase of subchain length leads to the enhancement of the trend for segment interpenetration and interchain coupling in the internal space of hyperbranched structure, which eventually leads to a similar segment density and draining property for AB3 LHPs with different subchain lengths. However, because of the lack of segment back-folding property, the interchain coupling reaction could occur only in the peripheral region of AB2 LHPs chains. Overall, the synergistic effect of segment interpenetration and segment back-folding, which does not exist in the AB2 system, could be the most probable origin resulting in the unique Mmacroindependent solution properties of the AB3 LHPs system. It is also worth noting that though the further increase of the degree of branching of macromonomer could promote the segment back-folding, it could simultaneously lead to the significant decrease of interpenetration factor Ψ. Consequently, the segment interpenetration could be completely prohibited for ABn LHPs systems with much stronger macromonomer branching effect. We expect that such a kind

with random conformations according to the chain structures illustrated in Scheme 3. Two different subchain lengths (Ls = 5 and Ls = 10) were used in the simulations for LHPs model chains. The simulation details can be found in the Experimental Section. Note that it is difficult to define the geometric center for randomly hyperbranched chains, so the simulation was also performed for dendrimer models made of ABn macromonomers (n = 2, 3, and 4) to better understand the segment back-folding property for ABn LHPs. In this way, the radial density function [ρ(r)] for the chain segments of different branching generations could be analyzed. In the analysis, we calculated ρ(r) only for dendrimers but Ψ for both LHPs and dendrimers. Figure 12 quantitatively shows how the radial density ρ(r) of G5 segments (dashed lines) changes with the type of

Figure 12. Simulation results of the radial density [ρ(r)] of segments belonging to G1 (solid lines) and G5 (dashed lines) generations for dendrimers made of AB2, AB3, and AB4 macromonomers (Ls = 10).

macromonomer for long-subchain dendrimers. The model structures used in the simulation are shown in Scheme 5. The Scheme 5. Simulation Snapshots for the Model Structures of Long-Subchain Dendrimers Made of AB2, AB3, and AB4 Macromonomers

simulation results illustrate that the ρ(r) curve for AB2 system presents a unimodal distribution, and the peak value is located at r ≃ 12. As the branching density of macromonomer increases, the distribution curve presents a bimodal distribution for the AB3 system and trimodal distribution for the AB4 system, indicating the prominent broadening of the distribution curve. More importantly, we observed that the unique

Table 4. Simulation Results of the Interpenetration Factor (Ψ) for Different Types of Polymers Ψ

AB2 dendrimer (Ls = 10) 1.10

AB3 dendrimer (Ls = 10) 1.64

AB2 LHPs (Ls = 10) 0.76 O

AB3 LHPs (Ls = 10) 1.15

AB2 LHPs (Ls = 5) 0.87

AB3 LHPs (Ls = 5) 1.21


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Macromolecules of synergistic effect might only exist for ABn LHPs systems with n ranging from 3 to 5. The study of AB4 and AB6 LHPs systems is undergoing in our lab to test our conjecture.

monomers; Figures S6 and S7: SEC curves and 1H NMR spectra of PS2, HPS2, “hyperbranched” and “macromonomer” fractions; Figure S8: molar mass distribution functions of hyperbranched samples; Figure S9: determination of concentration of HPS4 fractions 1− 3; Figure S10: simulation results of the radial density (PDF)

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CONCLUSION Using five well-characterized 3-arm star polystyrenes with different molar masses (Mmacro) as macromonomers, we have for the f irst time elucidated how the branching effect of macromonomer affects the polymerization, structural features, and solution properties of long-subchain hyperbranched polymers (LHPs). The result reveals that the macromonomer branching effect leads to suppressed chain extension and enhanced self-cyclization during click interchain polymerization process, which is attributed to the stronger steric hindrance effect for star AB3 macromonomers compared with linear AB2 macromonomers. Furthermore, via a combination of experimental study of the total molar mass (Mt) dependent intrinsic viscosity ([η]) and radius of gyration (Rg) for AB2 and AB3 LHPs systems, and the computational study of the segment interpenetration and segment back-folding property for dendrimers and LHPs model systems, we reveal that (i) the fractal dimensions (f) for LHPs are generally smaller than short-subchain hypebranched system, but f is not sensitive to the local segment density or branching pattern, and (ii) significantly different than AB2 LHPs system, both [η] and Rg are almost independent of Mmacro for the AB3 LHPs system, which is attributed to the unique synergistic effect of segment interpenetration and segment back-folding. In polymer physics, the increase of subchain length leads to the enhancement of the trend for segment interpenetration and interchain coupling in the internal space of hyperbranched structure, which eventually could lead to a similar segment density and draining property for AB3 LHPs with different subchain lengths. From a practical point of view, the observed independency relation between solution properties and internal subchain length for the AB3 LHPs system can be useful to simplify the quality control of hyperbranched polymer product in industrial production. Namely, a slight variation of molar mass for different batches of AB3 macromonomer product is acceptable, if we consider the fact that the material properties of AB3 LHPs are independent of Mmacro. Consequently, the strict control of molecular parameters of macromonomer product is not necessary for subsequent polymerization. The current study has not only provided meaningful experimental data for further theoretical modeling of a universal theory for LHPs systems with different internal branching patterns but also conferred a novel insight into the branching effect of macromonomer on the structural features and solution properties of hyperbranched polymers from an experimental perspective.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Hongjun Yang: 0000-0001-5631-4285 Lianwei Li: 0000-0002-1996-6046 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The National Natural Scientific Foundation of China Projects (21774116, 51703216, 21404103 and 51773192) are gratefully acknowledged.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b02364. Figure S1: 1H NMR spectra of the initiator and intermediate compound; Figures S2 and S3: 1H NMR spectra and FTIR spectra of macromonomers; Figure S4 and Table S1: the fitting curves and fitting parameters of cyclized macromonomers; Figure S5: SEC curves of cyclized products and their corresponding macroP


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