DielsâAlder Hyperbranched Pyridylphenylene Polymer Fractions as

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

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Diels−Alder Hyperbranched Pyridylphenylene Polymer Fractions as Alternatives to Dendrimers Alexander S. Gubarev,† Alexey A. Lezov,† Anna S. Senchukova,† Petr S. Vlasov,‡ Elena S. Serkova,§ Nina V. Kuchkina,§ Zinaida B. Shifrina,§ and Nikolai V. Tsvetkov*,† Department of Molecular Biophysics and Physics of Polymers, The Faculty of Physics, and ‡Department of Macromolecular Chemistry, Institute of Chemistry, St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia § Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilova str. 28, Moscow 119991, Russia Macromolecules Downloaded from pubs.acs.org by UNIV OF NEW ENGLAND on 02/15/19. For personal use only.

†

S Supporting Information *

ABSTRACT: The results of the hydrodynamic study of hyperbranched pyridylphenylene polymers synthesized via Diels−Alder cycloaddition reaction of multifunctional monomers are reported. The synthesized polymers were fractionated into a much narrowly dispersed fractions. The in-depth analysis of molecular characteristics and conformation of the initial polymers and corresponding fractions was performed using the unique combination of hydrodynamic approaches. The intercorrelation and self-consistency of obtained data were ensured using the hydrodynamic invariant concept and classical Kuhn−Mark−Houwink−Sakurada scaling relations. The evaluated data suggest that hyperbranched pyridylphenylene demonstrates the hydrodynamic behavior typical for asymmetrical compact macromolecular species. Furthermore, hydrodynamic characteristics of herein studied hyperbranched pyridylphenylene polymer fractions were compared with known hydrodynamic data for pyridylphenylene dendrimers. Nearly identical hydrodynamic behavior was found for the compared macromolecules, especially for low molecular mass fractions, which may suggest that the fractionation of hyperbranched polymers results in dendrimer-like structures. The oblate ellipsoid model provides reasonable correlation between hydrodynamic properties of hyperbranched pyridylphenylene polymer fractions and pyridylphenylene dendrimers.

1. INTRODUCTION Hyperbranched macromolecular structures have been known for a long time.1 Nevertheless, the term “hyperbranched” has appeared relatively recently, and since then tremendous attention has been directed to both the synthesis of new hyperbranched polymers (HBP) and studying their properties.2−5 Hyperbranched polymers demonstrate higher solubility and lower viscosity as compared to those of the linear polymers of similar composition; besides, they bear a much higher amount of functional groups that can be used for further modifications extending possible application areas.6,7 The branch length and location of branching points were found to have an influence on the HBP physicochemical properties and their hydrodynamic behavior.2,8,9 Typically, HBP are synthesized by a so-called “one-pot” procedure, which on the one hand facilitates and simplifies the overall preparation of such polymer structures but on the other hand limits an ability to control the molecular mass and leads to highly “heterogeneous” products. The heterogeneity originates from both a broad molecular mass distribution and branching irregularity in contrast to dendrimers, which are well-defined monodisperse macromolecules with regard to both size and structure. Notwithstanding this fact, HBP found wide application in catalysis, optoelectronic materials, drug release, medicine (for chelation, as sorbents for metal ions, and © XXXX American Chemical Society

in target drug delivery), and development of composites and functional materials (including materials with nonlinear optical properties).10−20 At the same time, as it was mentioned earlier HBP do not possess predictable regular structure; thus, the study of their conformation as well as molecular properties and detailed analysis of physicochemical characteristics represent an important assignment. Also, the molecular mass and its distribution as well as branching (both degree of branching and direction of growth) represent one of the most critical characteristics for hyperbranched polymers.8,9,21 The key task in creating polymers with predetermined properties is to choose an efficient synthetic procedure to achieve the same characteristic properties as dendrimers having similar chemical composition and to obtain perfect dendritic polymer structure by a one-pot procedure.22 A wide variety of organic reactions are known for the construction of HB polymers. Among them, the Diels−Alder reaction has been successfully used for the synthesis of dendrimers.23,24 Recently, hyperbranched pyridylphenylene polymers (HBPPP) based on first-generation dendrimer as a multifunctional monomer have been synthesized with the use of the Received: November 7, 2018 Revised: February 6, 2019

A

DOI: 10.1021/acs.macromol.8b02388 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

Figure 1. (A) Normalized semilogarithmic c(s) distributions on sedimentation coefficient s of initial macromolecules HBPPP1, HBPPP2, firstgeneration dendrimer (A6), and the resultant fractions of the first fractionation. (B) Normalized chromatograms on elution volume Ve of initial macromolecules HBPPP1, HBPPP2, first-generation dendrimer (A6), and the resultant fractions of the second fractionation. (C) Normalized specific viscosity ηsp/c on concentration c obtained for the resultant fractions of the second fractionation. (D) Relative scattered light intensity on hydrodynamic radius Rh plots obtained for fractions of second fractionation and initial polymer HBPPP2. The fraction numbers correspond to the numbering in Table 1.

and modified materials is mainly focused on the determination of their physicochemical properties such as viscous properties,29 glass transition,30 thermal degradation,31 crystallization and melting behavior,32 and their interrelation with the degree of branching. Notwithstanding the enormous efforts and a large amount of data available, a definite relationship between the architecture and the conformation of hyperbranched macromolecules and their physical properties has not yet been established.32 The development and search for the answer resolving this peculiarity of hyperbranched polymers represent one of the most crucial problems to be answered. However, papers dedicated to research of the hydrodynamic properties of individual hyperbranched macromolecules as well as their conformation in dilute solutions are limited.33,34 Such information can be revealed from the studies of HBP macromolecules in dilute solutions by complementary hydrodynamic and optical methods. The most reliable strategy in

Diels−Alder cyclocondensation reaction. The developed A6+B2 approach enabled a formation of HBP with high branching degree without gelation (Figure S1).25 Reaction conditions (temperature, reaction time, and monomer concentration) have been thoroughly investigated and selected to avoid gelation. Besides, the pyridylphenylene molecular structure demonstrated high potential toward the formation of metal nanoparticles.26−28 Also, differences in structure and conformation of individual molecules of a polymer can strongly influence its ability to form nanostructures and nanocomposites.2 The majority of studies regarding determination of molecular masses of HBP and in general synthetic and biopolymers allude to size-exclusion chromatography and different mass spectrometry techniques. Their limitations in terms of accuracy and suitability as well as the need to use some reference standards are known.8,21 The analysis of HBPs B


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Table 1. Hydrodynamic Parameters Determined for Pyridylphenylene Initial Polymers, Their Fractions, and First-Generation Dendrimer in THF Solutions at 25 °C samples

[η] (cm3/g)

HBPPP2 HBPPP1

18.0 12.2

1fr.II 1fr.III 1fr.IV 1fr.V 2fr.III−I 2fr.III−II 2fr.IV 2fr.V 2fr.VI 2fr.VII 2fr.VIII A6

k′/−k″

s0 (S)

(f/fsph)0

0.18/0.23 0.60/0.01

3.1 2.7

1.31 1.38

41 17.6 15.9 14.0 12.0 10.7 9.9

0.71/0.05 0.73/0.01 0.71/0.01 0.77/0.01 0.58/0.03 0.70/-0.01 0.53/0.06

3.0 2.2 1.7 1.2 7.2 3.9 3.4 2.8 2.5 2.4 2.0

1.5 1.51 1.5 1.45 1.5 1.8 2.3 2 1.36 1.46 1.55

5.5

−0.01/0.47

0.72

1.26

D0 × 107 (cm2/s)

MsDa (g/mol)

initial polymers 11 26000 12 20900 fractionsd 13800b 11500b 6400b 3500b 7.4 91000 8.2 44000 9.2 34000 13.5 19000 13.8 17000 16.5 13500 20.8 9000 first-generation dendrimer 42 1600

a

A0 × 1010 (g cm s−2 K−1 mol−1/3)

Mwc (g/mol)

Đc

3.0 2.7

21100 15600

2.22 2.4

4.1 2.7 2.7 3.1 2.9 3.1 3.3

57550 26350 20400 16200 10250 8100 6800

2.07 2.06 1.77 1.57 1.71 1.69 1.39

1050

1.08

3.1 b

The MsD values are determined with independent sedimentation−diffusion experiments, if not specified otherwise. Molecular masses evaluated with AUC data based on (f/fsph)0 values (also see Table S2). cSEC data based on polystyrene calibration. dThe fractions I and II from second fractionation as well as fraction I from first fractionation cannot be considered as well-defined fractions. Their molecular weight distributions are much alike to the initial sample distribution with redistribution tendency toward high-molecular-mass components. Also, according to obtained data from all implemented experimental techniques, the wideness of molecular mass distributions decreases with decrease of molecular mass of a fraction. experimentally determined at 25 °C: ρ0 = 0.8824 g/cm3 and η0 = 0.49 cP, respectively. 2.2. Synthesis. Polymer synthesis was performed according to ref 37. The molar ratio of A6/B2 monomers was 1/1.5, and the total concentration of monomers A6 and B2 was 0.010 mol/L, where B2 component corresponds to 3,3′-(oxydi-1,4-phenylene)bis(2,4,5-triphenylcyclopenta-2,4-dien-1-one), which was denoted as “R:2” in ref 37. The chosen synthesis conditions (the component feed ratio, total concentration, reaction time, etc.) allow us to avoid gelation. These conditions might lead to partial macrocyclization. We assume that possible partial macrocyclization does not have a pronounced effect on the hydrodynamic characteristics of studied macromolecules in solutions. Both hyperbranched pyridylphenylene polymers (HBPPP1 and HBPPP2) were synthesized according to the same procedure at independent synthesis. 2.3. Fractionation. We have performed two fractionations: the first fractionation was performed on low test amount (50 mg) of HBPPP2, and the second fractionation was brought to the large scale (up to 5 g). The results of the first fractionation made it possible to verify the fidelity of the chosen strategy by carrying out AUC measurements, and the results of second fractionation allowed to complete SEC, NMR, and the entire set of hydrodynamic experiments to ensure self-consistency and reliability of the obtained data. Fractional partial precipitation was performed from THF solutions (the polymer concentration ∼5 wt %) by n-hexane. A sample of polymer (50 mg) was dissolved in 1 mL of THF at room temperature. Then n-hexane (∼0.3 mL) was added until a cloud point appeared. After that, the solution was heated to 50 °C and stirred for 15 min to give a clear solution. Next, the solution was gradually cooled to room temperature while stirring and held at this temperature for 14−16 h. After separation by decantation of the supernatant, the first fraction was redissolved in a small amount of THF and reprecipitated with nhexane. The second and subsequent fractions were prepared in the same way as described above. Fractionation was performed until a large amount of precipitant had been required to separate the next fraction. The last fraction was obtained by evaporation in a vacuum of the supernatant liquid until a dry residue had been obtained. The second fractionation was performed with 5 g of HBPPP2 in the same manner, keeping polymer concentrations and precipitant amount in

dealing with this issue is fractionation of “one-pot” synthesis product and detailed analysis of resultant fractions. This technique was successfully applied to HBP on the basis of flexible macromolecules;34 however, to our best knowledge, no one tried it with rigid species like pyridylphenylene macromolecules. It should be emphasized that a combination of the hydrodynamic methods enables one to determine the absolute molecular mass with a great accuracy and the average hydrodynamic dimensions of macromolecules as well as to obtain data on the macromolecular shape. At the same time intrinsic viscosity measurements are much more sensitive to the macromolecular asymmetry in comparison to experimental techniques based on studying translational friction processes (analytical ultracentrifugation (AUC) and dynamic light scattering (DLS)).35,36 The chosen set of experiments was further extended by nuclear magnetic resonance (NMR) to ensure the chemical structure and size exclusion chromatography (SEC) to obtain independent data on molecular mass and its distribution. Thus, the aim of the presented research is the detailed analysis of pyridylphenylene fractions in dilute solutions by the unique combination of experimental techniques with further comparison of hydrodynamic behavior of herein studied fractions with dendrimers of analogous structure.

2. EXPERIMENTAL SECTION 2.1. Materials. For synthesis 1,3,5-triethynylbenzene (98%), Bu4NF (1 M solution in tetrahydrofuran), N-methylpyrrolidone (99%), tetrahydrofuran (anhydrous, 99.9%) (THF), diphenyl ether (99%), and o-xylene (anhydrous, 97%) were purchased from Aldrich and used as received. While studying hydrodynamic properties and performing fractionation, we further purified the THF by distillation under an atmosphere of dry argon in the presence of sodium hydroxide and hydroquinone. Its density and dynamic viscosity were C


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approximations s−1 = s0−1(1 + ksc) and f/fsph = (f/fsph)0(1 + ksc) (where ks is the Gralen coefficient, c the solution concentration, f the translational friction coefficient, and fsph the translational friction coefficient of equivalent sphere) can be used for the extrapolations. In such a manner the hydrodynamic parameters s0 and ( f/fsph)0 may be determined characterizing a macromolecule at the infinite dilution limit. Furthermore, the determination of s0 and (f/fsph)0 becomes possible with implementation of absorbance optics, especially while studying pyridylphenylene systems possessing very high absorbance properties. This, in turn, allows studying superdilute solutions with concentrations 3 order of magnitude lower than, for example, in viscometry or DLS measurements.47 As mentioned above, the D value may be extracted in some cases from the frictional ratio calculated by Sedfit program:

correspondence with the first procedure. Thus, the first fractionation allowed to produce five fractions and in the second one eight fractions. Some of the high molecular fractions in the second fractionation were refractionated.

3. METHODS 3.1. Nuclear Magnetic Resonance (NMR). The 1H NMR spectrum was recorded on an Avance-IIIHD-400 MHz NMR spectrometer operating at 400.13 MHz. Chemical shifts are given in parts per million (ppm), using the solvent signal as a reference. CD2Cl2 was used as solvent [δ(1H) = 5.32 ppm] (Figures S1 and S2). 3.2. Size Exclusion Chromatography (SEC). SEC analyses were performed using a Shimadzu LC-20AD chromatograph equipped with a TSKgel HHR-L guard column and a TSKgel G5000HHR column (7.8 mm × 30 cm, Tosoh Bioscience) using a Shimadzu RID-10A refractive index detector. SEC was performed in THF at 40 °C and a flow rate of 1.0 mL min−1 (Figure 1). The resultant molecular masses (Mn and Mw) were calculated by three calibration procedures (Figure S3). The first is based on third-order polynomial fit calibration with polystyrene standards (Table 1). The second was done by internal calibration based on sedimentation−diffusion analysis data, and the third one was made also with sedimentation−diffusion analysis data with implementation of procedures developed for optimized internal calibration with polydisperse standards (Table S1).38,39 3.3. Viscometry. Intrinsic viscosities [η] were determined with the data obtained using a Lovis 2000 M microviscometer (Anton Paar GmbH, Graz, Austria). The experiments were based on the rolling ball (Höppler) principle; standard dilution procedures were used. The setup included a capillary with an inner diameter of 1.59 mm equipped with a gold-coated steel ball (1.50 mm in diameter). The rolling times for a solvent (t0) and polymer solutions of various concentrations (t) were measured at a tilting angle of the capillary of 50° at the thermostat temperature of 25 °C. The values of relative viscosity ηr = η/η0 = t/t0 were determined. The concentration dependences of specific viscosity ηsp normalized by concentration c (ηsp/c = (t/t0 − 1)/c) as well as ln ηr/c were extrapolated to zero concentration. The dependences for extremely diluted polymer solutions in the 1.2 < t/t0 < 2.5 range were approximated by straight lines (Figure 1 and Figure S4); the intercept values correspond to intrinsic viscosity [η] of a solution, according to the Huggins and Kraemer equations, allowing to determine Huggins k′ and Kraemer k″ constants from the slopes of the dependences.40,41 Finally, the values [η] obtained in such manner were averaged and used for further analysis (Table 1). 3.4. Analytical Ultracentrifugation. The velocity sedimentation experiments were performed using a Beckman XLI analytical ultracentrifuge (ProteomeLab XLI Protein Characterization System) at a rotor speed of 55000−60000 rpm depending on a sample and at 25 °C using mainly the absorbance optical system at λ = 300 nm and double-sector cells with aluminum centerpieces with an optical path length of 12 mm. The sample and the reference sectors were loaded with 0.42 mL of studied solution and a solvent, respectively. The centrifuge chamber with loaded rotor and interferometer was vacuumized and thermostabilized for at least 60−90 min before the run. The average time of sedimentation process in experiments with the studied samples was about 17−19 h until full translation of material from meniscus to the bottom of a cell, and concentration profiles within the cell were registered at 2−3 min intervals. For the analysis of the sedimentation velocity data, the Sedfit program was used.42 Sedfit allows obtaining sedimentation coefficients distribution (Figure 1, Figures S5 and S6) using the Provencher regularization procedure.43,44 The two major characteristics of velocity sedimentation experiments were determined, viz. the sedimentation coefficient s and the frictional ratio (f/fsph). In some cases the frictional ratio values allow reliable estimation of diffusion coefficients, but the self-consistency of acquired data must be established.45,46 Both of the characteristics s and (f/fsph) should be extrapolated to zero solute concentration. Because the hydrodynamic investigations are usually performed in very dilute solutions, the linear

D0sf =

1/2 kBT (1 − υρ ̅ 0) η0 3/2 9π 2 ((f /fsph )0 )3/2 (s0υ ̅ )1/2

where kB is the Boltzmann constant, T is the absolute temperature, υ̅ is the partial specific volume, and ρ0 and η0 are the solvent density and viscosity, respectively.42 To eliminate the common solvent properties, the intrinsic values of the velocity sedimentation coefficient [s] and the translational diffusion coefficient [D] may be used: [s] ≡

s0η0 1 − υ ̅ ρ0

and [D] ≡

D0η0 T

.

Thus, the absolute values of molecular masses may be determined using the Svedberg equation: MsD =

s0RT [s ] R = D0(1 − υρ D] ) [ ̅ 0

(1)

where (1 − υ̅ ρ0) is the buoyancy factor and R the universal gas constant. 3.5. Partial Specific Volume. The density measurements were performed in THF solutions at 25 °C using the density meter DMA 5000 M (Anton Paar GmbH, Graz, Austria) according to the procedure of Kratky et al.48 The corresponding dependence of Δρ = ρ − ρ0 on the polymer concentration c was plotted and the value of the partial specific volume was calculated as δ(Δρ)/δc = (1 − υ̅ ρ0), which constituted υ̅ = 0.83 ± 0.01 cm3 g−1 (Figure 2). 3.6. Dynamic Light Scattering (DLS). DLS experiments were performed using a “Photocor Complex” instrument (Photocor Instruments Inc., Moscow, Russia) equipped with a real-time

Figure 2. Dependence of Δρ = ρ − ρ0 on the polymer concentration c determined for A6 (1), HBPPP2 (2), second fractionation III−I (3), second fractionation V (4), and second fractionation VIII (5) in THF solutions at 25 °C. D


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Macromolecules correlator (288 channels, the fastest sample time 10 ns) in the 30°− 140° scattering angle ϑ range at the temperature 25 °C with temperature stabilization up to 0.1 C; the wavelength of the used laser light source (λ0) is 654 nm. The cell (cylindrical glass cell 1 cm in diameter) with a studied solution or solvent was submerged in an immersion liquid possessing the same refractive index as the glass cell. The normalized intensity homodyne autocorrelation functions were fitted using the ILT regularization procedure incorporated in “DynaLS” software, which provides distributions of relaxation times and hydrodynamic radii.49,50 Because all the observed modes displayed diffusional nature (1/τ = D × q2), the values of the translational diffusion coefficients D were calculated from the slope of linear dependences of inverse relaxation time 1/τ on scattering vector squared q2 = (4πnλ0−1 sin(ϑ/2))2, where n is refractive index of the medium. The translational diffusion coefficients D0 corresponding to infinite dilution limit were determined by extrapolation to zero concentration.

The data are presented in Table 1. It must also be noted that the molecular mass determined for the first-generation dendrimer (A6) by sedimentation−diffusion analysis shows satisfactory correlation with the data reported earlier acquired with MALDI-TOF spectroscopy.37 It is worth noticing that such a comparison of the essential hydrodynamic characteristic made by completely different techniques represents a fundamental task of establishing the intercorrelation of the used methods, especially keeping in mind the AUC reaching the lower limit of molecular mass resolution close to 1000 g mol−1.54 In regard to the synthesized polymers (HBPPP1 and HBPPP2), their molecular masses correlate well with earlier studied systems and sedimentation coefficient distributions (Figure S5) resembled ones, which were resolved earlier.47 4.2. AUC and SEC of the Fractions. To ensure that the fractionation was successful, AUC was performed with the first set of fractions and then both AUC and SEC were performed with the second one. The results are shown in Figures 1 and S3 as well as Tables 1 and S1. Indeed, AUC and SEC data confirm the successfully performed fractionation. The best molecular mass correlation of sedimentation−diffusion analysis with SEC data was found for optimized internal calibration taking into account the polydispersity of fractions (Table S1). The internal calibration without optimization procedures also gives adequate results; however, the pronounced divergence was found for high molecular mass fractions. The least data correlation was found at calibration with polystyrene standard, which is an expected result, as there is an evident misfit in chemical composition and architecture comparing to the system of study. Quite the contrary is the situation in regard to the polydispersity index (Đ) values, which demonstrate good internal consistency independent of type of calibration.57 Although the initial polymer HBPPP2 possesses low Đ values itself (in terms of Đ values typical for systems of “onepot” synthesis), it can be easily seen that the resultant fractions show narrower distributions. 4.3. Branching of the Fractions. The degree of branching (DB) of initial polymer and resultant fractions was analyzed by using NMR data. The NMR spectra of initial polymer (Figure S1) and resultant fractions (Figure S2) are shown in the Supporting Information. According to NMR data, it was established that, on average, three out of six ethynyl groups are reacted during the synthesis. It suggests that the average degree of branching (DB) is close to 3 of herein studied initial polymers and resultant fractions keeping the same trend even for high molecular weight fractions (Figure 3). This result correlates well with the data obtained earlier.37 We believe that in the reported case the selected monomers ratio (A6:B2 = 1:1.5) and effective Diels−Alder condensation both are the crucial factors which caused the rather constant DB value for different fractions of the polymer. Thus, the Diels−Alder reaction indeed keeps unique features and provides great potential for creating new materials with regular structure.24,58 4.4. Hydrodynamic Study of Fractions. We have performed a complete set of the hydrodynamic experiments the same way it was applied earlier for the initial systems (Table 1), keeping to the proposed concept of “hydrodynamic homologues”.33,34 Homology of linear macromolecules is provided by the constant chemical structure of the repeating units, and the persistence of a structural parameterlinear density of the polymer chains, MLcan be defined as a

4. RESULTS AND DISCUSSION 4.1. Hydrodynamic Study of Initial Systems. Based on the results of performed hydrodynamic experiments with initial systems (a first-generation six-functional pyridylphenylene dendrimer (A6) and two hyperbranched pyridylphenylene polymers on its bases HBPPP1 and HBPPP2) (Figure S1), the self-consistency check of hydrodynamic characteristic must be fulfilled. To do so, the characteristics should be expressed as intrinsic values ([η], [s], [D]), which are independent from the common solvent properties−dynamic viscosity η0 and density ρ0 at the specific temperature T: V [η] = ν(p)NA (2) M [s ] ≡

[D ] ≡

s0η0 1 − υ ̅ ρ0 D0η0 T

=

η0M

=

NAf

(3)

kBη0 f

(4)

where v(p) is the Simha function, p the parameter of asymmetry, NA the Avogadro constant, V the hydrodynamic volume occupied by a molecule, and M the molecular mass. In such a manner determined hydrodynamic characteristics are related to the same basic macromolecular parameters, viz. a molecular mass and hydrodynamic size. The self-consistency check of hydrodynamic characteristic analysis can be established by a calculation of the hydrodynamic invariant A0:51,52 A 0 = (R[s][D]2 [η])1/3

(5)

The average values of the hydrodynamic invariant A0 were calculated, and it was found within the range of insignificant statistical deviations determined by sensitivity of implemented experimental techniques. This fact allows to state that the satisfactory correlation between the molecular characteristics ([η], [s], [D]) is determined from the independent measurements, which, in turn, enables further interpretation of the experimental data. The average values of A0 for A6 and HBPPP were found to be (3.1 ± 0.1) × 10−10 and (2.9 ± 0.2) × 10−10 g cm s−2 K−1mol−1/3, respectively. The determined values fall within physically sounded range which is known for compact nonpercolated molecules.51,53 Thus, the absolute values of the molecular mass can be calculated based on the determined values of the sedimentation coefficient and the diffusion coefficients using the Svedberg equation (eq 1). E


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and (2) flexible linear polymers (for example, polystyrene or PEG33) in a good solvent. To resolve this issue, we have to proceed to the discussion of scaling relations. The comparison of the hydrodynamic characteristics of the pyridylphenylene initial samples and their fractions with different molar masses allows to establish the classical Kuhn−Mark−Houwink−Sakurada (KMHS) scaling relationships. In general, they can be written as follows: b

Pi = K ijP j ij

(6)

where Pi is one of the hydrodynamic characteristics and Pj is another hydrodynamic characteristic or the molar mass. The corresponding KMHS plots are presented in Figure 4B, and the parameters of the scaling indices are given in Table 2. Next, the experimental errors associated with the determination of the scaling indices and the known relations connecting the scaling indices can be taken into account with |bD| = (1 + bη)/3;

Figure 3. Average degree of branching determined with NMR analysis and rounded to integer value for fractions of second fractionation. The line demonstrates the DB value for the major number of the fractions.

|bD| + bs = 1;

bD = − (bff + 1/3) (7)

where bD are the scaling indexes characterizing the slope of double-logarithm scale at the corresponding coordinates D0− M, bη is the same at [η]−M, as well as bs from s0−M and bf f from (f/fsph)0−M. The main three parameters (bD, bη, and bs) are found well correlated within the sensitivity of the implemented experimental techniques. As for the discrepancy observed between bD and bf f, this is a solid proof that the frictional ratio value must be carefully handled for estimation of the diffusion coefficient, especially with multimodal distributions. Such estimations would show more qualitative rather than quantitative results. Taking the aforesaid into account, the hydrodynamic characteristics of hyperbranched pyridylphenylene macromolecules in THF solution at 25 °C in the studied range of molar masses could be described by the following KMHS relationships:

structural homology. The homology of branched macromolecules is more difficult to define and much more difficult to achieve and control. That is why the concept of hydrodynamic homology was proposed, which is based on the scaling relations linking the hydrodynamic characteristics of each other and/or the molar mass. The fulfillment of such relations would mean the macromolecules compared behave hydrodynamically similar to each other and would allow interpreting the experimental results based on a single hydrodynamic model. The value of hydrodynamic invariant (eq 5) was determined for the set of studied fractions, and it also belongs to the physically sounded range known for the compact nonpercolated polymer molecules: (3.1 ± 0.2) × 10−10 g cm s−2 K−1 mol−1/3. Thus, the absolute values of the molecular mass can be calculated based on the determined values of the sedimentation coefficient and the diffusion coefficients using the Svedberg equation for the fractions, too (eq 1). The data are presented in Table 1. The visual representation of the hydrodynamic volume of a macromolecule of any kind can be done by plotting [η]M on M in a double-logarithmic scale (Figure 4A).59 The [η]M value is the key parameter in interpreting the results of size exclusion chromatography of polymers (Benoit universal calibration). It is proportional to the volume V occupied by a macromolecule in a solution. In the first approximation, the slope of the [η]M dependency on molar masses, in a double-logarithmic scale, will be inversely proportional to the average intracoil density (∼log(1/ρ)). The higher the curves are located along the ordinate, the lower will be the density of the polymer substance in the volume occupied by the polymer molecule. Thus, it can be easily seen that the herein determined hydrodynamic data for hyperbranched pyridylphenylene fractions and data obtained earlier for pyridylphenylene dendrimers,60 first, coincide well and, second, take the intermediate position between linear dependences (1) characterizing hydrodynamic volume of completely compact polymer species similar to dendrimers and globular proteins

[η] = 0.165 × M 0.45 ,

s0 = 0.017 × M 0.52 ,

D0 = 1505 × M −0.48

The herein found values of scaling indexes are quite interesting. On the one hand (in terms of the established viscosity exponent bη), they are in a satisfactory agreement with the previously observed data for hyperbranched polyester34 (bη = 0.39) and natural hyperbranched polysaccharide glycogen61 (bη = 0.40), but on the other hand, for hyperbranched poly(ethylene glycol)33 bη was found to be 0. In fact, there are also a number of dendrimer studies also demonstrating nonzero bη values.62−65 These findings (bη = 0− 0.40) are first attributed to the degree of shrinking effect in hyperbranched systems in comparison with the determined hydrodynamic parameters of equivalent linear polymer analogues, and second it is a matter of macromolecule structure asymmetry. Indeed, the herein studied samples possess a considerably asymmetric conformation defined by structures of initial components A6 and B2. Moreover, earlier we determined the molecular asymmetry parameter p characterizing the polymer analogues’ structures.47 It means that the oblate ellipsoid model might be reasonably implemented for describing the hydrodynamic behavior of hyperbranched pyridylphenylene fractions and pyridylphenylene dendrimers. F


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Macromolecules

Figure 4. (A) Hydrodynamic volume [η]M dependences on M. Dashed line 1: completely compact organization of the polymer species inside the occupied volume (similar to dendrimers, globular proteins); dashed line 2: behavior of flexible linear macromolecules; dashed line 3: behavior of rigid linear macromolecules (polysaccharides schizophyllan55 and xanthan56). The open symbols (4) represent data of herein studied samples, and stars (5) are the data obtained earlier for pyridylphenylene dendrimers. (B) Scaling relationships determined for intrinsic viscosity (1), sedimentation coefficients (2), diffusion coefficients (3), and frictional ratio (f/fsph)0 of pyridylphenylene macromolecules in THF solutions at 25 °C. Arrows indicate data obtained for initial samples: HBPPP1, HBPPP2, and first-generation dendrimer (A6). (C) Comparison of experimentally determined intrinsic viscosity values of pyridylphenylene macromolecules (4: HBPPPs and their fractions; 5: pyridylphenylene dendrimers) with the calculations made by implementation of the oblate ellipsoid model. The solid curves demonstrate model calculations with variation of parameter L (nm): 0.55 (1), 1.1 (2), 2.2 (3). (D) Comparison of experimentally determined sedimentation (4) and diffusion (5, 6) coefficient values of pyridylphenylene macromolecules (4, 5: HBPPPs and their fractions; 6: pyridylphenylene dendrimers) with the calculations made by implementation of the oblate ellipsoid model. The presented dependences demonstrate model calculations with variation of parameter L (nm): 0.55 (1, 1′), 1.1 (2, 2′), 2.2 (3, 3′). The solid ones correspond to sedimentation coefficient (1, 2, 3) calculations and dashed ones to diffusion coefficients (1′, 2′, 3′).

4.5. Oblate Ellipsoid Model. For the purpose of calculating the hydrodynamic parameters describing the hydrodynamic behavior of oblate ellipsoid model, we will consider the ellipsoid with the uniform density distribution (based on the experimentally determined value of the partial specific volume) with short axis L and long axis d. In the case of the oblate ellipsoid model the short axis L is the axis of rotation, and the asymmetry parameter p = L/d < 1. We will perform the calculations of intrinsic viscosity values describing the rotational friction processes based on eq 2 and the Simha function known for the chosen model:35,66

Table 2. Parameters of the KMHS Relationships for Pyridylphenylene Initial Polymers, Their Fractions, and First-Generation Dendrimer in THF Solutions at 25 °C [η]−M s0−M D0−M ( f/fsph)0

bij

Kij

ra

0.45 ± 0.06 0.52 ± 0.03 −0.47 ± 0.03 0.07 ± 0.04

0.165 0.017 1300 0.8

0.940 0.984 −0.988 0.424

a

The linear correlation coefficient.

G


Macromolecules ν(p) = 2.5 +

yz 1−p 32 ijj 1 jj − 1zzz − 0.628 z − 15π jk p 1 0.075p {

■

f = 3πη0L

i arctanjjjj k

p 1−p p

2

yz zz z {

*E-mail: [email protected]. ORCID

Alexander S. Gubarev: 0000-0002-2888-7526 Alexey A. Lezov: 0000-0001-7960-6889 Zinaida B. Shifrina: 0000-0001-5816-3118 Nikolai V. Tsvetkov: 0000-0003-2666-6073 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This research was financially supported by the Russian Science Foundation (project no. 16-13-10148).

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where p is the parameter of molecular asymmetry (p = L/d). The comparisons of experimental data and model calculations for rotational and translational friction coefficients are shown at Figures 4C and 4D, respectively. As a result of this comparison, it can be seen that the oblate ellipsoid model provides reasonable fit of hydrodynamic parameters of studied herein macromolecular structures. This fact also correlates well with determined scaling indexes and our previous findings on molecular asymmetry of polymer analogous structures.47 Also, it should be noted that the intrinsic viscosity coefficient ([η] ∼ Rh3) is much more sensitive characteristic to the model parameters (L, d) in comparison to both sedimentation (s) and diffusion (D) coefficients determined by translation friction coefficient (f ∼ Rh). This is directly reflected on model dependences at Figures 4C and 4D. The earlier studied pyridylphenylene dendrimers60 exhibit the identical hydrodynamic behavior according to Figure 4.

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5. CONCLUSION In summary, we report data on the hydrodynamic study of hyperbranched pyridylphenylene polymers. The unique combination of hydrodynamic experiments provides data for thorough analysis. The synthesized polymers were fractionated into much narrowly dispersed fractions. The intercorrelation and self-consistency of obtained data were ensured by calculation of hydrodynamic invariant value and canonic relations of KMHS scaling indexes. These data suggest that the system demonstrates the hydrodynamic behavior typical for asymmetrical compact macromolecular species. Furthermore, the comparison of hydrodynamic characteristics of herein studied fractions with hydrodynamic data known for pyridylphenylene dendrimers was made. Nearly the identical hydrodynamic behavior was found for these compared macromolecules, especially in low molecular range of obtained fractions, which suggests that the fractionation of hyperbranched polymers results in dendrimer-like structures in terms of degree of branching, low polydispersity, and identity in hydrodynamic behavior.

■

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as well as sedimentation and diffusion coefficients describing the translational friction processes according to eqs 3 and 4 and the Perrin expression of a translational friction coefficient known for an oblate ellipsoid:67,68 1 − p2

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b02388. Experimental details and additional analytical results (PDF) H


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