Temperature-Induced Changes in the Nanostructure of Hydrogels

Jul 25, 2016 - Copyright © 2016 American Chemical Society. *E-mail: [email protected]. Telephone number: +48 42 6803235. Cite this:J. Phys. Chem...
0 downloads 0 Views 4MB Size
Article pubs.acs.org/JPCC

Temperature-Induced Changes in the Nanostructure of Hydrogels Based on Reversibly Cross-Linked Hyperbranched Polyglycidol with B(OH)4⊖ Ions Mateusz Gosecki,† Bozena Zgardzinska,‡ and Monika Gosecka*,† †

Department of Engineering of Polymer Materials, Centre of Molecular and Macromolecular Studies of Polish Academy of Sciences, ul. Sienkiewicza 112, 90-363 Lodz, Poland ‡ Department of Nuclear Methods, Institute of Physics, Maria Curie-Sklodowska University, Pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland S Supporting Information *

ABSTRACT: Solid-state boron nuclear magnetic resonance (11B NMR) and positron annihilation lifetime spectroscopies (PALS) were used to study the molecular structure of selfhealing hydrogels based on cross-linked hyperbranched polyglycidol (HbPGL) with borax at basic pH. The lifetime and intensity of orthopositronium allowed characterizing the micro- and nanostucture of hydrogels at various thermal conditions. Stepwise changes in the free volume parameters were found in pure HbPGL as well as in hydrogels based on this polymer. However, the shift in the phase transition temperature suggests that the important properties of the hydrogel arise from the water building these systems. Rheological measurements demonstrated the subsequent reduction of the average cross-link lifetime within the polymer network under heating. Composition of boronic species within hydrogel systems also diverged upon change in temperature range from −10 °C to +70 °C. The reduced fraction of boronic diester upon heating was quantitatively rebuilt after cooling to ambient temperature. Heating the hydrogel at 70 °C launched the irreversible release of a small fraction of HbPGL macromolecules from the polymer network, generating its defects, still present after cooling. The structural studies carried out in a nanoscale facilitated the distinction in cross-linking density of two analyzed hydrogel systems. The PAL spectroscopy turned out to be a valuable tool to exclude entanglements between individual macromolecules of pristine HbPGL.

1. INTRODUCTION Hydrogels based on reversible covalent bonds are of great interest in the biomedical field as these materials are sensitive to various factors, such as pH, temperature, etc., enabling at certain conditions the release of encapsulated biomolecules or exhibiting self-healing properties.1 The most common reversible covalent interaction applied in hydrogel formation is the complexation of boronate ions (B(OH)4⊖) with hydrophilic polymers, such as poly(vinyl alcohol),2−5 polysaccharides,6−8 and synthetic glycopolymers,9 which contain two adjacent hydroxyl groups in the positions 1,2 or 1,3. As a result, five- or six-membered rings are formed, respectively. Commonly used polymers containing diol moieties have linear topology with either flexible chains, such as poly(vinyl alcohol), galactomannans, or rigid as in the case of Schizophyllan.10 Another example of a synthetic polymer which forms hydrogels in the presence of B(OH)4⊖ ions is hyperbranched polyglycidol.11 The presence of numerous 1,2-vicinal diol functional groups in the peripheral area of spherically shaped macromolecules of hyperbranched polyglycidol (HbPGL) facilitates the binding of individual macromolecules into a three-dimensional polymer © 2016 American Chemical Society

network due to reactivity and good accessibility of reactive groups in the cross-linking reaction. Applications of branched polymers for hydrogel formation based on didiol−boronic diacid complexation have not been widely described yet.12 The interest in the hydrogel built from hyperbranched polyglycidol results from its advantageous characteristics over those prepared from polymers of linear topology, i.e., its ability to compartmentalize various molecules. Hydrophobic modification of the inner region of hyperbranched polyglycidol macromolecules opens up the possibility of encapsulation of hydrophobic compounds, particularly drugs.13,14 Moreover, the highly flexible nature of HbPGL chains also facilitates an efficient encapsulation of compounds within the macromolecular structure.15 The synthesis of hyperbranched polyglycidol is a one-pot process yielding a product of controlled molecular weight and distribution, and its advantaReceived: June 23, 2016 Revised: July 22, 2016 Published: July 25, 2016 18323

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C

2. MATERIALS AND METHODS 2.1. Materials. Sodium tetraborate decahydrate (borax, Na2B4O7·10H2O) was purchased from Aldrich and used as received. Before usage, glycidol (Aldrich) was dried with 4 Å molecular sieves and freshly distilled under reduced pressure. Deionized water with the resistivity of 0.055 MΩ·cm−1 was produced with an Adrona Crystal system. 2.2. Synthesis of Hyperbranched Polyglycidol (HbPGL). Hyperbranched polyglycidol was synthesized by anionic polymerization according to the slightly modified procedure described by Sunder.23 Ten percent of the hydroxyl groups in 1,1,1-tris(hydroxymethyl)propane (0.0043 mol; 0.5770 g) were converted into alcoholate form in a reaction with sodium hydride (0.0129 mol; 0.031 g). Then, glycidol (0.4 mol; 29.60 g) was added at a rate of 2 mL/h to a reactor equipped with a mechanical stirrer. The reactor was kept in an oil bath at 95 °C over 14 h in the atmosphere of dry argon. The product obtained was dissolved in methanol. The sodium ions in alcoholate sites were exchanged into protons by passing the polymer through a cation-exchange resin (Dowex 50 WX 4). The product was thrice precipitated from methanol in acetone to remove cyclic byproducts, dried under vacuum, and characterized with 1H NMR, 13C NMR, and GPC methods (chromatogram and NMR spectra are shown in SI in Figures S1, S-2, and S-3, respectively). All experiments were carried out using HbPGL of M̅ n(GPC) = 6430; M̅ w/M̅ n = 1.65. Determination of molecular weight was performed with size exclusion chromatography (SEC) in aqueous solution with triple detection (TriSEC) using the chromatograph (Knauer K-501 HPLC pump) with LDC Analytical refractoMonitor IV detector and Viscotek 270 Dual Detector (laser light scattering at λ = 670 nm (Right Angle Light Scattering (RALS) and Low Angle Light Scattering (LALS)) and a differential viscometer). Three TSK-GEL columns, G5000 PWXL + 3000 PWXL + 2500 PWXL (7.8 × 300 mm; Tosho; 26 °C), were used in a series. To protect detectors against impurities coming from columns, an additional filter delivered by Viscotek was also used. An aqueous solution of NaN3 (0.1 wt %) was degassed (4-channel degasser; K-5004, Knauer) and used as a mobile phase at a flow rate of 1.0 mL min−1. OmniSEC software (Viscotek) was used for the data treatment. A sample with a concentration of polymer ca. 5 mg × mL−1 was filtered through 0.2 μm pore size membrane filters. Injection volumes of the sample solutions were 100 μL. The whole procedure of calculation based on RALS measurements and viscosimetry is given in one of the published papers, where a large part of the Viscotek manual is quoted.24 The fraction of vicinal diol units was estimated on the basis of the 13 C NMR spectrum23 and was equal 34.0 mol %. 2.3. Hydrogel Preparation. Two hydrogels were prepared by the addition of borax solution to an aqueous solution of HbPGL at room temperature and thorough mixing. Both solutions exhibited pH = 12 which was adjusted with sodium hydroxide solution. The weight concentration of HbPGL used for the formation of hydrogel systems H1 and H2 was 19.3 and 24.2 wt %, respectively. The initial molar ratio of diol groups per B(OH)4⊖ was equal to 1.8:1 for the H1 system and 5.5:1 in the case of H2. Interaction between hyperbranched polyglycidol and borax is based on the reactions of vicinal diol groups of HbPGL macromolecules and B(OH)4⊖ ions coming from borax dissociation. As a result, boronic monoester species (Scheme 1a) and diester species (Scheme 1b) are formed. The

geous biomedical characteristics (like nontoxicity, biocompatibility)16 open wide application possibilities. Generally, in contrast to irreversibly cross-linked gels, the dynamic character of covalent cross-links enables the network disassembly under the influence of a specific factor. In addition, contrary to polymers of linear topology, hyperbranched polyglycidol of molecular weight below 20 000 does not form entanglements.17,18 It means that covalent cross-links generated between the individual HbPGL macromolecules are the only factor deciding about the network formation and its strength. If the number of cross-links generated between macromolecules within the hydrogel system is not sufficient or the system is not completely homogeneously mixed, some macromolecules can remain detached, being solely embedded in the network, generating its imperfections. Defected polymer networks can result in a release of encapsulated compounds outside the hydrogel structure. Due to the fact that formation of bonds by didiol complexation with B(OH)4⊖ ions is an exothermic process,19 the increase of temperature is not a favorable factor for gelation. Thus, heating can be applied to avoid immediate gelation during hydrogel preparation causing the reduction of viscosity by decreasing the cross-link number or accelerating the exchange reaction. This approach ensures better distribution of all components building the hydrogel system. Within the scope of this article, for micron-sized porous hydrogel systems composed of hyperbranched polyglycidol of Mn = 6430 cross-linked with B(OH)4⊖ ions, we applied solidstate 11B nuclear magnetic resonance (11B NMR) to evaluate the influence of temperature on the concentration of boronic diesters, which play the role of cross-links within the hydrogels, and the lifetime of these bonds on the basis of rheological measurements. Moreover, we investigated the nanostructure variation of hydrogels upon the changes in temperature based on positron annihilation lifetime spectroscopy (PALS) measurements. PALS, as a noninvasive and noninterfering technique suitable for probing hole sizes, facilitates the studies of structure of the hydrogel in a nanoscale.20 This technique uses antimatter for the study of media in a subnanometer scale. Positron penetrating the medium can annihilate directly in contact with an electron (i.e., free positron annihilation) or to create with an electron a hydrogen-like atom, positronium (Ps). Positronium exists in two substates: orthopositronium (o-Ps), the triplet substate with parallel spins of particles, and the singlet parapositronium (p-Ps) substate with antiparallel spins. The lifetime of annihilation of the triplet state depends on the size of the free volume in which this atom can be found. This property is used to determine the size of the electron-less free volume in the matter. As PALS measurements can be conducted at various temperatures, in different solvents, structural changes of the free void sizes of the order of a few angstroms21,22 within materials can be identified. Based on these investigations, we wanted to determine, whether within hydrogels structures all HbPGL macromolecules are engaged in the formation of the polymer network, i.e., whether the concentration of polymer and cross-linker and applied molar ratio of 1,2-diol functional groups to B(OH)4⊖ ions are sufficient to generate the network. It is important to underline that for proper interpretation of PALS results obtained for hydrogels the knowledge about the sizes of free volumes typical for individual components is essential. Thus, this report is supplemented by structural studies of pure polyglycidol at various temperatures. 18324

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C

Scheme 1. Schematic Representation of the Complexation between HbPGL Macromolecules and the Boronic Cross-Linker at Basic Conditionsa

a Boronic acid in aqueous solution reacts preferentially with diol in tetrahedral form (above pKa of boronic acid, pKa borax = 8.9825), and then on the boron atom an anion charge exists.26

During the measurements, liquid nitrogen evaporator, controlled by the BVT3200 variable-temperature unit, was used. All spectra were collected and processed with the Top-Spin 2.1 software.

cross-linking reaction is based solely on diester linkages generated between individual HbPGL macromolecules. 2.4. Positron Annihilation Lifetime Spectroscopy (PALS). The 22Na positron source (activity 0.8 MBq) in a Kapton envelope and the sample were fixed in a measuring chamber. The PAL spectra were registered using a standard fast−slow coincidence spectrometer with the time resolution fwhm = 220 ps. The temperature was controlled by the computer program with accuracy at 0.1 K. The spectra statistics exceeded 1.5 million counts per spectrum collected during 1.5 h (standard measurement time). At selected temperatures the measuring time was extended, and the statistics of the spectrum were better than 10 million counts. The LT 9.227 and MELT28,29 programs were used to analyze the spectra. Three or four exponential lifetime components were fit to the spectrum. Two short-lived components corresponded to the free annihilation (τ ≈ 410 ps) and annihilation of p-Ps (τ ≈ 200 ps), respectively, and the other ones to the annihilation of o-Ps (τ ≈ 1.0−5.0 ns). Only the o-Ps component (or components) will be discussed below, as it carries the information about the structure of the studied medium. 2.5. Scanning Electron Microscopy (SEM). SEM micrographs of lyophilized hydrogel samples were recorded using a JEOL JSH 5500 LV electron microscope in high vacuum mode at the accelerating voltage of 10 kV. Samples were covered with a fine layer of gold using the ion coating Jeol JFC 1200 apparatus. 2.6. Rheology. Rheological measurements were carried out in an Ares rheometer in the viscoelastic regime at various temperatures between 23 and 47 °C. The samples were loaded onto parallel plates of 8 mm diameter. The gap distance between the two plates was kept at 1.4 mm. The changes in storage modulus (G′) and loss modulus (G″) were recorded as a function of frequency from 100 to 0.01 rad/s at 1% strain. 2.7. Solid-State 11B NMR. The solid-state 11B NMR experiments were performed on a BRUKER Avance III 400 spectrometer operating at 128.38 MHz for 11B and 400.15 MHz for 1H and equipped with a MAS probe head using 4 mm ZrO2 rotors. Spectra were recorded with MAS frequency of 8000 Hz, and a standard HPDec (High Power Decoupling) pulse program was utilized with a 11B 90° pulse of 4.0 μs in length and 9.0 μs 1 H 90° pulse length in spinal decoupling sequence. The repetition delay was 2 s, and the spectral width was 40.76 kHz. The FIDs were accumulated with a time domain size of 3584 data points, and 128 scans were accumulated for each FID.

3. RESULTS AND DISCUSSION 3.1. Microstructure of Hydrogels (SEM Analysis). For our studies we have chosen two hydrogels, which differ in the weight fraction of hyperbranched polyglycidol and the initial molar ratio of diol functional groups per boronate ion (details are given in the Materials and Methods Section). The reversible mechanism of the cross-linking reaction of hyperbranched polyglycidol with B(OH)4⊖ ions, which is responsible for selfhealing properties of such hydrogels, is presented in Scheme 1. The microstructure of hydrogel systems was visualized on the basis of SEM micrographs (Figure 1), revealing a highly porous structure of materials with micropores sized below 10 μm for H2 and even smaller for hydrogel H1. Some morphological differences between two hydrogel types are noticeable. For hydrogel H1, which contains 19 wt % of polymer, an aligned structure (arranged arrays) was observed, whereas the microstructure of hydrogel H2 (23 wt % of HbPGL) was irregular. This variation can result from different amounts of water and polymer in samples and the influence of freezing. For hydrogel which was less concentrated (H1), a highly arranged structure was obtained. It is the result of oriented growth of ice crystals, which is imposed by the direction of the sample cooling (hydrogel is placed on brass kept on dry ice). As a consequence, the polymer network is oriented along the freezing direction.30 The structure of hydrogel H2 is more influenced by the significant amount of polymer in the hydrogel system, so that water freezing does not generate any orientation. Probably, it results from the restricted area essential for the formation of ice crystals. 3.2. Dependence of Boronic Cross-Link Concentration on Temperature. The molar ratio of formed boronic diester to HbPGL macromolecules within the hydrogel at various temperatures was determined based on solid-state 11B NMR spectra (see Figure 2 and SI, Figures S-4 and S-5). The number of boronic diester (nD) was calculated according to the equation nD = 18325

ID·n0A ID + IM + IA

(1) DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C

macromolecules; i.e., the whole diester fraction corresponds to the number of cross-links responsible for the polymer network formation. In spite of the fact that the initial molar ratio of diol groups to boronate ions was different, the molar ratio of formed boronic diester species to HbPGL macromolecules at ambient temperature was very similar (around 1.8 boronic diester to HbPGL macromolecules). However, detailed analysis of hydrogels at various temperatures has demonstrated distinct differences in the stability of covalent junctions between macromolecules (Figure 3) for the investigated systems. The

Figure 1. SEM images of H1 (top) and H2 (bottom) hydrogels.

Figure 3. Changes of molar ratio of boronic diester species (crosslinks) to HbPGL macromolecules within hydrogel H1 (at the top) and H2 (at the bottom) at various temperatures. At first, the samples were gradually heated from 20 °C, and next cooled to −10 °C.

hydrogel containing the higher amount of polymer (H2, 23 wt % of HbPGL) turned out to be more sensitive to the increase of temperature than the less concentrated one (H1, 19 wt % of HbPGL). The increase of temperature above 30 °C resulted in a gradual decrease of diester concentration within hydrogel reaching at 50 °C around 1.20 boronic diester species to the HbPGL macromolecule. This value was still constant even at 70 °C. In the case of hydrogel composed of a lower amount of polymer, at temperatures ranging from 20 to 70 °C the number of cross-links hardly changed. It is noteworthy that the molar ratio of diester species to HbPGL macromolecules is similar in the heating and cooling cycles for both hydrogels (data are overlapped), which indicates that the composition of boronic species within the analyzed HbPGL/borax system is completely reversible. The reorganization of the structure is a quite fast process, as the equilibration at each temperature and the

11

Figure 2. Representative solid-state B NMR spectra for H1 and H2 hydrogels recorded at 30 °C. D, M, A denote boronic diester, monoester, and unreacted acid (B(OH)4⊖), respectively.

where ID, IM, and IA denote integration of signals corresponding to boronic diester (δ = 9.4 ppm), monoester (δ = 5.3 ppm), and unreacted acid (δ = 1.1 ppm), respectively, and n0A is the initial number of moles of B(OH)4⊖ ions applied for hydrogel formation. We have stated11 that the intramolecular cross-linking (i.e., reaction of B(OH)4⊖ ions with two diol functional groups coming from one macromolecule) is not favored for the HbPGL system. We establish that within the hydrogel structure all diester bonds are formed between individual HbPGL 18326

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C recording of the 11B NMR spectrum takes around 9 min. Among boronic species present within the hydrogel structure, mono- and diesters can be mainly distinguished (see SI Figures S-4 and S-5). The traces of unreacted B(OH)4⊖ were only detected in the case of H1 hydrogel (see SI Figure S-4). Gradual cooling of the hydrogel samples below ambient temperature resulted in a significant increase of boronic diester fraction (Figure 3). The number of diester species for both hydrogels was comparable. 3.3. Dependence of the Lifetime of Boronic CrossLinks on Temperature. The rheological measurements delivered additional information about the changes of lifetime of covalent cross-links (τ) within the analyzed hydrogel systems upon heating. The lifetime τ was estimated on the basis of the crossover point (ωc) corresponding to the gelation point (G′(ω) = G″(ω)), characteristic for the transient networks, i.e., the border between liquid and solid-like behavior (ωc = 1/2π·τ) observable in the frequency sweep test.31 Generally, the average lifetime of cross-links formed within hydrogel H2 was shorter than it was in the case of hydrogen H1. At 23 °C, the lifetime of bonds within the polymer network in hydrogel H1 was equal to 0.6 s, whereas within hydrogel H2 it was barely 0.056 s. The different values of bond lifetimes most probably result from the fact that within the hydrogel system composed of a higher amount of polymer (H2) and in addition a higher fraction of accessible diol groups per B(OH)4⊖ molecules (5.50:1) the exchange reactions based on transesterification between all esters species and free diol functional groups are more favorably reducing the lifetime of bonds. In the case of hydrogel H1, the distribution of HbPGL macromolecules in the hydrogel volume is not so dense, and consequently the concentration of reactive diol groups is less in the system, which probably leads to a lower rate of the exchange resulting in the increase of the lifetime of cross-links. The investigations carried out at a temperature range from 23 to 45 °C revealed gradual reduction of the cross-link lifetime with increasing temperature (Figure 4). For example, for hydrogel H1, at 23 °C the lifetime of the bonds was 0.64 s, whereas at 37 °C it was hardly 0.16 s. In the case of hydrogel H2, the lifetime of cross-links was reduced from 0.06 to 0.03 s during heating the sample from 23 to 37 °C. It means that upon heating an increased rate of cross-links breaking/reforming is observed. According to the Arrhenius

relationship (Figure 4), the apparent activation energy (Ea) of the overall gelation process10,32 within two hydrogel systems was estimated giving values with negative sign (i.e., EaH1 = −79.1 kJ/mol, EaH2 = −38.9 kJ/mol). These data imply that cross-links are less stable at higher temperature. Based on the negative value of the activation energy, we can predict that the possibility of polymer network formation diminishes with increasing temperature. Moreover, upon heating cross-links, dissociation within hydrogels also takes part, which is evident on the basis of 11B NMR data. Distinctive reduction of the number of diester bonds was especially visible within hydrogel H2. This behavior was consistent with a significantly small value of the cross-link lifetime in this network, in comparison to the lifetime of crosslinks building the network of hydrogel H1. Based on curve fitting of Arrhenius plots, we estimated that at 62 °C the lifetime of cross-links within both hydrogel systems reaches the same value (around 0.015 s), τH1 = τH2. Increase of temperature above 60 °C results in similar characteristics of both hydrogels; i.e., liquid-like behavior predominates. 3.4. PALS Investigations. The chemical reorganization of diester species within hydrogel systems after cooling from 70 °C to ambient temperature was determined by 11B NMR spectroscopy (Figure 3); however, there are no data about the structural reorganization of the polymer network, i.e., the evidence that all macromolecules are covalently bound in the polymer network. It seems to be interesting to estimate whether the distribution of cross-links within the whole volume of hydrogel is homogeneous ensuring engagement of all HbPGL macromolecules in the network. Detailed insight into the molecular structure of the polymer network is not simple, as most of the available techniques work at higher scales. Due to the fact that PALS is able to determine the size of free volumes present in the sample at various temperatures, it can be applied for detecting some structural changes upon the heating. During the PALS experiment, positronium (Ps) is formed by positrons emitted from the β+ source, with the probability of the process depending on physical and chemical properties of the sample. Positronium prefers the electronless regions, and when trapped there, it annihilates by the pick-off process, e.g., with e− of opposite spin from the medium. The smaller the free volume (FV) size, the shorter the o-Ps lifetime is. Using the respective models33−36 one can estimate this size. In the Tao-Eldrup model, the relationship between the FV radius RTE and the o-Ps lifetime τo‑Ps is described as follows33,34 1 τo ‐ Ps

⎛ 2πRTE ⎞ RTE 1 = λ b ⎜1 − + sin ⎟ RTE + Δ 2π RTE + Δ ⎠ ⎝

(2)

where λb = 2 ns−1 is the o-Ps decay constant in the bulk and the Δ = 0.166 nm is an empirical parameter. When the o-Ps lifetime is very short (less than 1.5 ns), as it happens in polymer and other organics, the radius determined from eq 2 needs a simple correction ζ to the RTE value (ζ = 0.068−0.066·ln τo‑Ps).36 In liquids, positronium is localized in a cavity, named “bubble”, worked up by strong exchange repulsion between the o-Ps electron and electrons of surrounding molecules.37 The bubble radius is determined by the minimum of energy

Figure 4. Arrhenius plots representing the network formation in aqueous solution based on didiol−boronic acid complexation for H1 and H2 hydrogels. For hydrogel H1, Ea = −79.1 kJ/mol, whereas for H2, Ea = −38.9 kJ/mol.

d ⎡ 4 3 ⎤ 2 ⎢⎣E Ps(R ) + 4πR σ + πR p⎥⎦ = 0 dR 3 18327

(3)

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C where EPs(R) is the Ps energy in the bubble; the second term describes the energy of surface tension σ; and the third one is the energy of external pressure p (the influence of pressure is by 3 orders of magnitude lower than the other two factors and usually can be neglected). For a better understanding of the obtained results, it is required to study individual building blocks of the analyzed material. The properties of water, the main component of hydrogels, from the viewpoint of positron techniques are wellknown.38−42 In pure water, in PAL spectra three components can be usually distinguished: p-Ps component with mean lifetime ∼200 ps, free positrons component ∼ 500 ps, and the longest-lived o-Ps component. In the ice, o-Ps is located in vacancies and other defects of structure, and its lifetime is about 1.2 ns. At the melting point, 0 °C, the lifetime increases stepwise up to 1.9 ns and decreases slowly (few ps/K) with further rise of temperature.40,41 This typical course of changes in PAL spectra parameters can be modified by impurities, the rate of temperature change, etc. In the systems composed mainly of water (mixtures with solvents and polymers, like discussed here hydrogels; immiscible systems) the results of PALS measurements are expected to resemble, at least partly, these for pure water. The amount of H2O molecules interacting with Ps due to the spatial limitation and the hydrophilicity of the system (interactions between components) are crucial. In hydrogels, the H2O molecules can exist in three physical states:43,44 (1) as a “free water”, (2) “intermediate water”, and (3) “bound water”. Free water shows behavior similar to bulk water; the interaction with the solute (e.g., polymer, etc.) can be neglected; and the freezing point is not shifted. The intermediate state of water assumes the existence of (chemical, host−guest) interaction with solute, though the properties of such water are still slightly different from the bulk ones; e.g., freezing point is shifted to lower temperatures. The water molecules in the bound state penetrate into the (hydrogel) network, where they can interact with the hydrophilic groups of polymer, e.g., create the hydrogen bonds. Using the positron probe, we can observe a shift of the melting point, hysteresis of phase transition, change of the lifetime value (FV size value) being determined by the size, and location of water-filled regions in the hydrogel structure. Until now, there were no PALS data about the structural characteristics of hyperbranched polyglycidol, being the second main building component of hydrogels analyzed here. Our measurements show the presence of two types of free volumes, with diameter (on the approximation of a spherical shape of FV, according to the Tao−Eldrup model) D1 = 0.57 ± 0.04 nm (smaller free volume, sFV) and D2 = 0.91 ± 0.05 nm (larger one, lFV) at room temperature. The average size of single HbPGL molecules, determined by DOSY NMR and GPC working with laser light scattering at λ = 670 nm (RALS and LALS detectors), was 4.36 and 3.84 nm, respectively. We assume that free volume voids of smaller size correspond to spaces between branches of the HbPGL macromolecule determined by random branching theory,45 whereas larger holes may come from the distances between individual macromolecules (Scheme 2a). Based on the presence of larger free volume, lack of the entanglements between individual HbPGL macromolecules is evident. Thermal analysis performed for HbPGL in the temperature range from −100 to +90 °C demonstrates an interesting influence of temperature on the sizes of free voids and their relative concentrations. The changes of fractions of holes can

Scheme 2. Schematic Distribution of Free Volumes and Their Sizes Around (a) HbPGL and (b) Hydrogel System Composed of Cross-Linked HbPGL with B(OH)4⊖ Ions

result mainly from two possible reasons on the molecular size level: the flexibility of branches of the macromolecule and the mobility of the whole macromolecule, which strongly depend on temperature and chemical structure of polyglycidol, i.e., numerous hydroxyl (monohydroxyl groups coming from L13 and L14 repeating units, 1,2-diol functional groups from terminal units (T))23 and polyether branches of the HbPGL macromolecule facilitate the formation of intra- and intermolecular hydrogen bonds. Osterwinter et al. reported for linear polyglycidol a gradual reduction of hydrogen bonds with the increasing temperature from 30 to 100 °C,46 so we assume that for hyperbranched polyglycidol similar behavior can be observed. Upon cooling of the hyperbranched polyglycidol, the formation of intra-/ intermolecular hydrogen bonds can be favored. To explain 18328

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C thermal fluctuations of free volume sizes, also other effects should be taken into consideration. The decrease of temperature leads to some limitations within the flexibility of macromolecule branches, which creates favorable conditions for the formation of hydrogen bonds between branches of the HbPGL macromolecule. Moreover, as HbPGL is a viscous oil, such macroscopic factors like HbPGL viscosity and surface tension,47 which are sensitive to temperature, can also affect the cavity size, as positronium in liquids forms a bubble. Figure 5 shows how both sizes of HbPGL change as a function of temperature. The size of sFV increases with the

Surprisingly, the PALS analyses do not reveal any significant change around temperature corresponding to glass transition value (Tg) of HbPGL, which was determined by DSC technique (Tg = −25.4 °C). Analogous PALS measurements as a function of temperature were performed for two hydrogels with different density of cross-linking (Figure 6). For such a probe as positronium, two

Figure 6. o-Ps lifetimes τo‑Ps and intensities Io‑Ps: (a) In hydrogels H1 (squares) and H2 (triangles) as a function of decreasing (full) and increasing (empty) temperature. Solid lines: taken from Figure 5 (for pure polyglicydol); dotted line: pure water; vertical dashed line: phase transition point at cooling; arrows indicate the direction of PALS parameters changes in time. (b) In hydrogel H2 as a function of increasing (empty triangles, diamonds, and circles) and decreasing (full diamonds and circles) temperature. Stars and crosses: H2O + 24% HbPGL. Figure 5. o-Ps lifetimes τo‑Ps and intensities Io‑Ps in pure HbPGL as a function of decreasing (empty) and increasing (full) temperature.

systems shown in Scheme 2 (i.e., HbPGL and hydrogel) differ significantlyin the hydrogel only one o-Ps component can be fit, and there is no component with a longer lifetime attributed to free volumes between the HbPGL macromolecules. This result suggests that within examined hydrogels all macromolecules are engaged in the network. The influence of temperature on the structure is also different from that presented previously for HbPGL. At low temperature the τo‑Ps changes like the shorter o-Ps lifetime in HbPGL and is close to the lifetime in frozen water (solid and dotted line on Figure 6a, respectively). The o-Ps lifetimes in ice42 and inside HbPGL have similar values, and distinguishing between these two types of free volumes corresponding to H2O and polyglycidol is impossible. It means that the FV sizes are close to each other. Based on the large micrometer-sized aqueous regions visible in SEM micrographs (see Figure 1), we expected that in the PALS measurements we should observe the water in the bulk phase and phase transition at 0 °C. In both hydrogels in the cooling cycle a stepwise change of PALS parameters (τo‑Ps, Io‑Ps) appears near −10 °C. Only at this temperature, the o-Ps lifetime reduces, while the intensity rises. The scale of instability in time is indicated by the length of arrows in Figure 6a, and the equilibrium of the system is obtained after about 2 h. Such a large shift (10 K) of solidification point cannot be due to hysteresis (supercooling), though this effect can be possibly explained by the spatial limitation. We conclude that the spaces within the structure of HbPGL macromolecules and the spaces between them engaged in the polymer network are filled with water (see Scheme 2b). Engagement of HbPGL macromolecules in the polymer network results in the disappearance of the larger-sized volume

temperaturethe radius varies from 0.24 to 0.30 nm, while the intensity decreases from 24% to 15%. The trend of o-Ps lifetime changes in lFV is shown by the upper lines in Figure 5. Lifetime increases in the range −100 to 20 °C (R = 0.34 ± 0.47 nm). Between 20 and 30 °C a discontinuity of lifetime is observed, whereby the τo‑Ps stabilizes the new slightly smaller value (R30°C = 0.44 nm). Above 30 °C the slope of τo‑Ps(T) of the lFV size is smaller. The o-Ps intensity of this component is small (∼4%) at low temperatures, and at 30 °C we see the significant increase of Io‑Ps. This stepwise-like change of PALS parameters (τo‑Ps and Io‑Ps) in lFV vs T near 30 °C suggests the existence of some changes in HbPGL which can probably be attributed to temperature-induced effects such as breaking of intra/ intermolecular hydrogen bonds of the OH groups with themselves and with the ether linkages, enhanced mobility of HbPGL macromolecules, increased flexibility of macromolecule branches, and enhanced mobility of e+. The observed increase of I3 can be the result of increased e+ mobility, as the probability of finding by e+ the free volume increases. We assume that the distinct change observed in the fraction of the free volume of larger size at 30 °C results from diverged segmental mobility of HbPGL branches and the mobility of the whole HbPGL macromolecule. Probably, the average mobility of macromolecule branches is higher in comparison to the mobility of individual HbPGL macromolecules. As a result, the fraction of smaller-sized free volume decreases, whereas the fraction of larger-sized free volume significantly increases. 18329

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C

presented in Figure 4), decreased fraction of diester cross-links (concomitant increase of monoester fraction), and enhanced mobility of macromolecules at high temperature. Most probably, detached HbPGL macromolecules come from the network regions being in the direct neighborhood with severalmicron-sized spaces filled with water. Macromolecules diffuse into these areas, where due to its small amount they cannot be newly embedded in the network. Combining solid-state 11B NMR results with PALS data helped us to scrutinize physicochemical properties of analyzed hydrogels. By 11B NMR analysis, the chemical composition of boronic species within hydrogel systems was determined, whereas by PALS we identified some structural fluctuations within the regularity of the polymer network at various temperatures. In spite of the fact that NMR data demonstrated that cooling the hydrogel system from 70 °C to ambient temperature causes the complete reconversion of boronic cross-links (diester species) to the original level (Figure 3), investigations carried out by PAL spectroscopy showed that heating the hydrogel H2 at 70 °C causes the formation of an additional type of free volume characteristic for un-cross-linked HbPGL. The fraction of this volume was kept on the same level at 80 °C and was still present after cooling to 20 °C. It means that a certain fraction of HbPGL macromolecules in hydrogel H2 are not involved in the network structure after cooling to room temperature. Some defects within the structure of the polymer network are formed. It can be explained by a significant increase of monoester fraction at the expense of diester species (the intensity of the 11 B NMR signal corresponding to the monoester is increasing, whereas the diester is decreasing) under the influence of overheating. The generation of higher monoester fraction causes the HbPGL macromolecules to be anionically charged. The repulsion effect can be created between individual HbPGL macromolecules. As a result, some macromolecules can diffuse to several-micron-size free spaces filled with water. The dilution of polymer in this area hinders the macromolecules to participate in the network formation. Decreasing the temperature of the system causes, in most part, homogeneous redistribution of newly formed diester connections (and consequently the reduction of monoester fraction) within the whole volume of the network, as PALS results demonstrate one o-Ps component only (like it was before heating). Nevertheless, the minor fraction of unbound macromolecules released from the polymer network was identified by PALS. We also cannot exclude the situation that locally a higher amount of diester bonds corresponding to one macromolecule can be formed, whereas some HbPGL macromolecules remain detached from the network. These studies imply the critical temperature Tc at which the completeness of the polymer network can be disturbed. At temperature T ≥ Tc, some irreversible structural changes within HbPGL hydrogels start appearing.

(i.e., related to the longer-lived component) typical for hyperbranched polyglycidol (in the native form). In comparison to unbound HbPGL macromolecules, their mobility in the polymer network is restricted. In the internal (smaller) spaces of HbPGL the number of water molecules is low, and they cannot form a structure identical to that in the bulk water system; moreover, there is no space for Ps bubble formation. The effect of changing the spectra parameters is mainly caused by the change of state of H2O contained in the sample. In a heating cycle the transition point (melting point) falls at 0 °C, when all of the H2O molecules (from the bound and free state) are in the liquid phase. The o-Ps lifetime is distinctive like in liquid water with impurities. The DSC analyses carried out for H1 and H2 hydrogels revealed consistent transition changes (data presented in SI, Figure S-6). In a cooling cycle, water crystallization was observed at −20 °C, whereas its melting point in a heating cycle was recorded at 0 °C. Above the water melting point (mp) the o-Ps intensity in both hydrogels is the same; however, below the mp, in the H2 hydrogel, the Io‑Ps is lower, while in the H1 hydrogel, intensity is higher than above the mp and resembles the tendency observed in pure water. Such differences in the o-Ps intensity in both hydrogels can result from different weight fractions of polymer in both analyzed hydrogel systems. Due to the fact that within both analyzed hydrogels the molar ratio of the formed boronic diester to HbPGL macromolecules was similar, the hydrogel H1 exhibits lower cross-linking density, as it was composed of a lower amount of polymer. Heating the hydrogels in the temperature range from −100 °C to +60 °C (Figure 6a) did not cause any destructive or deteriorating effects. At repeated PALS measurements, the results are completely reproducible, and hydrogels retain their properties. A simple thermal resistance test was performed on a hydrogel H2 exhibiting a higher density of cross-linking. It was found (Figure 6b) that heating the H2 hydrogel at 70 °C resulted in the appearance of an additional o-Ps component (empty circles in Figure 6b) with the lifetime similar to that estimated for larger FV in pure HbPGL but of smaller intensity (2%). This component is present in the sample even after decreasing the temperature to ambient temperature (full dots in Figure 6b), which suggests that the changes in sample are permanent and irreversible. Some local defects are generated due to the formation of a higher fraction of monoesters under the overheating. In addition, to be sure that free holes which appeared under heating come from HbPGL macromolecules released from the network, PALS measurements were performed for water with un-cross-linked HbPGL of the same concentration as in the H2 hydrogel. Obtained data were compared to the results for the overheated H2 hydrogel (stars and crosses in Figure 6b; for the sake of clarity the results at two selected temperatures are shown only). The high consistency of the results for lifetimes in both cases indicates that at high temperature it comes to the release of a certain amount of polyglycidol molecules from the polymer network to the micrometer-size spaces in hydrogel structure filled with water. Due to this fact, an additional longlived component, corresponding to pure polyglycidol, is generated in the hydrogel spectrum. These molecules remain intact in the hydrogel structure, as evidenced by the presence of a longer-lived component also at lower temperatures. The detachment of HbPGL macromolecules from the network can be addressed to reduced cross-link lifetime at 70 °C (which can be predicted based on the Arrhenius relationship



CONCLUSIONS The nanostructural studies of hyperbranched polyglycidol by PALS measurements delivered information about two sizes of free volumes characteristic for this polymer. Larger free volumes (0.91 nm) correspond to spaces between individual macromolecules, whereas the smaller ones (0.57 nm) can be ascribed to voids within the sphere-shaped HbPGL macromolecule. These studies indicate the possible molecular size of potential compounds which can be encapsulated within the 18330

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C

(2) Keita, G.; Ricard, A. Continuous swelling or collapse of chemically crosslinked gel of polyvinylalcohol by borate complexation. Polym. Bull. 1990, 24, 627−632. (3) Nemoto, N.; Koike, A.; Osaki, K. Dynamic Light Scattering and Dynamic Viscoelasticity of Poly(vinyl alcohol) in Aqueous Borax Solutions. 2. Polymer Concentration and Molecular Weight Effects. Macromolecules 1996, 29, 1445−1451. (4) Robb, I. D.; Smeulders, J. B. A. F. The rheological properties of weak gels of poly(vinyl alcohol) and sodium borate. Polymer 1997, 38, 2165−2169. (5) Loughlin, R. G.; Tunney, M. M.; Donnelly, R. F.; Murphy, D. J.; Jenkins, M.; McCarron, P. A. Modulation of gel formation and drugrelease characteristics of lidocaine-loaded poly(vinyl alcohol)-tetraborate hydrogel systems using scavenger polyol sugars. Eur. J. Pharm. Biopharm. 2008, 69, 1135−1146. (6) Kesavan, S.; Prud’homme, R. K. Rheology of guar and (hydroxypropyl) guar crosslinked by borate. Macromolecules 1992, 25, 2026−2032. (7) Pezron, E.; Ricard, A.; Lafuma, F.; Audebert, R. Reversible gel formation induced by ion complexation. 1. Borax-galactomannan interactions. Macromolecules 1988, 21, 1121−1125. (8) Ide, N.; Sato, T.; Miyamoto, T.; Fukuda, T. Thermoreversible Hydrogel of Short-Chain O-(2,3-Dihydroxypropyl)cellulose/Borax Aqueous Solution. Microscopic versus Macroscopic Properties. Macromolecules 1998, 31, 8878−8885. (9) Audebeau, E.; Oikonomou, E. K.; Norvez, S.; Iliapoulos, I. Onepot synthesis and gelation by borax of glycopolymers in water. Polym. Chem. 2014, 5, 2273−2281. (10) Fang, Y.; Takahashi, R.; Nishinari, K. A Gel Network Constituted by Rigid Schizophyllan Chains and Nonpermanent Cross-Links. Biomacromolecules 2004, 5, 126−136. (11) Gosecka, M.; Gosecki, M.; Kazmierski, S. DOSY NMR as a tool for predicting optimal conditions for hydrogel formation: The case of a hyperbranched polyglycidol cross-linked with boronic acids. J. Polym. Sci., Part B: Polym. Phys. 2016, DOI: 10.1002/polb.24126. (12) He, L.; Fullenkamp, D. E.; Rivera, J. G.; Messersmith, P. B. pH responsive self-healing hydrogels formed by boronate−catechol complexation. Chem. Commun. 2011, 47, 7497−7499. (13) Kurniasih, I. N.; Liang, H.; Kumar, S.; Mohr, A.; Sharma, S. K.; Rabe, J. P.; Haag, R. A bifunctional nanocarrier based on amphiphilic hyperbranched polyglycerol derivatives. J. Mater. Chem. B 2013, 1, 3569−3577. (14) Radowski, M. R.; Shukla, A.; von Berlepsch, H.; Boettcher, C.; Pickaert, G.; Rehage, H.; Haag, R. Supramolecular Aggregates of Dendritic Multishell Architectures as Universal Nanocarriers. Angew. Chem., Int. Ed. 2007, 46, 1265−1269. (15) Kurniasih, I. N.; Keilitz, J.; Haag, R. Dendritic nanocarriers based on hyperbranched polymers. Chem. Soc. Rev. 2015, 44, 4145− 4164. (16) Schömer, M.; Schüll, Ch.; Frey, H. Hyperbranched aliphatic polyether polyols. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 995− 1019. (17) Tonhauser, Ch.; Wilms, D.; Korth, Y.; Frey, H.; Friedrich, Ch. Entanglement Transition in Hyperbranched Polyether-Polyols. Macromol. Rapid Commun. 2010, 31, 2127−2132. (18) Kainthan, R. K.; Muliawan, E. B.; Hatzikiriakos, S. G.; Brooks, D. E. Synthesis, Characterization, and Viscoelastic Properties of High Molecular Weight Hyperbranched Polyglycerols. Macromolecules 2006, 39, 7708−771. (19) Robb, I. D.; Smeulders, J. B. A. F. The rheological properties of weak gels of poly(vinyl alcohol) and sodium borate. Polymer 1997, 38, 2165−2169. (20) Hodge, R. M.; Simon, G. P.; Whittaker, M. R.; Hill, D. J. T.; Whittaker, A. K. Free volume and water uptake in a copolymer hydrogel series. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 463−471. (21) Schrader, D. M.; Jean, Y. C. Positron and Positronium Chemistry, studies in physical and theoretical chemistry 57; Elsevier: Amsterdam, NY, 1988.

HbPGL macromolecule. The studies conducted at broad temperature range (from −100 °C to +90 °C) revealed the changes of free volumes sizes, which can be mainly explained by the variation of hydrogen bond strength. Application of hyperbranched polyglycidol to the hydrogel formation based on didiol interactions with B(OH)4⊖ ions causes the disappearance of larger free volumes. Within the broad temperature range (from −100 to +60 °C), solely one type of free volume is present. However, treating the hydrogel at 70 °C results in generating some molecular defects, as the second type of free volume (that size is characteristic for larger types of HbPGL free volume) was created and still present after cooling the hydrogel sample to ambient temperature. It indicates that a small fraction of HbPGL macromolecules were irreversibly detached from the polymer network and diffused to micrometer-sized spaces filled with water which were visible in SEM micrographs. This contribution implies the limitation of thermal processing of hydrogel systems based on cross-linked hyperbranched polyglycidol with boronate ions. Overheating the hydrogel material can result in the formation of irreversible structural defects. Solid-state 11B NMR analyses carried out at the range from −10 to +70 °C demonstrate that the amount of diester species under the influence of heating was decreasing; cooling the sample ensured quantitative rebuilding of diester bonds. We also have found that PALS measurements can be applied for the recognition of difference in the cross-linking density of investigated hydrogel systems. Moreover, structural studies presented here carried out by PALS confirm the literature data concerning the lack of entanglements between individual macromolecules of HbPGL of molecular weight below the critical value Mc = 20 000.



ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b06365. Characteristics of hyperbranched polyglycidol (GPC and NMR analyses) and characteristics of hydrogel systems (solid-state 11B NMR, DSC) (PDF)



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone number: +48 42 6803235. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work is cofinanced by the following projects: 2013/09/D/ ST2/03712 and 2015/17/D/ST5/02458 of National Science Centre, Poland. The authors thank Prof. Stan Slomkowski for his valuable help and comprehensive discussions. Great thanks for PhD Barbara Charmas for performing the DSC analyses and D.Sc. Grzegorz Łapienis for GPC analysis.



REFERENCES

(1) Stukalin, E. B.; Cai, L.-H.; Kumar, N. A.; Leibler, L.; Rubinstein, M. Self-Healing of Unentangled Polymer Networks with Reversible Bonds. Macromolecules 2013, 46, 7525−7541. 18331

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332

Article

The Journal of Physical Chemistry C (22) Mogensen, O. E. Positron and Positronium Chemistry, studies in physical and theoretical chemistry 58; Springer-Verlag: 1995. (23) Sunder, A.; Hanselmann, R.; Frey, H.; Mülhaupt, R. Controlled Synthesis of Hyperbranched Polyglycerols by Ring-Opening Multibranching Polymerization. Macromolecules 1999, 32, 4240−4246. (24) Huang, Y.; Peng, H.; Lam, J. W. Y.; Xu, Z.; Leung, F. S. M.; Mays, J. W.; Tang, B. Z. Linear or branched structure? Probing molecular architectures of fullerene−styrene copolymers by size exclusion chromatographs with online right-angle laser-light scattering and differential viscometric detectors. Polymer 2004, 45, 4811−4817. (25) Schott, J.; Kretzschmar, J.; Acker, M.; Eidner, S.; Kumke, M. U.; Drobot, B.; Barkleit, A.; Taut, S.; Brendler, V.; Stumpf, T. Formation of a Eu(III) borate solid species from a weak Eu(III) borate complex in aqueous solution. Dalton Transactions 2014, 43, 11516−11528. (26) Monajemi, H.; Cheah, M. H.; Lee, V. S.; Zain, S. M.; Abdullah, W. A.T. W. On the kinetics and reaction mechanisms of boronic acid in interaction with diols for non-enzymatic glucose monitoring applications: A hybrid DFT study. RSC Adv. 2014, 4, 10505−10513. (27) Kansy, J. Microcomputer program for analysis of positron annihilation lifetime spectra. Nucl. Instrum. Methods Phys. Res., Sect. A 1996, 374, 235−244. (28) Shukla, A.; Peter, M.; Hoffmann, I. Analysis of positron lifetime spectra using quantified maximum entropy and a general linear filter. Nucl. Instrum. Methods Phys. Res., Sect. A 1993, 335, 310−317. (29) Zaleski, R. Measurement and Analysis of the Positron Annihilation Lifetime Spectra for Mesoporous Silica. Acta Phys. Pol., A 2006, 110, 729−738. (30) Zhang, L.; Zhao, J.; Zhu, J.; He Ch; Wang, H. Anisotropic tough poly(vinyl alcohol) hydrogels. Soft Matter 2012, 8, 10439−10447. (31) Herbst, F.; Döhler, D.; Michael, P.; Binder, W. H. Self-Healing Polymers via Supramolecular Forces. Macromol. Rapid Commun. 2013, 34, 203−220. (32) Bansal, N. P. Influence of Several Metal Ions on the Gelation Activation Energy of Silicon Tetraethoxide. 1988, NASA Technical Memorandum 101380. (33) Tao, S. J. Positronium Annihilation in Molecular Substances. J. Chem. Phys. 1972, 56, 5499. (34) Eldrup, M.; Lightbody, D.; Sherwood, J. N. The temperature dependence of positron lifetimes in solid pivalic acid. Chem. Phys. 1981, 63, 51−58. (35) Goworek, T.; Ciesielski, K.; Jasinska, B.; Wawryszczuk, J. Positronium states in the pores of silica gel. Chem. Phys. 1998, 230, 305−315. (36) Zgardzińska, B. The size of smallest subnanometric voids estimated by positron annihilation method. Correction to the TaoEldrup model. Chem. Phys. Lett. 2015, 622, 20−22. (37) Ferrell, R. A. Long Lifetime of Positronium in Liquid Helium. Phys. Rev. 1957, 108, 167−168. (38) Mogensen, O. E.; Eldrup, M. Vacancies in pure ice studied by positron annihilation techniques. J. Glaciol. 1978, 21, 85−99. (39) Hirade, T. Positronium formation in H2O, D2O and HDO mixture. Mater. Sci. Forum 1995, 175−178, 675−678. (40) Kotera, K.; Saito, T.; Yamanaka, T. Measurement of positron lifetime to probe the mixed molecular states of liquid water. Phys. Lett. A 2005, 345, 184−190. (41) Stepanov, S. V.; Byakov, V. M.; Duplâtre, G.; Zvezhinskiy, D. S.; Lomachuk, Y. V. Positronium formation in a liquid phase: Influence of intratrack reactions and temperature. Phys. Status Solidi C 2009, 6, 2476−2481. (42) Zgardzińska, B.; Goworek, T. Search for premelting at the end of positron track in ice. Phys. Lett. A 2014, 378, 915−917. (43) Yao, K. D.; Liu, W. G.; Liu, J. The unique characteristics of water in chitosan−polyether semi-IPN hydrogel. J. Appl. Polym. Sci. 1999, 71, 449−453. (44) Akiyama, Y.; Shibahara, Y.; Takeda, S.; Izumi, Y.; Honda, Y.; Hishijima, S. The investigation of swollen process in gelatin gel by using positron annihilation spectroscopy. Phys. Status Solidi C 2007, 10, 3920−3923.

(45) Konkolewicz, D.; Gray-Weale, A.; Perrier, S. Describing the Structure of a Randomly Hyperbranched Polymer. Macromol. Theory Simul. 2010, 19, 219−227. (46) Osterwinter, C.; Schubert, C.; Tonhauser, C.; Wilms, D.; Frey, H.; Friedrich, C. Rheological Consequences of Hydrogen Bonding: Linear Viscoelastic Response of Linear Polyglycerol and Its Permethylated Analogues as a General Model for Hydroxyl-Functional Polymers. Macromolecules 2015, 48, 119−130. (47) Mackay, M. E.; Carmezini, G.; Sauer, B. B.; Kampert, W. On the Surface Properties of Hyperbranched Polymers. Langmuir 2001, 17, 1708.

18332

DOI: 10.1021/acs.jpcc.6b06365 J. Phys. Chem. C 2016, 120, 18323−18332