Mesoscopic Diffusion of Poly(ethylene oxide) in Pure and Mixed

Article pubs.acs.org/JPCB

Mesoscopic Diffusion of Poly(ethylene oxide) in Pure and Mixed Solvents Xiong Zheng,†,‡ Mikhail A. Anisimov,*,†,§ Jan V. Sengers,† and Maogang He‡ †

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Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, United States ‡ Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, People’s Republic of China § Oil and Gas Research Institute of the Russian Academy of Sciences, Moscow 117333, Russia S Supporting Information *

ABSTRACT: We present results from an experimental dynamic light-scattering study of poly(ethylene oxide) (PEO) in both a pure solvent (water) and a mixed solvent (tert-butanol + water). The concentration dependence of the diffusive relaxation of the PEO molecules is found to be typical of polymers in a good solvent. However, the mesoscopic diffusive behavior of PEO in the mixed solvent is very different, indicating an initial collapse and subsequent reswelling of PEO caused by co-nonsolvency. Furthermore, in the solutions of PEO with very large molecular weights, we found additional hydrodynamic modes indicating the presence of PEO clusters and aggregates similar to those found by some other investigators.

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INTRODUCTION Poly(ethylene oxide) (PEO), whose chemical formula is H− (O−CH2−CH2)n−OH, is a very important water-soluble polymer. It is commercially used in many areas, like cosmetics, agricultural applications, and pharmaceutical materials.1 Because of the specific interactions originating from its hydrophobic ethylene units and hydrophilic oxygen atoms, similar to those found in biomolecular interactions, the polymer is also relevant to bioengineering.2 The main purpose of the present work was to investigate how the behavior of this polymer in aqueous solutions is modified upon the addition of a hydrotrope. A hydrotrope is a substance consisting of amphiphilic molecules that are too small to exhibit equilibrium self-assembling in aqueous solutions but that can form shortlived dynamic molecular structures H-bonded with water molecules.3−6 Just as in some of our previous studies,7−9 we selected here as a typical hydrotrope tertiary butanol, denoted by TBA. Specifically, we want to investigate how the concentration dependence of the PEO chains in the mixed solvent differs from that in the pure solvent. In dilute solutions of a polymer in a good solvent, the coils are expanded by the excluded volume effect but are independent of the concentration. In the semidilute regime, the coils sizes decrease until they reach their unperturbed values at high concentrations.10−12 The diffusive relaxation of PEO in pure H2O, observed in our dynamic light-scattering (DLS) experiments, is consistent with this picture. However, in the solutions of PEO in TBA + H2O, © 2017 American Chemical Society

we found anomalous mesoscopic diffusive behavior as a function of the TBA concentration. Some investigations have indicated the existence of aggregates of PEO molecules in water.2,14−21 Polverari and van de Ven et al.16 found that PEO clusters and free coils coexist in thermodynamic equilibrium because of the hydrophobic interactions of PEO molecules. Hammouda et al.2,17,18 found clusters in PEO aqueous solutions due to hydrogen bonding and hydrophobicity; they systematically studied the influence of these two effects on the formation of aggregates. However, other investigators22−27 have concluded that there is no aggregate in aqueous PEO solutions; they have suggested that aggregate behavior may occasionally appear as a result of the presence of impurities or crystallites22,24,25 or be associated with air bubbles.27 Hence, we have also revisited the issue of aggregation of PEO in water. Our work is a comprehensive study of the mesoscopic diffusion of PEO in the pure solvent water and the mixed solvent TBA + water. First, in PEO + water, we prove that all of the observed relaxation modes in the entire concentration range are diffusive. Second, we show that the hydrodynamic radius of PEO deduced from the experimental diffusion coefficient in the dilute solution regime satisfies the asymptotic theoretical power Special Issue: Benjamin Widom Festschrift Received: October 24, 2017 Revised: November 13, 2017 Published: November 13, 2017 3454

DOI: 10.1021/acs.jpcb.7b10420 J. Phys. Chem. B 2018, 122, 3454−3464

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The Journal of Physical Chemistry B

Figure 1. Decay rates Γi observed in a semidilute solution of PEO with Mw = 100 000 g mol−1 at a PEO concentration of 1% mass fraction at 25 °C as a function of q2. (a) The first mode (black) is from PEO relaxation, the second mode (red) is from smaller clusters of PEO, and the third mode (blue) is from larger aggregates. (b) The third mode is shown at the enlarged scale.

law for large-degree polymerization provided that finite-size corrections are accounted for. Third, we show that the cooperative diffusion coefficient in the semidilute solution regime with PEO high molecular weights approaches an asymptotic scaling law, similar to that observed by other investigators.10 In addition, we investigated the presence of supramolecular aggregates in PEO + water, still a controversial subject in the literature. In the mixed solvent, we found an anomalous mesoscopic diffusive behavior of PEO, indicating swelling−collapse−swelling behavior of PEO chains that we attribute to cononsolvency13 reported in the literature for other polymers in alcohol + water mixtures. Our paper shows for the first time that PEO alcohol solutions also show this type of anomalous behavior.

For a single-exponentially decaying relaxation process, the intensity autocorrelation function g2(t) (obtained in the homodyning mode) is given by32,33 g2(t ) − 1 = [A exp(−Γt )]2 = A2 exp(− 2Γt )

(1)

where A is the amplitude of the relaxation process, t the delay time of the photon correlations, and Γ the decay rate of the relaxation mode. For a diffusive relaxation process, the decay rate is related to a diffusion coefficient D as

Γ = Dq2

(2)

where q is the wavenumber related to the refractive index of the medium and the angle of the scattered light by the Bragg− Williams relation.33 The refractive index of the solvents in this study was measured at room temperature with an Abbe refractometer. In view of the limited temperature range of our experiments, we have neglected any influence of temperature on the refractive index. We must note that the relaxation rate is the actual property directly measured by DLS. Contrarily, the hydrodynamic length scale, associated with the rate, is a subject of modeling and interpretation. In the dilute-solution regime, the diffusion coefficient D in eq 1 is a diffusion coefficient associated with the Brownian motion of the individual polymer molecules. The hydrodynamic radius RH of the polymer molecules is then related to this diffusion coefficient D and, hence, to the decay rate Γ by the Stokes− Einstein relation

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EXPERIMENTAL SECTION Materials. Six PEO samples with molecular weights of 200, 600, 2000, 20 000, 100 000, and 200 000 g mol−1 used in this study were all purchased from Sigma-Aldrich. Analytical-grade tert-butanol (TBA) with a purity of 99.5% was purchased from Alfa-Aesar. Deionized water was freshly made from a Millipore Direct-Q 3 ultrapure water system with a resistivity of 18.2 MΩ cm at 25 °C. Solution Preparation. The aqueous PEO solutions were prepared gravimetrically by using a weight balance. After PEO was dissolved in deionized water, the solution was gently shaken, but no stirring or ultrasonic agitation was applied. The solutions with PEO molecular weights of 200, 600, 2000, 20 000 g mol−1 were filtered through 20 nm Millipore filters. Those with 100 000 and 200 000 g mol−1 molecular weight were filtered through 100 nm Millipore filters. The TBA + H2O solvents were filtered through 20 nm Millipore filters (Cat. No. 6809-2002) at a temperature below 10 °C in order to remove any trace amount of hydrophobic impurities in TBA, which could cause aggregation in aqueous solutions of TBA.4,8,28 Light-Scattering Technique and Procedure. A DLS technique was used to study the PEO solutions. The setup was the same one used in our laboratory by Jacob et al.29 and by Subramanian et al.4,8,9 The temperature of the samples was controlled with an accuracy of ±0.1 °C. The time-dependent autocorrelation function was determined by using a commercial multitau photon correlator.30,31

RH =

kBT k T q2 = B 6πηD 6πη Γ

(3)

where kB is Boltzmann’s constant, T the temperature, and η the shear viscosity of the solvent. In the semidilute and concentrated solution regime, the diffusion coefficient D in eq 2 is no longer a diffusion coefficient associated with the diffusion of individual molecules but is commonly referred to as a collective or cooperative diffusion coefficient because it is now associated with cooperative motion of a number of monomers in a blob.10,11 In analogy to eq 3, in semidilute and concentrated solutions, one continues to define a length scale ξ through an effective Stokes−Einstein relation10,11,34−36 3455


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The Journal of Physical Chemistry B ξH =

kBT k T q2 = B 6πηD 6πη Γ

To investigate the effect of viscosity in the definition of the hydrodynamic correlation lengths through eq 7, we determined the viscosity of aqueous solutions of PEO with Mw = 200, 2000, and 20 000 g mol−1 by measuring Brownian diffusion of polystyrene latex particles (500 nm). The experimental values are shown in Figure S1 and Table S1 in the Supporting Information. As expected, at low concentrations, the viscosity of the solutions is similar to the viscosity of liquid water. However, the viscosity of the solutions increases rapidly with PEO concentration and PEO molecular weight, so much that using the viscosity of the solution at large PEO concentrations and large PEO molecular weights in eq 7 yields length scales that are unphysically small. Hence, we continued the common practice of defining hydrodynamic correlation lengths by using the viscosity of the solvent in eqs 3, 4, and 7. For the viscosity of liquid water, we used the values recommended by the International Association for the Properties of Water and Steam,39,40 and for the viscosity of TBA and of TBA + water, we used the values reported by Tanaka et al.41 Tables of all experimental diffusion coefficients D and the relevant hydrodynamic correlation lengths ξH are given in Tables S2−S6 in the Supporting Information. The average experimental uncertainty for the decay rate Γ, the diffusion coefficient D, and consequently, the hydrodynamic correlation length ξH is about 2%.

(4)

In the literature, ξH has been referred to as the hydrodynamic screening length or blob size. 11,34 Obviously, at low concentrations, ξH reduces to the hydrodynamic radius RH of the individual polymers in accordance with eq 3. In practice, the shear viscosity η in eq 4 is identified with the viscosity of the solvent, as will also be done in the present paper. A single diffusive mode was found in all aqueous solutions of PEO with lower molecular weights of 200, 600, 2000, and 20 000 g mol−1. However, in the aqueous solutions of PEO with large molecular weights of 100 000 and 200 000 g mol−1, two modes were observed at low PEO concentrations and even three modes at large PEO concentrations. These additional modes indicate the presence of PEO clusters and of aggregates. In principle, there is also a thermal diffusive decay of temperature fluctuations of the solvent water. This thermal diffusive decay is much faster than the diffusive decay of the PEO molecules and is totally negligible in our experimental light-scattering signals. However, in the PEO solutions in the mixed solvent TBA + H2O, not only diffusive relaxation of the PEO molecules but also relaxation of the TBA concentrations was observed. Thus, in general 2 g2(t ) − 1 = ⎡⎣∑ Ai exp( −Γit )⎤⎦

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(5)

RESULTS AND DISCUSSION We report several major experimental results. First, we measured the hydrodynamic radius of PEO coils in dilute aqueous solutions. Second, we studied the concentration dependence of the cooperative diffusion of PEO in water. Third, we investigated supramolecular aggregates of PEO in water. Finally, we found a collapse and reswelling of PEO chains in the mixed solvent TBA + water. Diffusive Relaxations in PEO + H 2 O. We have investigated aqueous solutions of PEO with six different molecular weights. Depending on the PEO molecular weight and concentration, one to three diffusive relaxation modes were observed: a first mode with D on an order of magnitude of 10−6 cm2 s−1, a second mode with D on an order of magnitude of 10−7 cm2 s−1, and a third mode with D on an order of magnitude of 10−8 cm2 s−1. For the aqueous solutions of PEO with molecular weights from Mw = 200 to 20 000 g mol−1, only the first mode was found in the entire polymer concentration range. For the aqueous solutions of PEO with Mw = 100 000 and 200 000 g mol−1, the first and second modes were observed at low polymer concentrations, and all three modes were observed at high concentration. These three modes will be discussed in detail below. First Mode (Brownian Diffusion) in Dilute PEO + H2O Solutions. In the dilute-solution regime, the first mode arises from the Brownian diffusion of individual PEO chains, and the diffusion coefficient is almost independent of the concentration in this regime. As mentioned earlier, in the dilute-solution regime, the Stokes−Einstein relation yields the hydrodynamic radius RH of the polymer chain, in accordance with eq 3. We have determined the hydrodynamic radius of PEO in water at PEO molecular weights ranging from 200 to 200 000 g mol−1. Figure 2 shows our experimental data, together with data previously reported in the literature,27,42−45 as a function of the degree of the polymerization N. Most of the experimental data have been obtained at 25 °C, except for those of Devanand and Selser,42 which have been obtained at 30 °C. While temperature

where Ai are the amplitudes and Γi the decay rates of the relaxation modes. We have verified that each relaxation mode is a diffusive relaxation mode by measuring the decay rates Γi at eight different scattering angles from 20 to 90°. As shown in Figure 1, all experimental decay rates indeed exhibit a q2 dependence on the wavenumber q, in accordance with eq 2. Hence, each experimental decay rate Γi yields a corresponding diffusion coefficient

Di = Γi/q2

(6)

and a corresponding length scale ξH, i =

kBT k T q2 = B 6πηDi 6πη Γi

(7)

In this paper, we shall refer to ξH, as defined by eq 4 or 7, as the hydrodynamic correlation length. Generally, interpretation of the length associated with diffusive relaxation, which is obtained through the Stokes−Einstein relation (eq 7), is a subtle issue. The value of the length extracted from the diffusion coefficient depends on the chosen viscosity. In the dilute solution, the viscosity of solvent is appropriate to use for obtaining the hydrodynamic radius. In semidilute and concentrated solution, the polymer chains are overlapping; the diffusion becomes collective. In this regime, the characteristic length scale calculated from the diffusion coefficient will depend on the chosen viscosity. Near the critical point of liquid−liquid phase separation, the diverging correlation length of critical concentration fluctuations is obtained with the use of the actual viscosity of solutions.29,37 It is known that PEO−water mixtures show a lower solution critical point above 100 °C.38 However, because our experiments were carried out far away from the critical temperature, the observed dynamic modes are not related to the relaxation of diverging critical concentration fluctuations. 3456


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simulation of a theoretical model for a dilute polymer solution, Dunweg et al.49 found a Flory exponent ν = 0.5877 in good agreement with the theoretical value of 0.589 ± 0.003. A fit of eq 9 to the experimental data with the value for ν from Dunweg et al.49 yields A0 = 9.855 nm−1, B = 1.280, and C = −0.825. For a deviation plot, the reader is referred to Figure S2 in the Supporting Information. When experimental light-scattering data are analyzed in terms of eq 8 without any nonasymptotic corrections, one commonly finds an effective value for the Flory exponent ν that is somewhat lower than the asymptotic theoretical value.50−53 First Mode in Semidilute and Concentrated PEO + H2O Solutions. The first mode arises from the relaxation of PEO and yields the cooperative diffusion coefficient D1 = Dc of PEO. This cooperative diffusion coefficient and the hydrodynamic correlation length ξH of the first mode obtained from our DLS experiments are shown as a function of the PEO concentration c in Figure 3. In the interpretation of the behavior of a polymer solution, one distinguishes between three concentration regimes: a dilute-solution regime c < c*, where c* is the overlap concentration, a semidilute regime c* < c < c**, and a concentrated-solution regime c > c**. In Figure 3, the broken lines indicate the location of the overlap concentration c* of the solutions of PEO with different Mw, calculated from54

Figure 2. Hydrodynamic radius RH of PEO in aqueous solutions as a function of the degree of polymerization N. The curve represents eq 9 with ν = 0.5877 and Δ = 0.5.

does affect the radius,46 this effect is small and within the experimental accuracy of the experimental light-scattering data. For very large N, the hydrodynamic radius RH is expected to vary with N as RH ∝ N ν

(8)

where the exponent ν is often referred to as the Flory exponent.47 Its average theoretical value48 is 0.589 ± 0.003, slightly lower than the mean-field value12 of 0.6. However, in analyzing experimental data obtained at finite values of N, one needs to account for nonasymptotic corrections to the asymptotic power law, eq 8. As pointed out by Dunweg et al.,49 incorporating the first two correction terms, one should consider A ⎛ 1 B C ⎞ = 0ν ⎜1 − 1 − ν − Δ ⎟ RH N ⎝ N N ⎠

c* =

4 Mw 3π R g 3NAρ

(10)

where NA is Avogadro’s number, ρ the density of the solution, and Rg the radius of gyration as calculated from a relation Rg ∝ Mw0.583 with an effective Flory exponent 0.583 provided for PEO by Devanand and Selser.41 For the aqueous solutions of PEO, Dc increases with the polymer concentration in the semidilute regime, except for PEO with Mw = 200 g mol−1, a molecular weight too small for PEO to behave as a normal polymer. In the semidilute regime, where the polymer chains begin to overlap with the neighboring chains, the cooperative diffusion coefficient is expected to vary with the polymer concentration3 as Dc ∝ (c/c*)xD with the asymptotic theoretical value xD = 0.75. However, experiments55,56 have yielded a somewhat lower

(9)

where the term proportional to N−(1−ν) accounts for a correction due to the finite number of beads of the polymer chain and where the term proportional to N−Δ accounts for a correction-to-scaling term47 with Δ = 0.5. From a numerical

Figure 3. (a) Diffusion coefficients D1 and (b) hydrodynamic correlation length ξH,1 of the first mode for the aqueous solutions of PEO with different molecular weights as a function of PEO concentration c at 25 °C. The broken lines indicate the location of the overlap concentration c* for the solutions of PEO with different molecular weights, calculated from eq 10. The dotted line shows the location of crossover concentration c** from the semidilute and to the concentrated regime, which is independent of Mw. The dashed line indicates the asymptotic slope of 0.65 commonly found for polymer solutions.55,56 3457


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Figure 4. (a) Experimental correlation functions g2(t) − 1 and (b) relative amplitudes Ai/(A1 + A2) of the two modes in a dilution solution at 0.05% mass fraction of PEO with Mw = 100 000 and 200 000 g mol−1.

asymptotic value xD ≃ 0.65, indicated by the dashed line in Figure 3. The possible origin of the difference between the experimental value 0.65 and the theoretical values 0.75 has been debated in ref 56 and mentioned in the references in ref 56. It has been suggested that there may be an additional phenomenon not included in the theory, but there is no consensus.56 For example, Brown and Nicolai57 suggested that the exponent xD could become larger once corrections for a counter motion in the solvent (induced by the motion of polymer segments) are applied to the collective diffusion coefficient data. In the concentrated regime c > c** (≃0.3 mass fraction for PEO + H2O), the polymer chain reaches its unperturbed value,10−12 so that D1 is expected to become again independent of the polymer concentration. From Figure 3, we see that our experimental data are consistent with this expectation. Note that the diffusion coefficient for the solution of PEO with Mw= 2000 g mol−1 is equal to that of PEO with Mw= 20 000 g mol−1 in the concentrated solution, which indicates that the diffusion coefficient PEO may become independent of the molecular weight at high concentrations. Second Mode (Clusters) in Aqueous Solutions of PEO with Mw = 100 000 and 200 000 g mol−1. In the aqueous solutions of PEO with Mw = 100 000 and 200 000 g mol−1, we found not only the first mode but also the second mode at all concentrations. As an example, Figure 4 shows the experimental correlation functions and relative amplitudes Ai/ (A1 + A2) of the two modes at a PEO mass fraction of 0.05%, which is in the dilute-solution regime. The hydrodynamic radius corresponding to these two modes is RH = 9.1 nm for the first mode and RH = 40 nm for the second mode. As discussed above, the first mode corresponds to the hydrodynamic radius of the individual PEO coils. Hammouda et al.2 have studied an aqueous solution of PEO with Mw = 100 000 g mol−1 at PEO mass fractions of 1−10% using small-angle neutron scattering (SANS); they found that PEO would form clusters in this concentration region, with the radius of gyration of these clusters changing from 20 to 60 nm with PEO concentration. The hydrodynamic radius of the second mode in our study appears to correspond to a hydrodynamic radius that is of the same order as the radius of gyration observed by Hammouda et al.2 Hence, just like Hammouda et al., we attribute the second mode to clusters formed by PEO molecules. The diffusion coefficient D2 and the corresponding hydrodynamic correlation length ξH,2 of the

clusters are plotted as a function of PEO concentration in Figure 5. Figure 5a shows that for the aqueous solutions of PEO with Mw = 100 000 g mol−1, the diffusion coefficient of the second mode increases first and then decreases when the PEO concentration becomes larger than 1 mass %. For the aqueous solution of PEO with Mw = 200 000 g mol−1, the diffusion

Figure 5. (a) Diffusion coefficient D2 and (b) hydrodynamic correlation length ξH,2 of the second mode as a function of the PEO concentration. The open squares represent the radius of gyration of PEO clusters in aqueous solutions of PEO with 100 000 g mol−1 as reported by Hammouda et al. from SANS.2 3458


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Figure 6. (a) Experimental correlation functions g2(t) − 1 and (b) relative amplitudes Ai/(A1 + A2 + A3) of the three modes in solutions at 1 and 4% mass fraction of PEO with Mw = 100 000 g mol−1.

Figure 7. (a) Diffusion coefficient D3 and (b) hydrodynamic correlation length ξH,3 of the third mode for aquoeus solutions at large concentrations of PEO with Mw = 100 000 and 200 000 g mol−1 (this paper) and for aquoeus solutions of PEO with Mw = 73 000 g mol−1 (ref 58).

Figure 8. (a) Diffusion coefficient D and (b) hydrodynamic correlation length ξH of the three modes for aqueous solutions of PEO with Mw = 100 000 g mol−1 at a PEO mass fraction of 0.3% as a function of temperature from 10 to 70 °C. Two characteristic lengths observed by Hammouda et al.2 at a PEO mass fraction of 0.4% are also shown in Figure 5b.

coefficient increases in the entire concentration range covered by our measurements. The clusters exist both in dilute solutions and in semidilute solutions. Figure 5b shows the hydrodynamic correlation length ξH,2 of the second mode as a function of the PEO concentration as well as the radius of gyration reported by Hammouda et al.2 We conclude that the PEO clusters observed

in our experiments are essentially consistent with the clusters previously observed by Hammouda et al. in these solutions of PEO with high molecular weights. Third Mode (Large Aggregates) in Aqueous Solutions of PEO with Mw = 100 000 and 200 000 g mol−1 at High Concentrations. When the PEO mass fraction became larger 3459


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Figure 9. (a) Diffusion coefficient and (b) hydrodynamic radius RH of the PEO chain (Mw = 20 000 g mol−1) and correlation length ξ of the TBA concentration fluctuations in PEO + TBA + H2O as functions of the TBA concentration at 25 °C. The dotted curves are empirical representations of these data.

poor solvent, the size of polymer chains is expected to shrink near the critical temperature,59 while the correlation length from our experiments and that from ref 2 show different tendency than that found in ref 58. The opposite effect may be attributed to two reasons. First, the concentration of our experiment and that in ref 2 are in the semidilute regime, where the polymer chains overlap with neighboring chains; therefore, the hydrodynamic correlation length is no longer the hydrodynamic radius but the blob size; the blob size may exhibit a different dependence on the temperature. Second, the temperature of our measurements is significantly below the critical temperature. There is no clear explanation in the literature about the nature of this third mode. Figures 7 and 8 show the dependence of the diffusion coefficient and the hydrodynamic correlation length on PEO concentration and temperature. We see that the hydrodynamic correlation length increases quickly with increasing PEO concentration and decreasing temperature. It is possible that the third mode is related to the formation of small crystallites or to clustering phenomena observed in protein solutions.60 Further research would be needed to resolve the origin of this phenomenon. PEO in the Mixed Solvent TBA + H2O. After completing our studies of PEO in the pure solvent water, we investigated the behavior of PEO in the mixed solvent TBA + H2O. The DLS measurements were performed in solutions of 1% mass fraction PEO with molecular weight 20 000 g mol−1 as a function of the TBA concentration cTBA at 25 °C. This PEO concentration is still in the dilute regime but at a concentration sufficiently high to make the scattering amplitude from PEO chains strong enough. The DLS correlation function reveals the presence of two relaxation modes: a relatively fast mode associated with the TBA concentration fluctuations yielding values for the correlation length ξ of these fluctuations and a slower mode associated with the relaxation of the PEO molecules yielding values for the hydrodynamic radius, RH, of PEO. The experimental values, obtained for the diffusion coefficient, the hydrodynamic radius RH of the PEO, and the correlation length ξ of the TBA concentration fluctuations, are shown in Figure 9 as a function of the TBA concentration. Note that the mixture of PEO and TBA at 25 °C is in the solid phase. The DLS technique could only be used for the solutions in the liquid phase, i.e., in solutions with cTBA < 0.9. Our data

than 0.15%, the presence of a third mode was observed in the aqueous solutions of PEO with Mw = 100 000 and 200 000 g mol−1. The experimental correlation functions and relative amplitudes Ai/(A1 + A2 + A3) of the three modes at PEO mass fractions of 1 and 4% are shown in Figure 6. It shows that at high concentration the third mode appears and gradually dominates the signal as the concentration increases. Figure 7 shows values of the diffusion coefficient D3 and the corresponding hydrodynamic correlation length ξH,3 of this mode obtained by us, as well as values obtained by Brown,58 as a function of the polymer concentration for these solutions. Figure 7a shows that the third mode observed in this work agrees well with the slow mode in ref 58. The diffusion coefficient increases with concentration at low PEO concentration and decreases upon further increase of concentration. The concentrations at which D3 exhibits a maximum and ξH,3 a minmum are more or less consistent with those of the second mode. Recently, Schwahn et al.21 found from SANS the presence of aggregates of about 100 nm in the semidilute concentration regime. We think that this third relaxation mode observed by us may be related to these aggregates. For a comparison between our results and those of Schwahn et al.21 and Brown,58 the reader is referred to Figures S3 and S4 in the Supporting Information. We have also studied these three modes in aqueous solution of PEO with Mw = 100 000 g mol−1 at a PEO mass fraction of 0.3% as a function of temperature from 10 to 70 °C. Our experimental results for the diffusion coefficient and hydrodynamic correlation length of these three modes are presented in Figure 8. Evidently, the diffusion coefficient of all three modes increases with temperature. While the hydrodynamic correlation length ξH of the first mode (blobs size) increases with temperature, the correlation lengths of the second and third modes decrease with temperature, indicating that the size of the clusters and large aggregates decreases with increasing temperature. Hydrogen bonding becomes less strong at higher temperatures. Thus, the observed decrease of the correlation length of the clusters with increasing temperatures may suggest that hydrogen bonding is responsible for the cluster formation. As can be seen from Figure 8, both our experiments as well as those of Hammouda et al.2 for the radius of gyration suggest that these characteristic lengths may merge at a temperature of about 180 °C, independent of the PEO concentration. In a 3460


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Figure 10. (a) Diffusion coefficient and (b) hydrodynamic correlation length ξH of the PEO chain and PEO clusters in a solution of 0.3% mass fraction PEO with Mw = 100 000 g mol−1 in TBA + H2O at 55 °C, as a function of the TBA concentration.

H2O, has been observed in polymers in alcohol + water mixtures by many investigators, such as in methanol + water,71−83 in ethanol + water,71−73,76,80 in 1-propanol + water,71,82 in 2-propanol+water,72,73 and also in TBA + water.71,76 This initial rapid collapse, followed by reswelling, is commonly referred to as a co-nonsolvency phenomenon. This co-nonsolvency phenomenon has been widely debated in the literature.80−83,85−89 A generally accepted explanation is that the initial collapse of the polymer is a generic phenomenon driven by preferential binding of the polymer with one of the two solvent components.13 We conclude that we have encountered the same phenomenon when PEO is dissolved in TBA + H2O. The detailed microscopic mechanism for the preferential adsorption of one of the solvent components is still somewhat controversial.80−82 Clusters of PEO with Mw = 100 000 g mol−1 in TBA + H2O. While clusters were absent for PEO with molecular weights Mw ≤ 20 000 g mol−1 in all aqueous solutions, we did find clusters of PEO with Mw = 100 000 g mol−1 not only in H2O but also in the mixed solvent TBA + H2O. Figure 10 shows our experimental results for the diffusion coefficient and hydrodynamic correlation length ξH of both PEO and the PEO clusters in TBA + H2O as a function of the TBA concentration. Two features are to be noticed. First, the magnitude of the correlation length of the PEO clusters in pure TBA is smaller than that of the PEO clusters in pure H2O, providing evidence that hydrogen bonding is responsible for the cluster formation; it is easier to form hydrogen bonding in H2O than in TBA. Second, there appears to exist a close correlation between the hydrodynamic correlation length of the PEO chains themselves and of the PEO clusters.

for the correlation length associated with the TBA concentration fluctuations are in basic agreement with the values determined earlier by Euliss and Sorensen;61 these authors have attributed the somewhat unusual behavior of the correlation length in aqueous solutions of TBA to the possible presence of a virtual critical demixing temperature above the boiling temperature of the mixture and possibly again below the temperature of crystallization.61 Most interestingly, our measurements show anomalous behavior of the dimension of the PEO chains. The PEO chains first precipitously collapse with increasing TBA concentrations, then reswell, pass through a maximum size, and ultimately decrease again upon further increase of the TBA concentration. Here, we want to emphasize that the effects in the mixed solvent that we found are not related to the helical conformation of PEO coils into helices experimentally observed by Greer and co-workers62 in isobutyric acid, isopentanoic, and n-propanoic acids, but not in butanol isomers. Our depolarization light-scattering measurements clearly show no helices in PEO + TBA + H2O, just like Greer and co-workers did not find such helices in isobutanol, n-butanol, or water. A theory for the concentration dependence of polymer chains in a mixed solvent has been formulated by Schultz and Flory63 and further developed by Noel et al.64 This theory yields an equation for the expansion factor as a function of the interaction parameters of the components in the ternary mixture and, hence, accounts for the nonideality of the mixture interactions. The interaction parameter of PEO and H2O is available in the literature,26 while the interaction parameter of TBA and H2O can be readily calculated from experimental data65 reported for the excess Gibb energy for TBA + H2O. However, with any realistic estimate for the interaction parameter of PEO and TBA, this theory yields an expansion factor that is positive for all TBA concentrations and does not allow for any shrinking of the dimension of PEO from its value in pure water. Collapse of polymer dimensions has been encountered in solvents with a critical point of mixing due to preferential adsorption induced by critical fluctuations.66−70 Although the fluctuations of TBA in water are reminiscent of precritical fluctuations,61 they are too small to account for the rapid collapse of the PEO at low TBA concentrations. However, a rapid collapse of polymer coils followed by a reswelling, like the behavior found by us for PEO in TBA +

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CONCLUSIONS We have performed a DLS study of PEO in the pure solvent water and in the mixed solvent TBA + water. In the solutions of PEO with Mw ≤ 20 000 g mol−1, a single diffusive mode was found at all concentrations. However, in the aqueous solution of PEO with Mw = 100 000 and 200 000 g mol−1, not only a first mode (∼10−6 cm2 s−1) but also a second (∼10−7 cm2 s−1) mode was found at all concentrations, and even a third mode (∼10−8 cm2 s−1) was found at high concentrations. In the dilute regime, the first mode arises from Brownian motion of the polymer molecules, and the values obtained for the hydrodynamic radius RH of PEO in our experiment are consistent 3461


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The Journal of Physical Chemistry B with an asymptotic power law RH ∝ Nν with the theoretical value of the Flory exponent ν = 0.5877. In the semidilute regime, the first mode is now associated with a cooperative diffusion coefficient Dc of the polymers. In the semidilute regime, this cooperative diffusion coefficient Dc increases with concentration in a similar manner as observed by other investigators for polymers in a good solvent. In the mixed solvent TBA + H2O, we found an anomalous dependence of the diffusion coefficient as a function of concentration, indicating an initial collapse and a subsequent reswelling of PEO. This anomalous behavior turns out to be similar to that observed for other polymers in alcohol + water mixtures.71−89 Specifically, the initial collapse of a polymer like PEO in TBA + H2O appears to be a general phenomenon caused by preferential adsorption in hydrogen-bonding solvent mixtures caused by preferential adsorption in hydrogenbonding solvents.13 In the solutions of PEO with very large molecular weights (100 000 and 200 000 g mol−1) in TBA + H2O, we have found an additional hydrodynamic mode, indicating the presence of PEO clusters in TBA + H2O, but somewhat smaller than that in pure H2O.

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(4) Subramanian, D.; Boughter, C. T.; Klauda, J. B.; Hammouda, B.; Anisimov, M. A. Mesoscale inhomogeneities in aqueous solutions of small amphilic molecules. Faraday Discuss. 2013, 167, 217−238. (5) Robertson, A. E.; Phan, D. H.; Macaluso, J. E.; Kuryakov, V. N.; Jouravleva, E. V.; Bertrand, C. E.; Yudin, I. K.; Anisimov, M. A. Mesoscale solubilization and critical phenomena. Fluid Phase Equilib. 2016, 407, 243−254. (6) Novikov, A. A.; Semenov, A. P.; Monje-Galvan, V.; Kuryakov, V. N.; Klauda, J. B.; Anisimov, M. A. Dual action of hydrotopes at the water/oil interface. J. Phys. Chem. C 2017, 121, 16423−16431. (7) Subramanian, D.; Klauda, J. B.; Collings, P. J.; Anisimov, M. A. Mesoscale phenomena in ternary solutions of tertiary butyl alcohol, water, and propylene oxide. J. Phys. Chem. B 2014, 118, 5994−6006. (8) Subramanian, D.; Anisimov, M. A. Resolving the mystery of aqueous solutions of tertiary butyl alcohol. J. Phys. Chem. B 2011, 115, 9179−9183. (9) Subramanian, D.; Ivanov, D.; Yudin, I. K.; Anisimov, M. A.; Sengers, J. V. Mesoscale inhomogeneities in aqueous solutions of 3methylpyridine and tertiary butyl alcohol. J. Chem. Eng. Data 2011, 56, 1238−1248. (10) De Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (11) Teraoka, I. Polymer Solutions; An Introduction to Physical Properties; Wiley: New York, 2002. (12) Graessley, W. W. Polymer chain dimensions and the dependence of viscoelastic properties on concentration, molecular weight and solvent power. Polymer 1980, 21, 258−262. (13) Mukherji, D.; Marques, C. M.; Kremer, K. Polymer collapse in miscible good solvents is a generic phenomenon driven by preferebnial adsorption. Nat. Commun. 2014, 5, 4882. (14) Kalashnikov, V. N.; Kudin, A. M. Size and volume concentration of aggregates in a drag-reducing polymer solution. Nature, Phys. Sci. 1973, 242, 92−94. (15) Polik, W. F.; Burchard, W. Static light scattering from aqueous poly (ethylene oxide) solutions in the temperature range 20−90°. Macromolecules 1983, 16, 978−982. (16) Polverari, M.; van de Ven, T. G. Dilute aqueous poly (ethylene oxide) solutions: clusters and single molecules in equilibrium. J. Phys. Chem. 1996, 100, 13687−13695. (17) Ho, D. L.; Hammouda, B.; Kline, S. R. Clustering of poly (ethylene oxide) in. water revisited. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 135−138. (18) Hammouda, B.; Ho, D. L.; Kline, S. R. Insight into clustering in poly (ethylene oxide) solutions. Macromolecules 2004, 37, 6932−6937. (19) Khan, M. S. Aggregates formation in poly (ethylene oxide) solutions. J. Appl. Polym. Sci. 2006, 102, 2578−2583. (20) Hammouda, B. The mystery of clustering in macromolecular media. Polymer 2009, 50, 5293−5297. (21) Schwahn, D.; Pipich, V. Aqueous solutions of poly (ethylene oxide): Crossover from ordinary to tricritical behavior. Macromolecules 2016, 49, 8228−8240. (22) Devanand, K.; Selser, J. C. Polyethylene oxide does not necessarily aggregate in water. Nature 1990, 343, 739−741. (23) Faraone, A.; Magazu, S.; Maisano, G.; Migliardo, P.; Tettamanti, E.; Villari, V. The puzzle of poly (ethylene oxide) aggregation in water: Experimental findings. J. Chem. Phys. 1999, 110, 1801−1806. (24) Kinugasa, S.; Nakahara, H.; Fudagawa, N.; Koga, Y. Aggregative behavior of poly (ethylene oxide) in water and methanol. Macromolecules 1994, 27, 6889−6892. (25) Porsch, B.; Sundeloef, L.-O. Apparent aggregation behavior of poly (ethylene oxide) in water as a result of the presence of an impurity. Macromolecules 1995, 28, 7165−7170. (26) Venohr, H.; Fraaije, V.; Strunk, H.; Borchard, W. Static and dynamic light scattering from aqueous poly(ethylene oxide) solutions. Eur. Polym. J. 1998, 34, 723−732. (27) Wang, J. Q. The origin of the slow mode in dilute aqueous solutions of PEO. Macromolecules 2015, 48, 1614−1620.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b10420. Figures showing the viscosity of aqueous solutions of PEO, deviations of experimental data for RH of PEO in water from eq 9, amplitudes of three dynamic modes, and comparison with the results of ref 58; tables showing the viscosity of aqueous solutions of PEO and the diffusion coefficient and hydrodynamic correlation length of PEO in pure and mixed solvents (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Tel (301) 405-8049. ORCID

Xiong Zheng: 0000-0003-2270-5899 Mikhail A. Anisimov: 0000-0002-8598-949X Jan V. Sengers: 0000-0003-2255-1332 Maogang He: 0000-0002-2364-2140 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge valuable discussions with Vivek Prabhu of the National Institute of Standards and Technology. The research of Xiong Zheng was supported by the China Scholarship Council (Grant No. 201606280242). Mikhail Anisimov acknowledges support by the Russian Foundation for Basic Research (Grant No. 16-03-00895-a).

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REFERENCES

(1) Bailey, F. J.; Koleske, J. V. Poly(ethylene oxide); Academic Press: New York, 1976. (2) Hammouda, B.; Ho, D. L.; Kline, S. R. SANS from poly (ethylene oxide)/water systems. Macromolecules 2002, 35, 8578−8585. (3) Kunz, W.; Holmberg, K.; Zemb, T. Hydrotopes. Curr. Opin. Colloid Interface Sci. 2016, 22, 99−107. 3462


Article

The Journal of Physical Chemistry B (28) Sedlak, M.; Rak, D. On the origin of mesoscale structures in aqueous solutions of tertiary butyl alcohol: the mystery resolved. J. Phys. Chem. B 2014, 118, 2726−2737. (29) Jacob, J.; Anisimov, M. A.; Sengers, J. V.; Dechabo, V.; Yudin, I. K.; Gammon, R. W. Light scattering and crossover critical phenomena in polymer solutions. Appl. Opt. 2001, 40, 4160−4169. (30) Brown, W. Dynamic light scattering: the method and some applications; Oxford University Press: New York, 1993. (31) Photocor. http://www.photocor.com (2017). (32) Berne, B. J.; Pecora, R. Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics; Wiley: New York, 1976. (33) Chu, B. Laser Light Scattering: Basic Principles and Practice; Academic Press: New York, 1991. (34) Brown, W.; Nicolai, T. Static and dynamic behavior of semidilute polymer solutions. Colloid Polym. Sci. 1990, 268, 977−990. (35) de Gennes, P. G. Dynamics of entangled polymer solutions II. Inclusion of hydrodynamic interactions. Macromolecules 1976, 9, 594− 598. (36) Nemoto, N.; Makita, Y.; Tsunashima, Y.; Kurata, M. Dynamic light scattering of polymer solutions. 4. Semidilute solutions of polystyrene and their binary blends in benzene. Macromolecules 1984, 17, 2629−2633. (37) Kostko, A. F.; Anisimov, M. A.; Sengers, J. V. Dynamics of critical fluctuations in polymer solutions. Phys. Rev. E 2007, 76, 021804. (38) Bae, Y. C.; Lambert, S. M.; Soane, D. S.; Prausnitz, J. M. Cloudpoint curves of polymer solutions from thermooptical measurements. Macromolecules 1991, 24, 4403−4407. (39) Huber, M. L.; Perkins, R. A.; Laesecke, A.; Friend, D. G.; Sengers, J. V.; Assael, M. J.; Metaxa, I. N.; Vogel, E.; Mareš, R.; Miyagawa, K. New international formulation for the viscosity of H2O. J. Phys. Chem. Ref. Data 2009, 38, 101−125. (40) IAPWS, Revised Supplementary Release on Properties of Liquid Water at 0.1 MPa. www.iapws.org (2017). (41) Tanaka, Y.; Matsuda, Y.; Fujiwara, H.; Kubota, H.; Makita, T. Viscosity of (water+alcohol) mixtures under high pressure. Int. J. Thermophys. 1987, 8, 147−163. (42) Devanand, K.; Selser, J. C. Asymptotic behavior and long-range interactions in aqueous solutions of poly (ethylene oxide). Macromolecules 1991, 24, 5943−5947. (43) Rangelov, S.; Brown, W. Microgel formation in high molecular weight poly (ethyleneoxide). Polymer 2000, 41, 4825−4830. (44) Xu, M.; Xu, M.; Chen, Q.; Zhang, S. M. Investigation on extremely dilute solution of PEO by PFG-NMR. Colloid Polym. Sci. 2010, 288, 85−89. (45) Linegar, K. L.; Adeniran, A. E.; Kostko, A. F.; Anisimov, M. A. Hydrodynamic radius of polyethylene glycol in solution obtained by dynamic light scattering. Colloid J. 2010, 72, 279−281. (46) Hammouda, B.; Ho, D. L. Insight into chain dimensions in PEO/water solutions. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 2196−2200. (47) Flory, P. J. Principles of polymer chemistry; Cornell University Press: Ithaca, NY, 1953. (48) Pelissetto, A.; Vicari, E. Critical phenomena and renormalization-group theory. Phys. Rep. 2002, 368, 549−727. (49) Dunweg, B.; Reith, D.; Steinhauser, M.; Kremer, K. Corrections to scaling in the hydrodynamic properties of dilute polymer solutions. J. Chem. Phys. 2002, 117, 914−924. (50) Adam, M.; Delsanti, M. Dynamical properties of polymer solutions in good solvent by Rayleigh scattering experiments. Macromolecules 1977, 10, 1229−1237. (51) Nemoto, N.; Makita, Y.; Tsunashima, Y.; Kurata, M. Dynamic light scattering studies of polymer solutions. 3. Translational diffusion and internal motion of high molecular weight polystyrenes in benzene at infinite dilution. Macromolecules 1984, 17, 425−430. (52) Venkataswamy, K.; Jamieson, A. M.; Petschek, R. G. Static and dynamic properties of polystyrene in good solvents: ethylbenzene and tetrahydrofuran. Macromolecules 1986, 19, 124−133.

(53) Reith, D.; Müller, B.; Müller-Plathe, F.; Wiegand, S. How does the chain extension of poly (acrylic acid) scale in aqueous solution? A combined study with light scattering and computer simulation. J. Chem. Phys. 2002, 116, 9100−9106. (54) Ying, Q.; Chu, B. Overlap concentration of macromolecules in solution. Macromolecules 1987, 20, 362−366. (55) Doi, M.; Edwards, S. F. The theory of polymer dynamics; Oxford University Press: New York, 1988. (56) Zhang, K. J.; Briggs, M. E.; Gammon, R. W.; Sengers, J. V.; Douglas, J. F. Thermal and mass diffusion in a semidilute good solvent-polymer solution. J. Chem. Phys. 1999, 111, 2270−2282. (57) Brown, W.; Nicolai, T. Static and dynamic behavior of semidilute polymer solutions. Colloid Polym. Sci. 1990, 268, 977−990. (58) Brown, W. Slow-mode diffusion in semidulute solutions examined by dynamic light scattering. Macromolecules 1984, 17, 66− 72. (59) Nierlich, M.; Cotton, J. P.; Farnoux, B. Observation of the collapse of a polymer chain in poor solvent by small angle neutron scattering. J. Chem. Phys. 1978, 69, 1379−1383. (60) Safari, M. S.; Byington, M. C.; Conrad, J. C.; Vekilov, P. G. Polymorphism of Lysozyme Condensates. J. Phys. Chem. B 2017, 121, 9091−9011. (61) Euliss, G. W.; Sorensen, C. M. Dynamic light scattering studies of concentration fluctuations in aqueous t-butyl alcohol solutions. J. Chem. Phys. 1984, 80, 4767−4773. (62) Norman, A. I.; Fei, Y.; Ho, D. L.; Greer, S. C. Folding and unfolding of polymer helices in solution. Macromolecules 2007, 40, 2559−2567. (63) Shultz, A. R.; Flory, P. J. Polymer chain dimensions in mixedsolvent media. J. Polym. Sci. 1955, 15, 231−242. (64) Noel, R.; Patterson, D.; Somcynsky, T. Polymer chain dimensions in mixed solvents. J. Polym. Sci. 1960, 42, 561−570. (65) Koga, Y.; Siu, W. W.; Wong, T. Y. H. Excess partial molar free energies and entropies in aqueous tert-butyl alcohol solutions at 25. degree. J. Phys. Chem. 1990, 94, 7700−7706. (66) Brochard, F.; De Gennes, P. G. Collapse of one polymer coil in a mixture of solvents. Ferroelectrics 1980, 30, 33−47. (67) He, L.; Cheng, G.; Melnichenko, Y. B. Partial Collapse and Reswelling of a Polymer in the Critical Demixing Region of Good Solvents. Phys. Rev. Lett. 2012, 109, 067801. (68) Grabowski, C. A.; Mukhopadhyay, A. Contraction and reswelling of a polymer chain near the critical point of a binary liquid mixture. Phys. Rev. Lett. 2007, 98, 207801. (69) Nierlich, M.; Cotton, J. P.; Farnoux, B. Observation of the collapse of a polymer chain in poor solvent by small angle neutron scattering. J. Chem. Phys. 1978, 69, 1379−1383. (70) To, K.; Choi, H. J. Polymer conformation near the critical point of a binary mixture. Phys. Rev. Lett. 1998, 80, 536−539. (71) Mukae, K.; Sakurai, M.; Sawamura, S.; Makino, K.; Kim, S. W.; Ueda, I.; Shirahama, K. Swelling of poly(N-isopropylacrylamide) gels in water-alcohol (C1-C4) mixed solvents. J. Phys. Chem. 1993, 97, 737−741. (72) Zhu, P. W.; Napper, D. H. Coil-to-globule type transitions and swelling of poly (N-isopropylacrylamide) and poly (acrylamide) at latex interfaces in alcohol−water mixtures. J. Colloid Interface Sci. 1996, 177, 343−352. (73) Crowther, H. M.; Vincent, B. Swelling behavior of poly-Nisopropylacrylamide microgel particles in alcoholic solutions. Colloid Polym. Sci. 1998, 276, 46−51. (74) Zhang, G.; Wu, C. The water/methanol complexation induced reentrant coil-to-globule-to-coil transition of individual homopolymer chains in extremely dilute solution. J. Am. Chem. Soc. 2001, 123, 1376− 1380. (75) Zhang, G.; Wu, C. Reentrant coil-to-globule-to-coil transition of a single linear homopolymer chain in a water/methanol mixture. Phys. Rev. Lett. 2001, 86, 822−825. (76) Hiroki, A.; Maekawa, Y.; Yoshida, M.; Kubota, K.; Katakai, R. Volume phase transitions of poly (acryloyl-l-proline methyl ester) gels 3463


Article

The Journal of Physical Chemistry B in response to water−alcohol composition. Polymer 2001, 42, 1863− 1867. (77) Scherzinger, C.; Lindner, P.; Keerl, M.; Richtering, W. Cononsolvency of Poly(N,N-diethylacrylamide) (PDEAAM) and Poly(N-isopropylacrylamide) (PNIPAM) Based Microgels in Water/ Methanol Mixtures: Copolymer vs Core−Shell Microgel. Macromolecules 2010, 43, 6829−6833. (78) Walter, J.; Sehrt, J.; Vrabec, J.; Hasse, H. Molecular dynamics and experimental study of conformation change of poly (Nisopropylacrylamide) hydrogels in mixtures of water and methanol. J. Phys. Chem. B 2012, 116, 5251−5259. (79) Kojima, H.; Tanaka, F.; Scherzinger, C.; Richtering, W. J. Temperature dependent phase behavior of PNIPAM microgels in mixed water/methanol solvents. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1100−1111. (80) Mukherji, D.; Wagner, M.; Watson, M. D.; Winzen, S.; de Oliveira, T. E.; Marques, C. M.; Kremer, K. Relating side chain organization of PNIPAm with its conformation in aqueous methanol. Soft Matter 2016, 12, 7995−8003. (81) van der Vegt, N. F. A.; Rodriguez-Ropero, F. Comment on “Relating side chain organization of PNIPAm with its conformation in aqueous methanol” by D. Mukherji, M. Wagner, M. D. Watson, S. Winzen, T. E. de Oliveira, C. M. Marques and K. Kremer, Soft Matter, 2016, 12, 7995. Soft Matter 2017, 13, 2289−2291. (82) Mukherji, D.; Wagner, M.; Watson, M. D.; Winzen, S.; de Oliveira, T. E.; Marques, C. M.; Kremer, K. Reply to the ‘Comment on “Relating side chain organization of PNIPAm with its conformation in aqueous methanol”’ by N. van der Vegt and F. Rodriguez-Ropero, Soft Matter, 2017, 13. Soft Matter 2017, 13, 2292−2294. (83) Dalgicdir, C.; Rodriguez-Ropero, F.; van der Vegt, N. F. A. Computational calorimetry of PNIPAM cononsolvency in water/ methanol mixtures. J. Phys. Chem. B 2017, 121, 7741−7748. (84) Hore, M. J.; Hammouda, B.; Li, Y.; Cheng, H. Co-nonsolvency of poly (n-isopropylacrylamide) in deuterated water/ethanol mixtures. Macromolecules 2013, 46, 7894−7901. (85) Schild, H. G. Poly (N-isopropylacrylamide): experiment, theory and application. Prog. Polym. Sci. 1992, 17, 163−249. (86) Hao, J.; Cheng, H.; Butler, P.; Zhang, L.; Han, C. C. Origin of cononsolvency, based on the structure of tetrahydrofuran-water mixture. J. Chem. Phys. 2010, 132, 154902. (87) Tanaka, F.; Koga, T.; Kojima, H.; Xue, N.; Winnik, F. M. Preferential adsorption and co-nonsolvency of thermoresponsive polymers in mixed solvents of water/methanol. Macromolecules 2011, 44, 2978−2989. (88) Tanaka, F.; Koga, T.; Winnik, F. M. Temperature-responsive polymers in mixed solvents: competitive hydrogen bonds cause cononsolvency. Phys. Rev. Lett. 2008, 101, 028302. (89) Zhang, Q.; Hoogenboom, R. Polymers with upper critical solution temperature behavior in alcohol/water solvent mixtures. Prog. Polym. Sci. 2015, 48, 122−142.

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Mesoscopic Diffusion of Poly(ethylene oxide) in Pure and Mixed

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