Microscopic Structure of the “Nonswellable” Thermoresponsive

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Microscopic Structure of the “Nonswellable” Thermoresponsive Amphiphilic Conetwork Shintaro Nakagawa,† Xiang Li,† Hiroyuki Kamata,‡ Takamasa Sakai,‡ Elliot Paul Gilbert,§ and Mitsuhiro Shibayama*,† †

Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Department of Bioengineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan § Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232, Australia ‡

S Supporting Information *

ABSTRACT: We investigated the microscopic structure of the nonswellable hydrogel using small-angle neutron scattering (SANS). The hydrogel consisted of four-armed thermoresponsive prepolymer units embedded in a homogeneous network of four-armed poly(ethylene glycol) (Tetra-PEG). The structure of the hydrogel was similar to that of the ordinary Tetra-PEG hydrogels at temperatures below 16.6 °C, whereas discrete spherical domains were formed at temperatures above 19.5 °C. The number of prepolymer units contained in one domain was much larger than unity, indicating that multiple thermoresponsive prepolymer units as well as Tetra-PEG units gathered to form a domain. Formation of domains much larger than a single prepolymer unit led to significant frustration of the matrix polymer network outside the domains. This frustration enhanced the elastic energy of the matrix network which would cancel the osmotic pressure and induce significant macroscopic shrinking. The selection mechanism of the domain size could qualitatively be explained by the balance between the interfacial and conformational free energies.

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behavior with the critical temperature of ∼20 °C. Upon raising temperature above this critical temperature, shrinking of PEMGE units induced macroscopic shrinking of the entire hydrogel, preventing the hydrogel from swelling. The mole fraction of Tetra-PEMGE r could easily be adjusted by the feed ratio of Tetra-PEG and Tetra-PEMGE at preparation. We found that the hydrogel with r = 0.4 was practically nonswellable at 37 °C (physiological temperature); the equilibrium swelling ratio V/V0 was ∼260% at 10 °C, whereas it dramatically decreased to ∼100% upon heating to 37 °C. In addition, this hydrogel remained transparent even after the macroscopic shrinking, suggesting that shrinking of PEMGE occurred microscopically in a length scale much smaller than the visible light wavelength. However, no structural study has been carried out, and thus the origin of the nonswellable feature of our hydrogel has not been elucidated. The structure of conetworks, which are prepared by endlinking between two chemically different polymers like our nonswellable hydrogel, has been studied by several authors including us.5−17 For example, we studied the structure of PEG−PDMS gel consisting of Tetra-PEG and linear poly(dimethylsiloxane) (PDMS) in various solvents.6 When the gel

INTRODUCTION Hydrogels, consisting of a large amount of water and a small amount of hydrophilic polymer network, are increasingly important in the biomedical fields. Among many highperformance hydrogels that have been developed recently, Tetra-PEG hydrogels prepared by end-linking between fourarmed poly(ethylene glycol) prepolymers are gaining attention because of their ease of preparation and mechanical toughness.1 However, hydrogels generally swell with surrounding water when they are placed in aqueous environment such as the human body. Swelling reduces the polymer concentration of the hydrogel and hence lowers the mechanical durability. Moreover, it has been reported that the swelling-induced volume expansion of hydrogels implanted in the body damages the surrounding tissues.2,3 Although some specific polymer− polymer and/or polymer−solvent interactions such as electrostatic interaction may facilitate swelling, the major reason for swelling is the osmotic pressure imbalance inside and outside the gel. Therefore, even Tetra-PEG hydrogels, which consist only of a neutral polymer, cannot escape from swelling. Recently, we developed a new hydrogel whose swelling behavior could be controlled via temperature.4 The hydrogel consisted of Tetra-PEG and a four-armed thermoresponsive polymer, poly(ethyl glycidyl ether-co-methyl glycidyl ether) (Tetra-PEMGE). Aqueous solution of Tetra-PEMGE had lower critical solution temperature (LCST)-type phase © XXXX American Chemical Society

Received: March 6, 2017 Revised: April 11, 2017

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Figure 1. Schematic illustration of the preparation method of the nonswellable gel (Gel40, a) and the ordinary Tetra-PEG gel (Gel0, b) used in this study. The chemical structure of PEMGE is also shown in the rightmost side of panel a. the equal volumes of TAPEG and TNPEG solutions were mixed. This sample is denoted as Gel0. Swelling Ratio. We measured the swelling ratio V/V0 of the hydrogel samples as a function of temperature. First, a cylindrical hydrogel sample was prepared in a glass tube with the inner diameter di of 720 μm. Then the sample was pushed out of the capillary, soaked in the excess amount of D2O buffer, and sealed in a cell constructed by two cover glasses separated by a silicone spacer. The cell was then placed on a handmade temperature-controlled sample stage, where the temperature was increased stepwise from 5 to 40 °C and then decreased from 40 to 5 °C in the same manner. We measured the diameter of the gel sample d using a digital optical microscope (BX-51, Olympus, Japan) at each temperature after holding for at least 3 h to attain the equilibrium swollen state. Finally, V/V0 was calculated as (d/ di)3. Small-Angle Neutron Scattering (SANS). SANS measurements were performed using QUOKKA installed at OPAL reactor, Australian Nuclear Science and Technology Organisation (ANSTO), Australia. We employed three instrument configurations with different sampleto-detector distances (SDDs) of 1.3, 8, and 20 m, respectively. The wavelength of the incident neutron beam λ was 5.0 Å with the resolution of 10%. The samples for SANS measurements were prepared in demountable cells sealed with quartz windows and placed in a 20-position temperature-controlled sample stage. The sample thickness was 2 mm. A thermocouple was directly attached to the cell to monitor the sample temperature. Temperature was raised stepwise during the experiment; SANS data were collected after equilibrating the sample at least for 20 min, followed by heating to the next target temperature. The stability of temperature was ±0.1 °C. Unlike the case in swelling ratio measurements, the samples for SANS measurements were not allowed to contact with the excess amount of the solvent; the solvent was neither absorbed into nor expelled from the samples during the whole experiment. We call this condition isochoric in order to discriminate it from the isobaric condition adopted for the swelling ratio measurements. Data collected in each of the three configurations were circular-averaged and merged in a single one-dimensional SANS profile. The detector counts were converted to the absolute scale by the attenuated direct beam method. The three configurations covered the q-range of 0.004 < q < 0.3 Å−1, where q is the magnitude of the scattering vector defined as q = (4π/λ) sin θ (2θ: scattering angle). The intensity was then corrected for the solvent and incoherent scattering. To avoid complications in model fitting, all the data were desmeared using the Lake algorithm19 and then smoothed using the filter proposed by Vad and Sager.20 Figure S1 shows an example of the data before and after desmearing.

was swollen with water (good solvent for PEG but poor solvent for PDMS), multiple PDMS chains aggregated to form nanometer-scale core−shell spherical domains with a PEG core and PDMS shell. Mortensen and Annaka studied the structure of a thermoresponsive conetwork hydrogel prepared by end-linking of four-armed PEG-block-poly(propylene oxide) (Tetra-PEG-b-PPO) units where PPO had an LCST-type phase behavior in water.7 They found that PPO chains aggregated into nanometer-scale hexagonally packed cylindrical domains above the critical temperature of PPO. Although the architecture of the sample and/or driving force of structure formation are different between the past studies and the present one, it is expected that a nanometer-scale ordered structure is also formed in our hydrogel upon shrinking. In the present study, we investigate the microscopic structure of the nonswellable hydrogel using small-angle neutron scattering (SANS) to clarify the structural origin of the shrinking behavior of our nonswellable hydrogel.

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EXPERIMENTAL SECTION

Samples. Figure 1 shows the schematic illustration of the sample preparation method. The sample was the nonswellable hydrogel with the fraction of thermoresponsive units r = 0.4. We hereafter call this sample Gel40. Three types of polymers were used to prepare Gel40: four-armed poly(ethylene glycol) terminated with amine groups (TAPEG), that terminated with N-hydroxysuccinimide ester groups (TNPEG), and four-armed poly((ethyl glycidyl ether)190-co-(methyl glycidyl ether) 47 ) (PEMGE) terminated with amine groups (TAPEMGE). TAPEG and TNPEG were purchased from NOF Corporation (Tokyo, Japan) and used as received. The detailed method of synthesis for TAPEMGE has been described elsewhere.4 The number-average molecular weight of TAPEG and TNPEG was 20.0 × 103 g mol−1, and that of TAPEMGE was 23.5 × 103 g mol−1. All the three prepolymers had narrow molecular weight distribution (Mw/Mn < 1.1).4,18 First, TAPEG and TAPEMGE were separately dissolved in the D2O phosphate buffer (pH 7.4, ionic strength 100 mM), while TNPEG was dissolved in the D2O citric−phosphate buffer (pH 5.8, ionic strength 100 mM). The polymer concentration was 6 mM. These solutions were mixed so that the molar ratio of TAPEMGE:TAPEG:TNPEG was 4:1:5 and left for a day. The temperature was kept below 10 °C throughout the preparation process to ensure that TAPEMGE completely dissolved in D2O. A hydrogel sample with r = 0, i.e., an ordinary Tetra-PEG hydrogel, was also prepared following the same procedure described above, except that B

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RESULTS AND DISCUSSION Isobaric Swelling Behavior. Figures 2a−c are the optical microscope images of Gel40 equilibrated at selected temper-

but also PEG chains in the network tend to shrink upon heating, leading to the gradual decrease of V/V0. After the measurements during the heating process, we also measured V/ V0 of Gel40 during the subsequent stepwise cooling process. The result, also shown in Figure 3 with squares, clearly demonstrates the perfect reversibility of the process without any hysteresis. Structure at Low Temperatures. Figures 4a and 4b show the SANS profiles of Gel40 in the temperature range of 6.9− 16.6 °C and those of Gel0 in 6.9−31.1 °C, respectively. Note that all the SANS measurements were carried out under an isochoric condition and should be distinguished with the isobaric swelling behavior shown in Figures 2 and 3. The scattering profiles of Gel40 are qualitatively similar to those of Gel0; they have an upturn in q ≤ 0.03 Å−1 and plateau followed by a power-law decrease in q ≥ 0.03 Å−1. These profiles are qualitatively similar to those previously reported for Tetra-PEG hydrogels.23,24 The upturn in the low-q region is also observed for the solution of linear PEG and is mainly ascribed to the clustering of the end groups.25 The scattering intensity in q ≥ 0.03 Å−1 could be explained by the Ornstein−Zernike (OZ) function which holds for semidilute solutions and gels

Figure 2. Optical microscope photographs of Gel40 equilibrated in D2O buffer at selected temperatures (a: 19.0 °C; b: 22.0 °C; c: 25.5 °C) taken during a stepwise heating process under the isobaric condition.

atures in the D2O buffer. The sample significantly reduces its diameter upon heating from 19.0 to 25.5 °C, while it keeps its overall shape and remains transparent throughout the entire shrinking process. This is in marked contrast with the case of thermoresponsive hydrogels consisting only of thermoresponsive polymer chains where the samples undergo macroscopic phase separation and become clouded and sometimes significantly deformed.21 The fact that Gel40 remains transparent even after macroscopic shrinking suggests that the length scale of the phase separation is suppressed below the visible light wavelength. As is discussed later on, this hypothesis is consistent with the results of SANS measurements. Figure 3 shows the swelling ratio V/V0 of Gel40 equilibrated in the D2O buffer at each temperature during a stepwise heating

I(q) =

IOZ(0) 1 + ξ 2q2

(1)

where IOZ(0) is the scattering intensity at the limit of q = 0 and ξ is the correlation length associated with the concentration fluctuation of the network. Solid curves in Figure 4 represent the results of model fitting using the OZ function. Only data points in q ≥ 0.03 Å−1 were used for fitting to avoid the influence of the low-q upturn. Good agreement between the observed intensity and the OZ function indicates that polymer chains in Gel40 at 6.9−16.6 °C and Gel0 at 6.9−31.1 °C are molecularly dispersed in water. It should be noted here that both ξ and IOZ(0) of Gel40 and Gel0 increase upon heating (Figure S3), indicating the increase of both the amplitude and wavelength of concentration fluctuations. This behavior is typical for hydrogels exhibiting LCST-type phase behavior such as poly(N-isopropylacrylamide) (PNIPA) hydrogels.26 In the case of PNIPA hydrogels, both ξ and IOZ(0) diverge at a certain critical point. At a first glance, ξ and IOZ(0) of Gel40 also appear to diverge at a temperature slightly above 16.6 °C. However, as has been pointed out earlier, Gel40 never undergoes macroscopic phase separation, meaning that the concentration fluctuations would cease to grow at a certain point and thus ξ and IOZ(0) would not diverge. Structure at High Temperatures. Figure 5 shows the SANS profiles of Gel40 at 19.5−31.1 °C. At 19.5 °C, a broad peak centered at q ∼ 0.028 Å−1 is observed, suggesting the formation of a periodic structure with the length scale of ∼200 Å. This temperature roughly coincides with the onset temperature of macroscopic shrinking under the isobaric condition (Figure 3). The length scale of the structure is much smaller than the visible light wavelength, which agrees with the fact that Gel40 remains transparent after macroscopic shrinking (Figure 2). The broad peak becomes higher and sharper with raising temperature, while its position is almost unchanged. An additional shoulder and small peak in q ∼ 0.04− 0.1 Å−1 are observed at temperatures above 21.4 °C. The primary peak in the lower-q side can be attributed to the interdomain correlation (= structure factor), whereas the

Figure 3. Temperature dependence of the equilibrium swelling ratio V/V0 of Gel40 in D2O buffer during heating and subsequent cooling.

process. V/V0 was measured after equilibrating at each temperature for a sufficiently long time (∼3 h). The temperature dependence of V/V0 in the D2O buffer is quantitatively similar to that in the H2O buffer reported in our previous study (Figure S2). V/V0 is ∼300% at 10 °C and starts to drop at a transition point of ∼20 °C. Thus, the isotope effect of deuterium is insignificant in our sample, justifying the use of D2O instead of H2O in SANS measurements. The sudden decrease of V/V0 is clearly due to shrinking of PEMGE units. Interestingly, V/V0 gradually decreases upon heating even at temperatures below 20 °C. It is known that aqueous solution of PEG undergoes the LCST-type phase separation at the critical point of >120 °C.22 Therefore, not only PEMGE chains C

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Figure 4. SANS profiles of Gel40 at 6.9−16.6 °C (a) and Gel0 at 6.9−31.1 °C (b). Solid curves represent the fitting results of the OZ function.

Figure 6. SANS profiles of Gel40 at 6.9 °C before and after heating to 31.1 °C.

profiles similar to those in Figure 5 and concluded that core− shell spherical domains with a PEG core and PDMS shell were formed.6 Given the similarity of the scattering profiles of the PEG−PDMS hydrogel and Gel40, it may be appropriate to use the core−shell sphere model as a first choice also for Gel40. However, the difference of the scattering length density (SLD) between PEG (6.82 × 10−7 Å−2) and PEMGE (6.16 × 10−7 Å−2) is much lower than that between the solvent (6.38 × 10−6 Å−2) and PEG or PEMGE. Therefore, even if the actual structure of the domain is the core−shell sphere with the PEMGE shell and PEG core (or vice versa), SANS is not able to discriminate the core from the shell. For this reason, we assumed that the domains were of a simple spherical shape with a uniform SLD. We also assumed that the SLD of PEMGE was equal to that of PEG and the temperature dependence of the physical density and SLD was negligible (the variation of these quantities with temperature was less than 1% in the temperature range involved in this study). The form factor we used was thus the sphere model with the Schulz distribution of the radius and diffuse interface

Figure 5. SANS profiles of Gel40 at temperatures in the range of 19.5−31.1 °C corrected for background scattering, incoherent scattering, and instrumental smearing. The curves at 21.4, 23.4, and 31.1 °C were vertically shifted by a factor of decades.

shoulder and peak in the higher-q side represent the shape of individual domains (= form factor). We note here that this microscopic structure is completely reversible. Figure 6 shows the SANS profiles of Gel40 at 6.9 °C before and after heating to 31.1 °C; the latter data were obtained after slow cooling from 31.1 to 6.9 °C at a rate of ca. 0.5 °C/min. The two data completely overlap with each other, indicating that the domain formation process is completely reversible. This is in agreement with the fact that the macroscopic swelling ratio under the isobaric condition is also reversible (Figure 3). In order to extract quantitative information on the domain structure, we constructed a model scattering function to be fitted to the observed data. The scattering intensity from discrete domains dispersed in the matrix network is written as I(q) = P(q)S(q) + Imatrix(q)

P(q) = n(Δρ)2 F(q; σinterf )

∫0

∞

D(R ; ⟨R ⟩, prad )|A(q; R )|2 dR (3)

(2)

where

where P(q) is the form factor, S(q) is the structure factor, and Imatrix(q) is the scattering intensity from the matrix. In our previous study on PEG−PDMS hydrogel, we obtained SANS

A (q ; R ) = D

4 3 3(sin qR − qR cos qR ) πR 3 (qR )3

(4)

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Figure 7. Scattering intensity from the domains Idomain(q) plotted against q. The results of two fitting procedures are separately presented in panels a and b with solid curves; the f ull fitting using the data points in 0.01 Å−1 ≤ q ≤ 0.2 Å−1 (a) and partial fitting in 0.03 Å−1 ≤ q ≤ 0.2 Å−1 (b). 2⎞ ⎛ q 2σ F(q; σinterf ) = exp⎜ − interf ⎟ 2 ⎝ ⎠

D(R ; ⟨R ⟩, prad

⟨R ⟩ s

−s

( ) )=

(5)

(

R

Rs − 1 exp − ⟨R⟩ s Γ(s)

content of the hydrogel consisting only of PEMGE. The detailed derivation of the expression and method for estimation of W are described in the Supporting Information, and we present only the final result here:

)

(Δρ)2 = 2.026 × 10−11 (6)

⎛ ⎞−2 4 × ⎜1 − nπ ⟨R ⟩3 (1 + prad 2 )(1 + 2prad 2 )⎟ [Å−4] ⎝ ⎠ 3

n, ⟨V⟩, and ⟨R⟩ are the number density, the mean volume, and the mean radius of the domains, respectively; Δρ is the difference of SLD between the domain and matrix, and σinterf is the interface thickness of the domain. s = 1/prad2 where prad is the variation coefficient (polydispersity) of the domain radius. The integral in the right-hand side of eq 3 was evaluated using the analytical expression derived by Kotlarchyk and Chen.27 We employed the modified hard-sphere (mHS) structure factor as the structure factor, which used the effective radius ⟨RHS⟩ instead of ⟨R⟩ (⟨RHS⟩ > ⟨R⟩).5,6 ⟨RHS⟩ was introduced to take into account the limited spatial arrangement of domains due to fixation of the domains to the matrix network. The polydispersity of RHS was assumed to be equal to prad. In the case of a polydisperse hard sphere system, S(q) in eq 2 is no longer a direct interparticle structure factor but an apparent, measurable structure factor.28 The measurable structure factor for polydisperse hard spheres was calculated using the scaling approximation proposed by Gazzillo et al.29 Finally, we assumed that Imatrix(q) was proportional to the scattering intensity at 16.6 °C (the highest temperature where the SANS profile did not have a peak; see Figure 4), I16.6(q), i.e.

Imatrix(q) = fI16.6(q)

(8)

Consequently, we had a model scattering function with five free parameters n, ⟨R⟩, prad, σinterf, and ⟨RHS⟩. We carried out least-squares fitting to the scattering intensity from the domains Idomain(q) = I(q) − Imatrix(q) at 21.4, 23.4, and 31.1 °C. We did not perform fitting for the data at 19.5 °C because the scattering profile lacked a significant high-q shoulder and peak, and hence it was impossible to determine a unique set of parameters. Figure 7a shows the experimental (symbols) and theoretical (solid curves) Idomain(q) obtained by fitting in the wide q-range (0.01 Å−1 ≤ q ≤ 0.2 Å−1). This f ull fitting successfully reproduces the intensity and position of the low-q peak but fails to capture the high-q features (a shoulder and peak) mainly arising from the form factor. Therefore, we carried out partial fitting using the same model but for the narrower q-range (0.03 Å−1 ≤ q ≤ 0.2 Å−1), excluding the left half of the low-q peak. The results are shown in Figure 7b, where the high-q features are well reproduced, though the position and width of the low-q peak deviate from the observed ones. Unfortunately, we could not find a set of parameters that gave a good agreement between the model and experimental data in the entire q-range. The deviation in Figure 7b is mainly ascribed to the difference in interdomain correlation. The observed peak is much broader than that of the assumed mHS structure factor, suggesting that the arrangement of domains is more disordered in Gel40 than in an interacting hard sphere system. This is presumably because the translational motion of the domains is severely restricted and hence the effective potential between domains is perturbed by the stretched network. Figures 8a−d show the parameters n, ⟨R⟩, prad, and σinterf, obtained by partial fitting in Figure 5b, as a function of temperature. These parameters are also tabulated in Table S2

(7)

The factor f was adjusted so that Imatrix(q) and observed I(q) overlapped in the high-q region (q ≥ 0.2 Å−1). Figure S4 shows an example of subtraction of Imatrix(q) from I(q) of Gel40 at 31.1 °C. This assumption might be crude but is better than adding more adjustable parameters to the model. Nevertheless, six independent parameters (n, Δρ, ⟨R⟩, pR, σinterf, and ⟨RHS⟩) were still too many to obtain appropriate convergence of leastsquares fitting. As the SLDs and volume fractions of D2O, PEG, and PEMGE were known, we could write Δρ as a function of the other parameters if we assume that the volume fraction of water in each domain W was equal to the equilibrium water E

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ideal, spherically symmetric domain may take one of discrete values of Nagg = 1, 5, 17, 41, 83, ..., because Gel40 is a discrete combination of Tetra-PEG and Tetra-PEMGE units. The observed values of ⟨Nagg⟩ (between 14 and 21) is roughly close to 17, meaning that up to second-nearest-neighbor TetraPEMGE and Tetra-PEG units aggregate into a domain. Formation of such relatively large domains inevitably leads to significant frustration of the surrounding unshrunk matrix network. Therefore, Gel40 is nonswellable because of the excess elastic energy of this frustrated matrix network which cancels the osmotic pressure. Although there are only three data points for each parameter in Figure 8, it is tempting to discuss the temperature dependence of the domain structure. The number density of the domains n is almost constant independent of temperature, suggesting that the domains tend to keep their position while increasing their size. This is because the domains are embedded in the matrix network and hence are allowed only limited translational motion. The invariance of n is consistent with the fact that the position of the primary peak, representing the interdomain correlation, is almost constant independent of temperature (Figure 5). prad decreases with increasing temperature because the domains larger or smaller than the most thermodynamically stable one become increasingly unstable as the segregation strength between PEMGE chains and the solvent increases. The gradual decrease of σinterf is also ascribed to the increasing segregation strength between the polymers and solvent. Thermodynamical Mechanism of Shrinking. The reason why multiple polymer units, rather than a single PEMGE unit, aggregate into a domain can be understood by considering the free energy of the domain formation ΔG. Here we write ΔG as the sum of three contributions:

Figure 8. Temperature dependences of the parameters in the form factor obtained by model fitting in Figure 7b (partial fitting); the number density n (a), mean radius ⟨R⟩ (b), variation coefficient of the radius prad (c), interfacial thickness σinterf (d), and mean aggregation number ⟨Nagg⟩ (e).

along with those obtained by full fitting. Because the partial fitting does not reproduce the low-q peak reflecting the structure factor, we do not discuss about ⟨RHS⟩ here. The mean aggregation number ⟨Nagg⟩ of a single domain is also shown in Figure 8e. ⟨Nagg⟩ is defined as ⟨V⟩(1 − W)/vu where ⟨V⟩ is the mean volume of the domains and vu is the number-averaged volume of Tetra-PEG and Tetra-PEMGE units. The most prominent finding in Figure 8 is that ⟨Nagg⟩ is much larger than unity; multiple prepolymer units, rather than a single TetraPEMGE unit, gather in one place to form a single domain. Moreover, not only PEMGE but also PEG should be incorporated in the domains because there is at least one Tetra-PEG unit between two adjacent Tetra-PEMGE units. Figure 9 shows a possible schematic picture of the domain structure and the origin of nonswellable feature of Gel40. An

ΔG = ΔGdemix + ΔGinterf + ΔGconf

(9)

ΔGdemix is the free energy of demixing between the polymers (PEMGE and PEG) and solvent and is negative above the critical temperature of PEMGE. Although ΔGdemix is the main driving force of domain formation, it is essentially constant independent of Nagg if the total number of shrinking polymers in the system is constant. Therefore, we exclude ΔGdemix in the following discussion. The other two contributions should always be positive and depend on Nagg. One is the interfacial free energy ΔGinterf necessary to create interfaces between the

Figure 9. Schematic illustration showing the domain structure and nonswellable feature of Gel40. F

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polymer-rich domains and solvent-rich matrix. The other is the conformational free energy ΔGconf associated with stretching of the matrix network and confinement of polymer chains in the domains. Figure 10a is a schematic graph showing these two

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00486.

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Figures S1−S3 and Tables S1, S2 (PDF)

AUTHOR INFORMATION

Corresponding Author

*Phone +81-4-7136-3418; Fax +81-4-7134-6069; e-mail [email protected] (M.S.). ORCID

Xiang Li: 0000-0001-6194-3676 Mitsuhiro Shibayama: 0000-0002-8683-5070 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a Grant-in-Aids for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology (No. 16H02277 and 15J10502). The SANS experiment was performed using QUOKKA at the OPAL reactor, Australian Nuclear Science and Technology Organisation, Australia (Proposal No. 5314), which was transferred from SANS-U at JRR-3, Institute for Solid State Physics, Japan (Proposal No. 16907).

Figure 10. (a) Schematic graph showing the free energy penalties due to creation of domain interfaces ΔGinterf and conformational change ΔGconf for discrete values of Nagg for ideal spherical domains. Panels b−d schematically illustrate the domain structures for small, intermediate, and large values of Nagg, respectively.

free energy penalties at discrete values of Nagg for ideal spherical domains. Illustrations of the domain structure having different values of Nagg are also shown in Figures 10b,c. ΔGinterf is a decreasing function of Nagg because the total interfacial area would be larger if a larger number of domains with smaller Nagg were formed (b). ΔGconf increases with increasing Nagg mainly because the matrix network would be more severely distorted by the formation of domains with larger Nagg (d). The system would choose Nagg so that the total free energy penalty is minimized (c).

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REFERENCES

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CONCLUSION We examined the microscopic structure of the nonswellable hydrogel, which consisted of end-linked Tetra-PEG and thermoresponsive Tetra-PEMGE units, to elucidate the origin of its nonswellable feature. SANS measurements during the stepwise heating process revealed that a discrete domain structure was formed at a temperature between 16.6 and 19.5 °C, which roughly corresponded to the temperature at which the macroscopic swelling ratio V/V0 started to decrease. We found by model fitting analyses that the domains were spherical in shape, although the spatial correlation between domains was not satisfactorily explained by a simple hard-sphere interaction potential. We evaluated the size of the domains by the aggregation number Nagg, the number of prepolymer units in a single domain, and found that roughly up to second-nearestneighbor Tetra-PEG and Tetra-PEMGE units aggregated into a spherical domain. The nonswellable feature of our hydrogel would be mainly ascribed to the frustration of the matrix network induced by the formation of relatively large domain with Nagg ∼ 17. The value of Nagg was chosen so that the sum of the two free energy penalties was minimized: the one arising from the interfaces between the polymer-rich domain and solvent-rich matrix and the other from the restricted conformation of polymer chains in the frustrated matrix network and the domains. G

DOI: 10.1021/acs.macromol.7b00486 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.7b00486 Macromolecules XXXX, XXX, XXX−XXX