Insight into the Microscopic Structure of Module-Assembled

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Insight into the Microscopic Structure of Module-Assembled Thermoresponsive Conetwork Hydrogels Shintaro Nakagawa, Xiang Li, and Mitsuhiro Shibayama* The Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8581, Japan

Macromolecules Downloaded from pubs.acs.org by UNIV PIERRE ET MARIE CURIE on 08/22/18. For personal use only.

Hiroyuki Kamata and Takamasa Sakai Department of Bioengineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Elliot Paul Gilbert Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232, Australia S Supporting Information *

ABSTRACT: The microscopic structure of module-assembled thermoresponsive conetworks was systematically investigated as a function of both temperature T and the mole fraction of the thermoresponsive modules r using small-angle neutron scattering (SANS). The conetworks were prepared by end-linking of hydrophilic modules and LCST-type thermoresponsive modules in water by the molar ratio of (1 − r):r. When the hydrogels with 0.02 ≤ r ≤ 0.10 were heated above certain T, nanometer-scale spherical domains were formed by aggregation of several prepolymer modules, whereas for the hydrogel with r = 0.01 such domain formation was not detected in the T range investigated. The size of spherical domains increased with increasing r and T. The observed r dependence of the domain size was theoretically explained by considering the free energy of domain formation, from which we concluded that the equilibrium domain size was determined mainly by the balance between two free energy contributions: the interfacial free energy of domain−matrix interface ΔGinterf and the conformational free energy of the matrix network ΔGconf.

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INTRODUCTION Hydrogels are a class of soft materials consisting of a large amount of water and a cross-linked polymer network. One of the difficulties encountered in the practical use of synthetic hydrogels is swelling. When an as-prepared hydrogel contacts with an excess amount of water, it absorbs water, i.e., swells mainly due to the osmotic pressure difference inside and outside the hydrogel. Swelling leads to deterioration of mechanical durability and volume expansion which may damage surrounding tissues when used in the human body.1,2 A promising way to overcome the swelling problem is to incorporate a stimuli-responsive polymer that endows the hydrogels with the ability to change its size by external stimuli. © XXXX American Chemical Society

We have recently developed a novel thermoresponsive hydrogel whose swelling ratio could be precisely tuned by polymer composition and temperature.3 The hydrogel was a conetwork constructed based on the idea of the Tetra-PEG gel.4 Two chemically different prepolymer modules, namely four-armed poly(ethylene glycol) (Tetra-PEG) and poly(ethyl glycidyl ether-co-methyl glycidyl ether) (Tetra-PEMGE), were end-linked to form an amphiphilic conetwork with homogeneous network structure. PEG served as a hydrophilic Received: April 24, 2018 Revised: August 7, 2018

A

DOI: 10.1021/acs.macromol.8b00868 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Schematic illustration of the samples and their preparation method.

a scaling argument that can explain semiquantitatively the r dependence of the equilibrium domain size. We choose r smaller than 0.40 to avoid macroscopic shrinking of the asprepared gel and possible macroscopic phase separation.

component while PEMGE was a thermoresponsive polymer exhibiting lower critical solution temperature (LCST) in water at around 20 °C. The hydrogel prepared at a temperature below the LCST of PEMGE swelled with water but shrank by raising the temperature above the LCST. Above the LCST, the swelling ratio decreased by increasing the mole fraction, r, of PEMGE modules in the total prepolymer modules. The hydrogel with r = 0.40 exhibited the swelling ratio of ∼100% at 37 °C, indicating that it was nonswellable in the human body. In the previous study, we examined the microscopic structure of the nonswellable hydrogel (i.e., r = 0.40) by means of smallangle neutron scattering (SANS).5 We found that above the LCST of PEMGE modules more than ten prepolymer modules aggregated into a single spherical domain. The increase of elastic pressure of the network by domain formation canceled out the osmotic pressure imbalance and eventually made the hydrogel nonswellable. Because the macroscopic swelling ratio of our hydrogel changed with the mole fraction of thermoresponsive modules r, it would also be possible to tune the microscopic structure simply by changing r. Structures of conetworks with different copolymer compositions have been investigated from both experimental6−18 and theoretical19−22 points of view. However, systematic studies on the effects of the prepolymer ratio have rarely been conducted to date. Recently, we investigated the microscopic structure of conetworks constructed by endlinking between Tetra-PEG and linear telechelic poly(dimethylsiloxane) (PDMS) by a combination of SANS and small-angle X-ray scattering (SAXS).15 The hydrophobicity of PDMS induced the formation of core−shell spherical domains with a PEG core and a PDMS shell in water. Partial replacement of linear PDMS with linear PEG led to a drastic change of the SANS profile, clearly indicating that the ratio of two modules affected the domain structure. Therefore, it is expected that the microscopic structure of our thermoresponsive hydrogel can also be controlled by changing the fraction of the thermoresponsive prepolymer modules r. In this study, we investigate the microscopic structure of our thermoresponsive hydrogel as a function of r in addition to temperature T. Our aim is to understand the detailed formation mechanism that determines the equilibrium microscopic structure. In our previous study, we have revealed a qualitative picture of structure formation at r = 0.40. Here we further extend the study to the different values of r and develop

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EXPERIMENTAL SECTION

Samples. Figure 1 schematically describes the samples used in this study. We prepared four samples with different r of 0.01, 0.02, 0.05, and 0.10, which are termed Gel01, Gel02, Gel05, and Gel10, respectively. The samples were synthesized using three kinds of prepolymer module: four-armed poly((ethyl glycidyl ether)190-co(methyl glycidyl ether)47) (PEMGE) terminated with amine groups (TAPEMGE), four-armed poly(ethylene glycol) terminated with amine groups (TAPEG), and that terminated with N-hydroxysuccinimidyl ester groups (TNPEG). These polymers can be endlinked through the rapid reaction between terminal amine and Nhydroxysuccinimidyl ester. TAPEMGE used in this study was the same as that used in our previous study;3 the synthetic method as well as the chemical characterization has been described therein. TAPEG and TNPEG were purchased from NOF Corporation (Tokyo, Japan). TAPEMGE, TAPEG, and TNPEG had the number-averaged molecular weight of 23.5 × 103, 20.0 × 103, and 20.0 × 103 g mol−1, respectively, with low polydispersity index ( Tc. Scattering from homogeneous semidilute solutions and gels is dominated by concentration fluctuations and is expressed by the OZ function:

P(q) = n(Δρ)2 F(q; σinterf )

∫0

∞

D(R ; ⟨R ⟩, prad )|A(q; R )|2 (3)

dR

where A (q ; R ) =

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

(4)

ij (qσ )2 yz F(q; σinterf ) = expjjj− interf zzz j z 2 k {

(5)

and D(R;⟨R⟩,prad) is the Schulz distribution. Δρ is calculated using volume fraction of the polymeric component in the domains ϕpd, that in the matrix ϕpm, that of the solvent in the domains ϕsd, and that in the matrix ϕsm; Δρ = (ϕpdρp + ϕsdρs)/(ϕpd + ϕsd) − (ϕpmρp + ϕsmρs)/(ϕpm + ϕsm) where ρp and ρs are SLD of PEG and D2O, respectively. Here we ignore the subtle difference of SLD between PEG and PEMGE. We can uniquely determine ϕpd, ϕpm, ϕsd, and ϕsm from the other parameters n, ⟨R⟩, prad, and r assuming that the volume fraction of water in a domain W is a known constant (W = 0.11 taken from the previous report).5 Here we give only the result 32,33

I(q) =

I(0) 1 + (qξ)2

(2)

where I(0) is the scattering intensity at the limit of q = 0 and ξ is the correlation length defining the length scale of the concentration fluctuations. It should be noted, however, that I(q) for PEG/water solutions and gels often shows an upturn in the low-q region due to large-scale clustering of PEG end groups.27,28 Indeed, I(q) at T < Tc in Figure 2 shows an upturn in q ≤ 2.0 × 10−2 Å−1. The q at which the upturn starts to emerge corresponds to a length scale of ∼50 Å, being much larger than the observed length scale of the concentration fluctuations ξ (∼10−20 Å, Figure S1b). Therefore, the data at q ≤ 2.0 × 10−2 Å−1 are excluded from the model fitting. The results of the model fitting using the OZ function for the data at T < Tc are shown in Figure 2 with dashed curves. The OZ function satisfactorily reproduces the experimental data except for the low-q upturn, from which we confirm that the samples before domain formation are essentially homogeneous just like an ordinary Tetra-PEG hydrogel, aside from the large-scale clustering. I(0) and ξ thus obtained are plotted as a function of T in Figures S1a and S1b, respectively. Both I(0) and ξ are increasing functions of T, suggesting that both the amplitude and length scale of the concentration fluctuations increase with increasing T. In solutions and gels comprising only a thermoresponsive polymer and solvent, they would diverge at the critical point where the system undergoes macroscopic phase separation.29 However, I(0) and ξ of our hydrogels do not diverge at the LCST of PEMGE because aggregation of PEMGE units does not lead to macroscopic phase separation but only results in formation of nanometer-scale domains. These parameters would eventually diverge if the LCST of PEG (>120 °C30) were reached. For T > Tc, the polydisperse sphere model with fuzzy interfaces is used. The model is a sum of the scattering intensity from the domain structure Idomain(q) and that from the matrix network Imatrix(q). Idomain(q) is a product of the form factor P(q) representing the scattering from individual domains and structure factor S(q) representing the correlation between domains. P(q) and S(q) are the same as those used in our previous study.5 Briefly, P(q) is the form factor of polydisperse spheres with a fuzzy interface. The number density of the spheres is n and the radius has the Schulz distribution31 with the mean ⟨R⟩ and the polydispersity (= standard deviation divided by the mean) prad. The interfacial thickness is introduced by the standard deviation σinterf of a Gaussian profile. Δρ is the difference of scattering length density (SLD) between the domain and surrounding matrix.

Δρ =

1 − W − n pre(rvPEMGE + (1 − r )vPEG) 1 − n⟨V ⟩

(ρp − ρs ) (6)

npre is the number density of prepolymer modules. vPEMGE and vPEG are the volumes of single PEMGE and PEG modules, respectively; vk = Mk/(dkNA) where Mk and dk are the molecular weight and the physical density of component k, respectively, and NA is the Avogadro number. ⟨V⟩ = (4/ 3)π⟨R⟩3(1 + prad2)(1 + 2prad2) is the mean volume of Schulzdistributed domains.32 Now we have P(q) characterized by four independent parameters: n, ⟨R⟩, prad, and σinterf. S(q) is the measurable structure factor34 of polydisperse hard spheres calculated using the Percus−Yevick structure factor and the scaling approximation.32 The mean radius in S(q) is taken as ⟨Rstr⟩ (>⟨R⟩) to take into account the limited spatial arrangement of domains fixed to the matrix network.7,15 The polydispersity of the hard sphere radius is taken to be prad. In the previous study, we ignored the T dependence of Imatrix(q) in the T range investigated (T < 31.1 °C) and assumed that Imatrix(q) was proportional to I(q) of the same sample at T just below Tc. However, the wider T range employed in this study would make the variation of I(q) non-negligible. Therefore, we assume that Imatrix(q) is proportional to the scattering intensity of Gel01 IGel01(q) at the same T. That is, Imatrix(q, T) = a(T) IGel01(q,T) where a(T) is an appropriate factor to ensure that I(q,T) = a(T)IGel01(q,T) in the high-q region (0.1 Å−1 ≤ q ≤ 0.5 Å−1). Figure S2 shows a(T) for each sample versusT. a(T) is always close to unity for all the samples in the entire T range investigated. The slight decrease with increasing T and r may reflect the decrease in polymer concentration in the matrix network when increasing amount of PEMGE modules participate in the domains. Imatrix(q,T) thus determined is plotted in Figure 2 with a dotted curve. Finally, we have the model scattering function with five independent parameters: n, ⟨R⟩, prad, σinterf, and ⟨Rstr⟩. The model scattering function P(q)S(q) was optimized to the observed I(q) − Imatrix(q) in the limited range of 0.03 Å−1 ≤ q ≤ 0.15 Å−1 as we did in our previous study. Figures S3a−c show the results of model fitting for Gel02, Gel05, and Gel10 D

DOI: 10.1021/acs.macromol.8b00868 Macromolecules XXXX, XXX, XXX−XXX

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the number density of domains n decreases while the mean radius ⟨R⟩ increases. The polydispersity of the radius prad and the interfacial thickness σinterf are almost independent of T. In discussing the domain formation mechanism, it is convenient to measure the domain size by the mean aggregation number ⟨Nagg⟩, the mean number of prepolymer modules constituting a single domain. We define ⟨Nagg⟩ as the ratio of the mean volume of prepolymer modules in a domain against that of a single collapsed PEMGE module. The volume of the polymeric component in the domain is ⟨V⟩(1 − W) = (4/3)π⟨R⟩3(1 + prad2)(1 + 2prad2)(1 − W) where W is the volume fraction of water in the domains. The volume of a single PEMGE module is vPEMGE = MPEMGE/(dPEMGENA) where MPEMGE and dPEMGE are the molecular weight and the physical density of PEMGE, respectively. Hence

at selected T, respectively. Although the position and intensity of the primary peak deviate from the observed ones, the model well reproduces the shoulder in the high-q region mainly arising from the form factor. The same results are also plotted in the form of I(q) = P(q)S(q) + Imatrix(q) in Figure 2 with solid curves. Again the shoulder and the additional peak are well reproduced. Excellent agreement between the chosen model and experimental data indicates that at T > Tc the system undergoes microphase separation into spherical polymer-rich domains and a matrix consisting of the remaining polymers and the solvent. We note here that model fitting using almost the entire q-region (0.01 Å−1 ≤ q ≤ 0.15 Å−1) does not reproduce the high-q features, as is shown in Figures S3d−f. This tendency was also observed in our previous study of the sample with r = 0.40 and may indicate the deviation of the assumed structure factor from the real one. It should also be noted that the experimental P(q)S(q) at T just above Tc (T < 29.9 °C for Gel02, T ≤ 26.1 °C for Gel05, and T < 22.1 °C for Gel10) was too small to obtain reliable model fitting results, presumably due to immaturity of the domain structure. Temperature and Composition Dependence of the Structure. Figures 4a−d show the temperature dependence of the form factor parameters, n, ⟨R⟩, prad, and σinterf, obtained by model fitting analyses. The values are also tabulated in Table S1. In general, the difference in r does not affect the qualitative aspects of the parameters’ T dependence. With increasing T,

⟨Nagg⟩ = =

⟨V ⟩(1 − W ) vPEMGE

(4/3)π ⟨R ⟩3 (1 + prad 2 )(1 + 2prad 2 )(1 − W ) MPEMGE /dPEMGENA

(7)

⟨Nagg⟩ is plotted as a function of T in Figure 4e where it increases with increasing T. At this moment it is unknown if all the PEMGE modules are incorporated in the domains or some of them are left in the matrix. To clarify this point, we estimate the mole fraction of prepolymer modules participating in the domains rd from n and ⟨Nagg⟩ and compare it with the mole fraction of PEMGE modules in the original network. The number of prepolymer modules participating in the domains (measured in the unit of the volume of a single PEMGE module) per unit volume of the sample is n⟨Nagg⟩. Using the number density of all prepolymer modules in the sample npre rd =

n⟨Nagg⟩ n pre

(8)

Figure 4f shows the T dependence of rd for each sample. At T near Tc, rd is smaller than r, indicating that some of the PEMGE modules still remain in the matrix network in the unshrunk state. rd increases upon further heating, suggesting that more PEMGE modules leave the solvent-rich matrix and aggregate into the domains at higher T. At T sufficiently above Tc, rd exceeds r, from which we speculate that some PEG modules are drawn into the domains due to shrinking of nearby PEMGE modules, as is schematically depicted in Figure 5. The architecture of our hydrogel ensures that two adjacent PEMGE modules are separated by at least one PEG module. If multiple PEMGE modules gather at a point, some PEG

Figure 4. Temperature dependence of the structural parameters obtained by the model fitting analysis; domain number density n (a), mean domain radius ⟨R⟩ (b), polydispersity of the domain radius prad (c), and domain interfacial width σinterf (d). Two additional quantities derived from the above parameters are also shown; domain aggregation number ⟨Nagg⟩ (e) and the mole fraction of prepolymer modules participating in the domains rd (f). The horizontal dashed lines in panel f indicates r of each sample.

Figure 5. Schematic illustration showing PEG modules drawn into a domain by aggregation of nearby PEMGE modules. E

DOI: 10.1021/acs.macromol.8b00868 Macromolecules XXXX, XXX, XXX−XXX

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Figure 6. Number density n (a), mean aggregation number ⟨Nagg⟩ (b), and their product n⟨Nagg⟩ (c) plotted as a function of the mole fraction of PEMGE modules r. The value at r = 0.40 was taken from the previous study5 (actual T was 31.1 °C). The dashed line in panel c is just a guide for the eye.

insignificant because the conformation of chains in the bulk state is identical to that in the Θ solvent. To derive the dependence of the latter contribution to r and ⟨Nagg⟩, let us consider a simple case where two neighboring PEMGE modules are separated by several PEG modules, as is schematically depicted in Figure 7. Before the domain

modules between the PEMGE modules are inevitably drawn into the domain. Figures 6a and 6b show the r dependence of n and ⟨Nagg⟩, respectively, at three different temperatures well above Tc. Qualitatively, both n and ⟨Nagg⟩ increase with increasing r; more PEMGE modules lead to the larger number and size of domains. We have already seen that at T well above Tc the mole fraction of prepolymer modules participating in the domains rd is close to r. Because npre is kept constant independent of r, this is equivalent to the relation n⟨Nagg⟩ ∼ r according to eq 8. Figure 6c shows n⟨Nagg⟩ against r in which we can clearly confirm the proportionality between these two quantities. The selection mechanism of the size and the number of domains can be explained in terms of the free energy of domain formation per unit volume ΔG. ΔG may be written, by analogy with the microphase separation in block copolymer solutions,35 as a sum of the following contributions:5,19 ΔG = ΔGdemix + ΔGinterf + ΔGconf

(9)

where ΔGdemix is the demixing free energy between the prepolymer modules (PEMGE + PEG) and solvent (water), ΔGinterf is the interfacial free energy between the domains and the matrix, and ΔGconf is the conformational free energy of the chains upon domain formation. Because it is difficult to calculate the exact form of each term, we try to establish a scaling argument. For the sake of simplicity, we assume that rd = r and ignore the polydispersity of the domain size. The terms in ΔG may depend on both the aggregation number ⟨Nagg⟩ and the number density n of the domains. However, using the relationship n⟨Nagg⟩ ∼ r confirmed in Figure 6c, we can write ΔG as a function of ⟨Nagg⟩ only. ΔGdemix depends only on the total number of PEMGE modules that aggregate into the domains n⟨Nagg⟩ and hence ΔGdemix ∼ ⟨Nagg⟩0 under the current assumption. Therefore, although ΔGdemix is the only negative term and thus the main driving force of microphase separation, we do not consider ΔGdemix for the calculation of equilibrium ⟨Nagg⟩. ΔGinterf is proportional to the total interfacial area and the interfacial free energy per area between the domains and the matrix γ. In general, γ ∼ Tχ1/2 where χ is the Flory−Huggins interaction parameter between the polymer and the solvent,36 in our case PEMGE and water. Because the radius of a domain is ∼⟨Nagg⟩1/3, the total interfacial area is ∼n⟨Nagg⟩2/3. Using the relationship n⟨Nagg⟩ ∼ r, we get ΔGinterf ∼ γn⟨Nagg⟩2/3 ∼ Tχ 1/2 r⟨Nagg⟩−1/3

Figure 7. Schematic illustration showing how PEG modules between neighboring PEMGE modules (a) are stretched when each PEMGE module aggregates into neighboring domains (b).

formation, each PEMGE module is dispersed in space with the number density ∼r. Hence, the one-dimensional distance between two neighboring PEMGE modules is on average ∼r−1/3. When the two modules move apart from each other and participate in two domains, the distance between the two modules is stretched to be that between two neighboring domains. The one-dimensional distance between two neighboring domains is on average ∼n−1/3 ∼ r−1/3⟨Nagg⟩1/3 using the relationship n⟨Nagg⟩ ∼ r. Therefore, the extension ratio λe of PEG strands due to the displacement of PEMGE modules is given as λe ∼ r−1/3⟨Nagg⟩1/3/r−1/3 ∼ ⟨Nagg⟩1/3. The change of conformational free energy of a PEG strand is ∼Tλe2 by assuming entropy elasticity. The number of PEG strands in the matrix that suffer from this extension would scale as ∼(1 − r). Eventually we get

(10)

The conformational changes of the chains inside and outside the domains could contribute to ΔGconf. The former would be F

DOI: 10.1021/acs.macromol.8b00868 Macromolecules XXXX, XXX, XXX−XXX

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thermoresponsive modules r at different temperature T. We found that spherical domains with the polydisperse radius and a fuzzy interface were formed above a certain T = Tc for the hydrogels with 0.10 ≥ r ≥ 0.02 whereas for the hydrogel with r = 0.01 such domain formation was not observed. We focused on two important parameters of the domain structure: the number density n and the aggregation number ⟨Nagg⟩ of the domains. With increasing T, n decreased while ⟨Nagg⟩ increased. Both n and ⟨Nagg⟩ increased with increasing r at constant T. At T sufficiently higher than Tc, the mole fraction of the prepolymer modules constituting the domains rd was almost equal to or slightly exceeds r, indicating that all the PEMGE modules plus few PEG modules aggregated into the domains. A scaling theory of the equilibrium ⟨Nagg⟩ with respect to r was proposed by considering two different contributions to the free energy of domain formation process: the interfacial free energy between the domains and the matrix ΔGinterf and conformational free energy associated with the stretching of the matrix network ΔGconf. The proposed theory explained the r dependence of ⟨Nagg⟩, suggesting that the above two contributions determined the equilibrium domain structure. The knowledge obtained in this study would help understanding and controlling the microscopic structure and the macroscopic property of amphiphilic conetwork systems.

(11)

Because ΔGdemix does not depend on ⟨Nagg⟩ under the current assumption n⟨Nagg⟩ ∼ r, it suffices to consider only the sum of ΔGinterf and ΔGconf to find equilibrium ⟨Nagg⟩. Figure 8a

Figure 8. (a) Schematic illustration of the proposed dependence of free energy contributions ΔGconf and ΔGinterf as well as their sum on the mean aggregation number ⟨Nagg⟩. Thicker curves correspond to the values at larger r. (b) Double-logarithmic plot of ⟨Nagg⟩ against r(1 − r)−1 according to eq 12. The value at r = 0.40 was taken from the previous study5 (T = 31.1 °C). The solid line is a guide for the eye showing the power law ⟨Nagg⟩ ∼ r(1 − r)−1.

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schematically shows the ⟨Nagg⟩ dependence of ΔGinterf (eq 10), ΔGconf (eq 11), and their sum. The minimum in ΔGinterf + ΔGconf shifts to larger ⟨Nagg⟩ when r is increased. The equilibrium value of ⟨Nagg⟩ is obtained by differentiating ΔGinterf + ΔGconf by ⟨Nagg⟩ and equating it to zero, which eventually reads ⟨Nagg⟩ ∼ χ

1/2

−1

r(1 − r )

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00868. Temperature dependence of ξ and I(0) obtained by OZ fitting analysis; temperature dependence of the factor a(T); comparison of model fitting results using different q ranges; structural parameters obtained by the model fitting analysis (PDF)

(12)

Because χ is essentially independent of r at constant T, we get a simple relation ⟨Nagg⟩ ∼ r(1 − r)−1. Figure 8b shows the double-logarithmic plot of ⟨Nagg⟩ against r(1 − r)−1. The experimental data seem to have the exponent close to unity in the small-r limit. Although we considered only a simple, limited case of chain stretching in the matrix network (Figure 7 and eq 11) and ignored all other possible contributions to ΔGconf, the resulting scaling relationship roughly explains the experimental data. Therefore, we conclude that the balance between the domain−matrix interfacial free energy ΔGinterf and the conformational free energy of the stretched matrix network ΔGconf determines the equilibrium domain structure. The T dependence of ⟨Nagg⟩ and n in Figures 4a and 4e can also be explained qualitatively from the above consideration. Equation 12 states that ⟨Nagg⟩ ∼ χ1/2 at constant r. χ should be an increasing function of T in the PEMGE/water system showing the LCST-type behavior. Thus, ⟨Nagg⟩ would increase while n decreases with increasing T, as is actually observed in Figures 4a and 4e, respectively. It is, however, difficult to predict the quantitative T dependence because χ of the present system is not known. Moreover, r d (= n⟨N agg ⟩/npre ) significantly depends on T at relatively low T (Figure 4f), breaking the assumption that n⟨Nagg⟩ depends only on r.

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AUTHOR INFORMATION

Corresponding Author

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

Shintaro Nakagawa: 0000-0002-9848-2823 Xiang Li: 0000-0001-6194-3676 Mitsuhiro Shibayama: 0000-0002-8683-5070 Takamasa Sakai: 0000-0001-5052-0512 Present Address

S.N.: Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, Japan. 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, Japan (No. 16H02277). The SANS experiment was performed using QUOKKA at the OPAL reactor, Australian Nuclear Science and Technology Organisation, Australia (Proposal No. 5693), which was transferred from SANS-U at JRR-3, Institute for Solid State Physics, Japan (Proposal No. 16919).

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CONCLUSIONS We investigated the microscopic structure of thermoresponsive conetwork hydrogels assembled from four-armed hydrophilic and thermoresponsive modules. SANS measurements were performed for the hydrogels with varying fraction of G

DOI: 10.1021/acs.macromol.8b00868 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b00868 Macromolecules XXXX, XXX, XXX−XXX