Probe Diffusion of Sol–Gel Transition in an ... - ACS Publications

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Probe Diffusion of Sol−Gel Transition in an Isorefractive Polymer Solution Xiang Li,*,† Nobuyuki Watanabe,† Takamasa Sakai,‡ and Mitsuhiro Shibayama*,† †

Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba, Japan Department of Bioengineering, The University of Tokyo, Yayoi, Tokyo, Japan

‡

S Supporting Information *

ABSTRACT: The sol−gel transition of tetrafunctional polymers with mutual reactive end-groups was investigated by analyzing the dynamics of probe particles via dynamic light scattering. The dynamics of probe particles was exclusively observed by matching the refractive index of the solvent and the polymers. The sol−gel transition point, decreasing of sol fraction and increasing of gel fraction with the reaction, the onset of formation of closed structure inside branched polymer clusters, and a piece of evidence for the decrease of the local viscosity in postgel regime were observed via the dynamics of probe particles. In addition, a scaling relationship ηeff ∼ ε−1.13±0.06 was found in a wide range of cross-linking conversion (p) before the gel point, where ηeff is the effective viscosity estimated from probe particles’ dynamics and ε ≡ |p − pc|/pc is the relative distance from the sol−gel transition point (pc is the cross-linking conversion at gel point).

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motion of a single particle in a limited space of 1 μm3 and provide the information at the specific location; by contrast, DLS monitors millions of particles simultaneously in a region of ∼106 μm3 and provides averaged information on these particles, which is of great use in discussing the statistical characteristics. A comprehensive study of probe diffusion for the sol−gel transition was reported by Shibayama’s group.7 They used DLS to monitor the dynamics of polystyrene beads in polymer solutions and gels with various cross-linker densities. Two relaxation modes were observed in the time-correlation functions. The fast mode was attributed to the dynamics of the polymers, and the slow mode was assigned to the dynamics of the probe particles. However, quantitative analyses were limited because the two relaxation modes were partially merged. Fadda et al. attempted to resolve this issue by increasing the intensity gap between the probe particles and the polymers such that the scattered intensity originating from the polymer chains could be ignored.8 Although a lower polymer concentration was used and DLS was performed at a specific scattering angle at which the scattered intensity gap was maximized, a gap of only a factor of 5 was achieved. The scattered intensity originating from the polymers could not be fully eliminated, and two relaxation modes were still observed. Joosten et al. pointed out in their study that even 40 times difference between the probe particles and polymers was still

INTRODUCTION Sol−gel transition is a critical phenomenon for a polymer or colloidal system changing from a fluidic state (sol) to a solid state (gel).1 This process plays a crucial role in industry and in our daily life (e.g., in fabrication of resins and rubbers, preparation of jelly, and the cooking of eggs). The sol−gel transition in a polymer system is caused by the growth of branched polymers as a result of chemical reactions or physical bonding between the polymer chains. When a branched polymer grows to reach the size of the system, the system loses its fluidity and becomes a gel. Experimentally, gelling processes have been extensively studied using scattering and rheology methods. Numerous interesting physical phenomena have been observed near the sol−gel transition, including self-similar structures in branched polymers and the scaling law for the polymer size distribution, among others.1 An indirect method of “probe diffusion” that differs from these direct measurements has also been suggested.2,3 Instead of observing the dynamics of polymer chains, one monitors the motion of probe particles (generally several nanometers to several hundred nanometers in size) dispersed in polymer solutions and gels. The motion of probe particles reflects the structure of the polymers. Because the size of the probe particles is comparable to the size of the mesh of the polymer networks, probe diffusion may provide more detailed information about the sol−gel transition than general scattering and rheology measurements. Fluorescence correlation spectroscopy (FCS), single particle tracking (SPT), and dynamic light scattering (DLS) are the major tools used to detect the motion of probe particles in polymer solutions and gels.4−6 FCS and SPT monitor the © XXXX American Chemical Society

Received: November 29, 2016 Revised: March 19, 2017

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DOI: 10.1021/acs.macromol.6b02573 Macromolecules XXXX, XXX, XXX−XXX

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DMSO significantly changes the viscosity of DMSO and the solubility of PEG polymers in DMSO. DLS measurements were carried out every 30 s during the gelation using an ALV 5000 scattering instrument; measurements were performed at a wavelength of 632.8 nm at a scattering angle of 90° at a temperature of 25 ± 0.1 °C. The time to reach the gel point was approximately 1 h, which was sufficiently long to enable monitoring of the gelling process in real time with DLS (25 s for one measurement). The reaction conversion (p) of the end-groups of the tetra-armed PEG polymers (maleimide groups) was measured using UV spectroscopy (JASCO V-630) at wavelength of 300 nm. The dynamic viscoelastic measurement was carried out by using a rheometer (Anton Paar MCR-501) with concentric cylinder module at a shear strain of 2% and an angular frequency of 1 Hz. The viscosity of the polymer solution was performed by using the same rheometer with cone plate module at shear rate from 0.1 to 5 s−1. The rheometer was covered with an argon bag filled with argon gas to prevent contamination of water into DMSO. Small-angle X-ray scattering (SAXS) experiment was performed on BL03XU at SPring-8, Japan (the detector was Pilatus3 1M, the wavelength of X-ray was 1.0 Å, the attenuator was molybdenum of 20 μm thickness, and the exposure time for each sample was 1 s). All of the experiments were performed at a temperature of 25 ± 0.1 °C. DLS, UV absorption, rheology, and SAXS measurements were performed separately.

not enough to eliminate the effect of the dynamics of polymers.9 Camins and Russo proposed an interesting idea to extract the rotational dynamics of probe particles in polymer solutions and gels by measuring the zero-angle scattering of optically anisotropic particles.10 If the polymers are not depolarized, only the rotational motion of the probe particles is supposed to be observed at zero angle. Useful information such as the fraction of mobile particles, relaxation time, and the distribution of the relaxation time was obtained via the rotational dynamics of probe particles; these parameters changed with the structure evolution of the polymer clusters and gel networks. However, the information via transitional dynamics of probe particles was still inaccessible even with their technique. Isorefractive scattering is an optical technique to extract the scattering information on one component from a multicomponent system by matching the refractive indices of solvent and the components that one does not want to see. Because light scattering only occurs in an optically heterogeneous system, the components with the same refractive indices with the solvent only scatter little light.11 This technique is an optical analogue of deuterium-labeling in neutron scattering. Martin introduced isorefractive scattering into DLS and successfully observed the dynamics of polystyrene in a ternary system consisting of a solvent (toluene), an isorefractive matrix polymer (poly(vinyl methyl ether)), and polystyrene with a large refractive index increment to the solvent.12 Although isorefractive scattering is well-known for DLS and has been used in several studies for probe diffusion in polymer solutions and gels,9,13,14 this scattering technique has never been applied for observing the process of sol−gel transition. In this study, we applied the isorefractive scattering to extract the transitional dynamics of probe particles during the sol−gel transition process of a polymer solution of tetrafunctional polymers. The reaction conversion of the tetrafunctional polymers can be precisely estimated by measuring the amount of their end-groups with UV absorption experiments. Beside using the isorefractive solvent, we used gold nanoparticles as the probes, which have a greatly different refractive index from the polymers and solvent. The obtained time-correlation function only contained the dynamics of probe particles and could be well fitted by a simple stretched exponential function. The gel point was successfully determined from the fitting parameters and a monotonic decrease in the stretched exponent was observed as reported in the previous studies.7,8,10 In addition, an up-and-down transition in the relaxation time of probe particles was observed for the first time.

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RESULTS AND DISCUSSION In order to confirm the effect of isorefractive scattering, we measured the scattered intensity from poly(ethylene glycol) (PEG) with refractive index (n) 1.47 in two solvents with different n (acetonitrile, n = 1.34, and dimethyl sulfoxide (DMSO), n = 1.48). Noticeable scattered intensity from the polymers was observed in the nonisorefractive polymer solution (PEG/acetonitrile), whereas almost no excess scattered light was observed in the isorefractive polymer solution (PEG/ DMSO) (Fiugre 1). The scattered intensity originating from the polymers was greatly reduced by matching the refractive indices of the polymer and the solvent. We note that the scattered intensity from polymers may not be eliminated well when the derivative of the refractive index with respect to polymer concentration (dn/dc) is not negligible. However, it is not the case for the polymers (PEG) and the solvent (DMSO).

EXPERIMENTAL SECTION

Gold nanoparticles coated with polyvinylpyrrolidone (PVP) (diameter 30, 50, and 100 nm, refractive index n = 0.14,15 nanoComposix) were used as the probe particles at final concentration lower than 0.001 wt %. The hydrodynamic radii of the nanoparticles were measured by DLS (Rh = 28, 42, and 57 nm in PEG polymer solutions with the same concentration with the gelling polymer solution). Two different tetraarmed poly(ethylene glycol)s (PEG) (Mw = 20k, n = 1.47, NOF Corp.) with mutual reactive end-groups (either maleimide or amine) were dissolved in acetonitrile (n = 1.34) or anhydrous DMSO (n = 1.48) at final concentration 50 g/L as the gelling polymer solution. Detailed information about the polymer gels used in this study has been reported elsewhere.16−25 All of the samples were prepared in a glovebox (Glovebox Japan, GBJF080) filled with argon gas to prevent the contamination of water to DMSO; the contamination of water into

Figure 1. Scattered intensity from (a) a nonisorefractive polymer solution (polymer: PEG, n = 1.47; solvent: acetonitrile, n = 1.34) and (b) a isorefractive polymer solution (polymer: PEG, n = 1.47; solvent: DMSO, n = 1.48). Scattered intensity of the solvents is shown as controls. The refractive indices shown here are literature values at 20 °C. B

DOI: 10.1021/acs.macromol.6b02573 Macromolecules XXXX, XXX, XXX−XXX

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Figure 2. Schematic picture of the reaction scheme of the mutual reactive tetra-armed PEGs in acetonitrile and DMSO at room temperature. X is a maleimide terminated group, and Y is an amine-terminated group.

= 37 ± 1% according to the UV absorption experiments; this difference is within the experimental errors. The G′ at t ≈ 40 000 s is the final storage shear modulus obtained in this study, which was almost the same regardless of the presence of the probe particles. The good reproducibility in the gel point and final storage shear modulus indicates that the addition of particles into the polymer solution did not affect the gelation process. The SAXS profiles of gold nanoparticles with Rh = 42 nm in the polymer solutions and gels are shown in Figure 4.

On the basis of the results in Figure 1, we performed a series of probe diffusion experiments with DLS in a gelling polymer solution. The probe was gold nanoparticles (n = 0.14) coated with polyvinylpyrrolidone (PVP) with different hydrodynamic radii (Rh = 28, 42, and 57 nm); the Rh of these probes was measured by DLS in linear-PEG/DMSO solutions with the same polymer concentration of the gelling polymer solution. The gelling polymers were two different tetra-armed PEG polymers with mutual reactive end-groups (maleimide and amine) (Figure 2); the nonisorefractive solvent was acetonitrile, and the isorefractive solvent was DMSO. In the isorefractive solvent, the scattering intensity of probe particles was nearly a million times larger than that of polymers. The reaction conversion (p) of the gelling polymer solutions was measured by monitoring the amount of unreacted maleimide groups with UV absorption spectroscopy (SFigure 1). The influence of the probe particles on gelation was examined by dynamic viscoelastic measurements (Figure 3). The cross-points of storage shear modulus (G′) and loss shear modulus (G″) are the gel points, which were estimated to be p

Figure 4. SAXS profiles of gold nanoparticles with Rh = 42 nm in unreacted polymer solutions (p = 0%) and polymer gels (p ∼ 90%). The polymer solutions and gels were formed by the tetrafunctional PEG polymers with mutual reactive end-groups. The solvent was DMSO. I is the scattered intensity, and q is the scattering vector.

Because the electron density of gold nanoparticles is much higher than that of PEG and PVP, only the profiles of bare gold nanoparticles were observed. The profiles of gold nanoparticles in polymer solution (p = 0%) and polymer gel (p ∼ 90%) were almost identical. The gyration radius (Rg) of gold nanoparticles was estimated by Guinier plot (Rg2 = −3 d(ln I)/dq2) to be 21.3 nm in the polymer solution and 21.5 nm in the polymer gel. There was no obvious aggregation of gold nanoparticles during the gelation. Rh of the gold nanoparticles was calculated to be approximately 28 nm from the values of Rg of SAXS experiments by using the relationship between Rh and Rg for

Figure 3. Dynamic viscoelasticity measurement for gelling polymer solutions with or without probe particles. The polymer solutions were tetrafunctional PEG polymers with mutual reactive end-groups and the probe particles were gold nanoparticles with different hydrodynamic radius (circle, no particle; rhombus, Rh = 28 nm; triangle, Rh = 42 nm; square, Rh = 57 nm). The solid curves denote G′, and the dashed curves denote G″. C

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Macromolecules hard sphere (Rh = (5/3)1/2Rg). The relatively big difference between the Rh by DLS (= 42 nm) and by SAXS (= 28 nm) is due to the thick PVP coating on the surface of the gold nanoparticles, which is not visible in SAXS experiments with the presence of gold nanoparticles that scatter X-ray much more than PVP does. The normalized time-correlation functions (g(2)(τ) − 1) of the scattered intensity from the gelling polymer solutions are shown in Figure 5. Two relaxation modes were observed in the

location, the light from those particles becomes nonfluctuating; the value of A decreases from 1 to 0 in response to an increase of the fraction of the fixed particles. Regarding particles in a nonergodic system such as a polymer gel, the local environments for the particles differ from one to another and thus the relaxation times of the particles also differ from one to another. Because DLS observes millions of particles in different locations simultaneously, the timecorrelation function is a superposition of multiple particles with different relaxation times (eq 2). The merged time correlation functions are generally simplified as a stretched exponential function.29 g(2)(τ ) − 1 =

∑i Ai2 exp( − 2τ /τi*) ∑i Ai2

≈ A2 exp{−2(τ /τ *)β }

(2)

where β is a stretched exponent, a measure of the variety of the particles’ relaxation time. If all the particles relax over the same time scale, β = 1, whereas if the relaxation times of the particles are different from one to another, β < 1. The degree of deviation of β from unity is a measure of the extent of the disorder of a system. Because eq 2 is a generalized equation for dynamics, we used it to fit all the time-correlation functions in Figure 5b. Good fits were obtained regardless of p (Figure 5b). Besides the particles with Rh = 42 nm, we also performed the same experiments for probe particles with different hydrodynamic radii (Rh = 57 and 28 nm). All of the obtained fitting parameters for these three different particles are shown in Figure 6 as functions of p. The heterodyne correction was performed for τ* to remove the

Figure 5. Time-correlation function of probe particles in gelling polymer solutions: (a) a nonisorefractive polymer solution (PEG/ acetonitrile); (b) an isorefractive polymer solution (PEG/DMSO). The probe particles shown in this figure were gold nanoparticles (Rh = 42 nm). Percentages show the reaction conversion (p) of gelling polymer solution.

nonisorefractive polymer solution (Figure 5a); judging from the relaxation time, the fast mode is related to the dynamics of polymers and the slow mode is related to the dynamics of probe particles. However, quantitative analysis was almost impossible because there were too many fitting parameters. By contrast, in the isorefractive polymer solution, no fast mode was observed (Figure 5b); the dynamics of polymers was successfully masked, and the time-correlation functions only consist of the dynamics of probe particles. We also performed DLS measurement for the isorefractive polymer solution without the particles using the same DLS setup; no scattered light from the polymers was observed during the sol−gel transition in this isorefractive polymer solution (SFigure 2). DLS analyzes the fluctuations of the scattered intensity from scatters (particles or polymers) I(t) = ⟨I(t) + δI(t)⟩ via the time correlation function g(2)(τ) = ⟨I(t)I(t + τ)⟩/⟨I(t)⟩2. Considering a group of particles with identical size that move randomly, the time-correlation function of the particles can be expressed by a simple exponential function: g(2)(τ ) − 1 = A2 exp( −2τ /τ *)

Figure 6. Obtained fitting parameters A, τ*, and β from Figure 5b are plotted as a function of p for probe particles with different sizes (circles, Rh = 57 nm; squares, Rh = 42 nm; triangles, Rh = 28 nm). The dashed line shows the gel point determined by dynamic viscoelastic measurements (pc = 37 ± 1%).

(1)

where A is the fraction of fluctuating component (⟨δI(t)⟩) of the scattered intensity (⟨I(t)⟩), τ is the time length, and τ* is the relaxation time.26−28 If some particles are tightly fixed to a D

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at different shear rates (SFigure 5).) ηeff was in good agreement with η0. This result suggests that the increase of τ* along the gelling reaction is mainly caused by the increase of the viscosity of the polymer solution. The viscosity is not defined in the postgel regime because the system is a solid. However, inside the gel networks there are still many unreacted polymers and polymer clusters when p is close to pc. According to the percolation theory for 3D lattice, at the gel point, the largest branched polymer percolates the system and form the gel network; at the same time, the sol regions also percolate the system as well as the gel network.30 The particles in the gel network are fixed, but the particles in the sol regions can move around. The dynamics of particles should be positively correlated to the viscosity in the sol regions although their dynamics is no more diffusional due to the appearance of the gel network, which hinders some paths of the translational movement of the particles. After the gel point, the gel network grows and the sol region starts to be divided into small isolated regions. Because DLS estimates the relaxation time from the fluctuation of the scattered intensity, the nonfluctuating light from the fixed particles in the gel network does not contribute to the relaxation time; the obtained relaxation time reflects the dynamics in the sol regions. Thus, the decrease in τ* after the gel point suggests the decrease of the viscosity in the sol regions inside a gel. Several simulations predict that the weight-averaged molecular weight of the polymer clusters in the sol region in postgel regime decreases with the reaction progress.31,32 Because the viscosity in a polymer solution is positively correlated with the weightaveraged molecular weight, the result of the simulation predicts a decrease of viscosity in the sol regions in postgel regime. This prediction is well consistent with the decrease of τ* in postgel regime observed in this study. We further plotted log(ηeff) against log(ε) for the data before gel point (Figure 8), where ε is the relative distance to the gel

effect of stray light and the scattered light from the fixed particles that influence the correct estimation of τ*.26−28 First, let us examine the parameter A, which remained constant (≈ 1) below p ≈ 37% and started to decrease after that point (Figure 6). The size effect of probe particles was not observed. The slight deviation of A from unity in the pregel regime is due to the instrument coherence. The critical point of A was in good agreement with the sol−gel transition point (pc, pc = 37 ± 1%) determined by the dynamic viscoelastic measurement (Figure3), indicating that the gel point can be determined from the probe dynamics via the parameter A. As we mentioned above, the value of A decreased from 1 to 0 in response to the increase of the fraction of the immobilized particles. The decrease of A after the gel point suggests that the probe particles are gradually immobilized by the gel network (or gel phase) with the reaction progresses. Thus, the parameter 1 − A is a rough measure for gel fraction and A is a rough measure for sol fraction from the viewpoints of probe particles (A = 0 means that there are no sol regions larger than the sizes of the probe particles.). The behavior of A was the same at the other scattering angles (60° and 120° in SFigure 3). Another parameter is the characteristic relaxation time of probe particles, τ*, which increased with the reaction progress in pregel regime but turned out to decrease in postgel regime, resulting in an up-and-down transition at the gel point. The similar up-and-down transition of τ* was observed for the other scattering angles (60° and 120° in SFigure 3). The diffusional dynamics, in which 1/τ* ∼ q2, was confirmed in pregel regime but not in postgel regime (SFigure 4), indicating that the diffusional dynamics of particles is hindered by the appearance of the gel network. When the dynamics of the particles is not diffusional, the relaxation time increases with decreasing q and may be even longer than before gelling at small q, i.e., when probing over larger distances. However, the τ* decreased after the gel point, indicating that the effect of the nondiffusional dynamics is not significant in the q-range used in this study (q = 0.001 47, 0.002 08, and 0.002 54 Å−1, which correspond to the scattering angle of 60°, 90°, and 120°, respectively, and the distance (d) in real space of 428, 302, and 247 nm, respectively, by assuming d = 2π/q). We converted τ* in the pregel regime into effective viscosity (ηeff) using the Einstein−Stokes equation (ηeff = kBT/(6πRhD)) and the assumption of diffusional dynamics (D = (q2τ*)−1), where kB is the Boltzmann constant, T is absolute temperature, and D is the diffusion coefficient of the probe particles. Figure 7 shows ηeff and zero-shear viscosity (η0) as a function of p. (η0 was measured by a series of steady flow viscosity measurement

Figure 8. Effective viscosities (ηeff) before the gel point (pc) and zeroshear viscosity (η0) as a function of the relative distance from the gel point (ε). The gel point was determined to be pc = 37 ± 1% by the dynamic viscosity elasticity measurement. The plots at p = 36% are removed from the figure due to the uncertainness of p. The line shows a fitting curve of ηeff ∼ ε−1.13±0.06.

point defined as ε ≡ |p − pc|/pc. A scaling relationship was found between ηeff and ε as ηeff ∼ ε−1.13±0.06 over a wide range of ε. Similar scaling relationships have been found in the previous studies but only for ε ≪ 1. In the previous studies, the exponent s varies from 0.7 to 6.1,33,34 The big variation of s in the previous studies may be because of the different manner in which the p is interpreted; cross-linker concentration or

Figure 7. Effective viscosities (ηeff) estimated from τ* of probes by DLS and zero-shear viscosity (η0) measured by a series of steady flow viscosity measurement are displayed as a function of p. E

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Macromolecules reaction time were used as p to calculate ε. In terms of the estimation of ε, the chemical system used in this study is better than those in previous studies. The obtained s in this study is not well consistent with the theoretical predictions for s: s = 1.32 in the Rouse model and s = 0.66 in the electrical analogy.1 This may be because the scaling relationship found in this study, which is valid even far from the gel point, is not related to the critical phenomenon of sol−gel transition. The physical meaning of s obtained in this study is not clear yet. At the end of this study, we discuss the stretched exponent β. In Figure 6, the values of β were almost constant (0.8−1.0) for p < 30% but began to decrease for p > 30%. As we mentioned above, β is related to the distribution width of the relaxation time.35 The values of β of the particles with Rh = 28 nm were slightly lower than the values of the particles with the other sizes because they have a wider size distribution and thus a wider distribution of relaxation time. The behavior of β was the same at the other scattering angles (SFigure 3). As we mentioned in the discussion for τ*, the q-range may influence β as well as τ* especially in the postgel regime because the diffusion mode depends on the length of observation. When the observation length is very small (large-q), all the mobile particles are diffusional because the mobile particles are in a ”pool” of sol region and undergo diffusional motion. By contrast, when the observation length is large (small q), particles need to travel over several “sol pools” connected by fractal channels (maze). Hence, the motion must be nondiffusional. However, in the q-range used in this study, the values of β were almost the same regardless of the scattering angles (SFigure 3). Therefore, the decrease of β in the postgel regime is likely due to another reason but not the effect of the nondiffusional dynamics. We need to note that the fixed particles, which do not fluctuate the scattered light, do not contribute to β. The decrease of β in the postgel regime is easy to explain. As we mentioned above, at the gel point, a sol region percolates the system, and most of the sol regions should be a part of the big percolating sol region. As the reaction proceeds, the percolating sol region begins to be divided into small isolated regions, in which the size distribution of polymer clusters should be different from one another. The difference of the size distribution of clusters in each sol region leads to the difference in the local viscosity and thus the difference in the relaxation time of particles in each sol region, resulting in the decrease in β as the reaction proceeding. What is interesting is that the decrease of β started at p ∼ 30%, which is before the gel point (pc ∼ 37%). If we follow the similar discussion that we just mentioned above, the early decrease of β suggests that the isolated sol regions are formed even before the gel point. The most possible origin of the isolated sol regions in pregel regime is the closed structure in each big branched polymer cluster. This explanation is acceptable if we assume the intramolecular reactions inside the branched polymer clusters in the pregel regime. Thus, the onset of the decreasing of β may be correlated to the initiation point of the intramolecular reaction in the branched polymer clusters.

were probed via the particles dynamics. In addition, an up-anddown transition was observed for the first time at the gel point for the relaxation time of probe particles. The increase of relaxation time in pregel regime corresponds to the increase of macroscopic viscosity of the polymer solution; the decrease of the relaxation time in the postgel regime may correspond to the decrease of the weight-averaged molecular weight in the sol regions of the gel, which is generally observed in simulations for the sol−gel transition. Moreover, the width of relaxation time distribution started to broaden with the reaction progress and the onset was before the gel point, suggesting that the particles started to be trapped by the polymer clusters even before the gel point. The size effect of the particles was insignificant in all the parameters A, τ*, and β except for the absolute values of τ*.

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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.6b02573. UV absorption measurement, DLS of the same system but without probe particles, probe diffusion at different scattering angles, q2 dependence of τ*, and the zero shear viscosity measurements (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected]; Ph +81-471363419; Fax +81471346069 (X.L.). *E-mail [email protected]; Ph +81-471363418; Fax +81-471346069 (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 has been financially supported by Grant-in-Aids for Scientific Research from the Ministry of Education, Culture, Sport, Science, and Technology (no. 16H02277 to M.S.). The SAXS experiment was performed at the Frontier Soft Matter Beamline (FSBL; BL03XU), SPring-8, Hyogo, Japan, with the assistance of Atsushi Izumi, Sumitomo Bakelite, Co., Ltd. (Proposal No. 2016B7260). This work was supported by Photon and Quantum Basic Research Coordinated Development Program by MEXT Grant No. 13004017.

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REFERENCES

(1) Addad, J. P. C. Physical Properties of Polymeric Gels; Wiley: 1996. (2) Langevin, D.; Rondelez, F. Sedimentation of large colloidal particles through semidilute polymer solutions. Polymer 1978, 19, 875−882. (3) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (4) Michelman-Ribeiro, A.; Horkay, F.; Nossal, R.; Boukari, H. Probe Diffusion in Aqueous Poly(vinyl alcohol) Solutions Studied by Fluorescence Correlation Spectroscopy. Biomacromolecules 2007, 8, 1595−1600. (5) Mason, T. G.; Ganesan, K.; van Zanten, J. H.; Wirtz, D.; Kuo, S. C. Particle Tracking Microrheology of Complex Fluids. Phys. Rev. Lett. 1997, 79, 3282−3285.

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CONCLUSION We for the first time observed the dynamics of probe particles over a sol−gel transition in an isorefractive polymer solution via DLS. The sol−gel transition point was successfully determined with the parameter relating to the fraction of the fixed particles. The decreasing of sol fraction and the increasing of gel fraction F

DOI: 10.1021/acs.macromol.6b02573 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.6b02573 Macromolecules XXXX, XXX, XXX−XXX