Friction Coefficient of Well-Defined Hydrogel ... - ACS Publications

Jan 13, 2016 - Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, D306, 2100 København, Denmark. •S Supporting Information...
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Friction Coefficient of Well-Defined Hydrogel Networks Midori Fujiki,† Masaya Ito,† Kell Mortensen,∥ Shintaro Yashima,† Masayuki Tokita,‡ and Masahiko Annaka*,†,§ †

Department of Chemistry, ‡Department of Physics, and §International Research Center for Molecular Systems (IRCMS), Kyushu University, Fukuoka 819-0395, Japan ∥ Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, D306, 2100 København, Denmark S Supporting Information *

ABSTRACT: The friction coefficient between Tetronic gel and water is measured as a function of the polymer concentration of the gel and the temperature by a simply designed apparatus. Tetronic gel was prepared by cross-linking Tetronic macromonomers through activated ester chemistry. The gel is expected to have homogeneous network structure. The polymer concentration Cp dependence of the friction coefficient f is well expressed by a power law relationship f ∼ Cpν with the exponent of ν = 1.5, which is in a good agreement with the prediction of the scaling theory. The friction coefficient normalized by viscosity of water, f(T)/η(T), increases with temperature. When the network is homogeneous, the mesh size is given by the average distance between the nearest polymer−polymer contacts. Therefore, the increase in the ratio f(T)/η(T) with temperature attributed to the decrease in the average mesh size of the network due to the dehydration of the chains at higher temperature. The friction coefficient for randomly cross-linked Tetronic gel prepared by enzyme-mediated cross-linking reaction of tyrosin-modified Tetronic is compared with that of the homogeneous Tetronic gel. The friction coefficient for the randomly cross-linked gel is about an order of magnitude smaller than that for homogeneous gel. It suggests that the friction coefficient is mainly governed by the spatial inhomogeneity frozen in the gel rather than the average cross-linking density of the gel.

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INTRODUCTION The unique physical properties of hydrogel arise from its network structure. Despite significant progress in understanding the basic structure−property relationship of network, much remains to be learned about how the foundational macromolecular building blocks transport properties across the length scales to the macroscopic sample. Fundamental investigations include understanding the relationship among network structure, dynamics, and mechanical properties. The ability to manipulate and predict the structure and resulting physical properties of polymer networks by changing specific valuables, i.e., polymer molecular weight, polymer concentration, or cross-linking degree, is advantageous for applications. One key step to developing the structure− property relationship of polymer networks is reduction of network defects, i.e., highly cross-linked junctions, loops, or dangling ends. These defects typically form in an unpredictable manner and impact the resulting physical properties of the networks. The need for more homogeneous polymer networks has led to the development of cross-linking techniques that allow for greater control over the resulting network microstructure. A recent approach by Sakai and co-workers1,2 utilized 4-arm star-shaped polymers to reduce network defects and form highly elastic, homogeneous hydrogels. They achieved this © XXXX American Chemical Society

by utilizing tetra-arm poly(ethylene glycol) macromonomers that cross-link through activated ester chemistry. The gels, referred as tetra-PEG gels, were found to have remarkably homogeneous network structure by small-angle neutron scattering.3 Another recent approach utilizes click chemistry to control cross-linking in networks.4,5 Click reactions are highly efficient, have high functional group tolerance, and are highly active in water, making them ideal for use as a hydrogel cross-linking strategy.5,6 Hydrogel formed through click chemistry have demonstrated high moduli, suggesting that this cross-linking strategy can reduce the formation of defects in the networks.4,7 Tew and co-workers8 recently developed a novel cross-linking technique that utilizes thiol−norbornene chemistry to form PEG-based hydrogel networks to minimize defects in the network. The highly resilient mechanical properties of these systems suggest that this cross-linking method yields homogeneous network structures. The unique properties of a gel arise from its network structure. The collective diffusion coefficient of the gel Dc is Received: September 12, 2015 Revised: December 23, 2015

A

DOI: 10.1021/acs.macromol.5b01997 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Scheme 1. Synthetic Route of Tet-TA

scopic scale.24,25 This gel state confers special properties to living systems, which is heterogeneous on a wide range of length scales. This is very important for the local diffusion properties, which vary as a function of the spatial position and the degree of heterogeneity. Diffusion properties in soft matter strongly depend on obstruction, interactions, and structure dynamics. Hydrogels represent an important group of soft materials with many properties that are related to living cells. An understanding of the frictional properties of gel networks is therefore an essential first step for elucidating many fundamental aspects of transport properties in gels and gel state in living systems. When water passes through a polymer network, a frictional resistance arises between the network and water. The friction coefficient of the polymer network and water is proportional to the ratio of the viscosity of water passing though the gel network η and the average mesh size of the network:31,32

related to the mechanical properties of a gel and expressed as follows:9−13 Dc =

K + (4/3)μ κ = f f

(1)

where κ is the longitudinal modulus of the polymer network, K the osmotic bulk modulus, μ the shear modulus, and f the friction coefficient between the polymer network and the solvent. From eq 1, it is clear that both elasticity and the friction determine the dynamic properties of the gel network. The elastic properties of various gels are investigated extensively.10,11,14−16 There have been, however, few systematic studies on the frictional properties of gels. Tokita and Tanaka precisely measured the rate at which pressurized water could be forced through poly(acrylamide) gel17 and poly(N-isopropylacrylamide) gel.18 For poly(acrylamide) gel, the friction normalized by the viscosity of water was independent of temperature. On the other hand, as the poly(N-isopropylacrylamide) gel approached to the transition temperature, the penetration rate increased reversibly by a factor of ∼1000, which means that the friction decreased by 3 orders of magnitude. The knowledge of friction coefficients in gels is also of great importance to probe the structure of a variety of gel networks to mimic transport across natural and synthetic gel networks. Network structures of gels are well recognized to influence the solvent permeability, the diffusion of small and large molecules, and more indirectly the swelling and the elastic properties of gels.19−21 Network structure of gel is also known to be an important factor for diverse applications including separation techniques22 and polymeric gels as “solid-state” storage for liquids and their controlled release.23 These applications aside, many biological media display gel characteristics at a macro-

f∝

η ξ2

Here ξ represents the correlation length of the gel corresponds to the average distance between the neighboring contact points of the polymers. The gel−solvent friction is primarily determined by the mesh size of the polymer network and the viscosity of the solvent. The latter should not show any anomaly. When the network is homogeneous, the mesh size should be given by the average distance between the nearest polymer−polymer contacts. When the networks of polymer gels have the frozen-in disorder in the connectivity resulting from a random cross-linking, some portions of the gel swell while the other portions shrink maintaining the total gel volume constant. The effective pore size is then given by the distance over which network density fluctuations are corrected. B

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Macromolecules Scheme 2. Synthetic Route of Tet-TSI

Scheme 3. Synthetic Route of Tet-Tyr

The water is expected to pass through the swollen open space avoiding the shrunken regions. In the present work, Tetronic was selected as the main structural component for hydrogel network due to its thermosensitivity. Tetronic is a tetrafunctional star-shaped block copolymer that is produced from the sequential addition of propylene oxide (PPO) and ethylene oxide (PEO) to form ethylenediamine.33 They have been used for various biomedical applications such as injectable hydrogels for tissue engineering and micelle-like drug delivery carriers for drug delivery systems.34−36

The purpose of this paper to compare the mechanical properties of friction coefficient of well-defined network of Tetronic gel with that of randomly cross-linked Tetronic gel. We prepare homogeneous Tetronic gel by cross-linking Tetronic macromonomers through activated ester chemistry utilizing the method developed by Sakai and co-workers.1 We expect to prepare randomly cross-linked Tetronic gels by enzyme-mediated cross-linking reaction of tyrosin-modified Tetronic containing four Boc-tyrosin end groups.36 It worthy to mention that the “randomly cross-link networks” are networks that are inhomogeneous on the length scale compare to the C

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(0.50 mL of 1 wt % stock solution) and gently shaken. HRP and H2O2 stock solution used were dissolved in 10 mM PBS (pH 7.4). The final concentration of the Tet-Tyr was 30 wt %. Cross-linking reaction was carried out for 24 h at 25 °C. Determination of Phase Diagram. The equilibrium swelling degree was defined by W/W25 °C, where W and W25 °C are the weights of gels in the equilibrium state at observed temperature and that at 25 °C, respectively. The temperature was controlled to within 0.1 °C of the desired temperature. Reversibility and/or hysteresis were checked with all gels by bringing them back to 25 °C. Rheology. The viscoelastic properties were investigated by oscillatory measurements on the controlled on a Rheometrics RSAII instrument (TA Instruments, New Castle, DE) equipped with a cone−plate geometry (diameter: 20 mm) and solvent trap. A frequency sweep test was conducted with a shear amplitude γ = 1% under an oscillating frequency of 0.1−100 s−1. Friction Coefficient Measurement. The principle of the mechanical measurement of the friction coefficient of a gel is schematically shown in Figure 1a. A gel of thickness L is held at the

mean spacing of the cross-links. The gels are formed under physiological condition using horseradish peroxidase (HRP) and hydrogen peroxide (H2O2). HRP is a hemoprotein that catalyzes the conjugation of phenol and aniline derivatives via decomposed H2O2 molecules.

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EXPERIMENTAL PART

Materials. Tetronic 1304 (Mn = 10 500) was purchased from BASF and was purified by chromatography on activated alumina and lyophilized. All other reagents were purchased from Aldrich or WAKO and were used without further purification. Preparation of Tetraamine-Terminated Tetronic (Tet-TA). Tet-TA was prepared by amine alkylation reaction between Tet chloride and ammonia (Scheme 1). Tetronic 1304 (5.00 g) was dissolved in 2.21 mL of thionyl chloride. The reaction was allowed to stir 18 h under reflux conditions and concentrated. The residue was dissolved in 5.00 mL of 1,4-dioxane and added dropwise to ca. 500 mL of petroleum ether. The precipitated Tetronic tetrachloride was filtered and dried. To a stirred solution of dried Tetronic tetrachloride (4.00 g) in 12.0 mL of distilled water was added 42.0 mL of concentrated ammonia−water (28%), and the reaction mixture was allowed to stir for 4 days at 60 °C. Addition of saturated aqueous solution of Na2CO3 (20.0 mL) was followed by extraction with dichloromethane (3 × 40 mL) gave the crude Tet-TA, which was purified by precipitation three times in petroleum ether, filtered, and dried (4.29 g, 85.5%). Preparation of Tetra-N-hydroxysuccinimide Glutarate-Terminated Tetronic (Tet-TSI). The dicyclohexylcarbodiimide method of ester synthesis was used for the preparation of the N-hydroxysuccinimide esters of Tetronic tetraglutamate (Scheme 2). To a stirred solution of Tetronic 1304 (5.00 g) in 25.0 mL of dry toluene was added glutaric anhydride (2.50 equiv/OH group) (0.550 g, 4.80 mmol) and sodium acetate (0.0250 g, 0.305 mmol). The reaction was stirred for 12 h under reflux conditions. The reaction mixture was cooled to 40 °C, and N-hydroxysuccinimide (11.0 equiv/COOH group) (3.23 g, 21.4 mmol) and N,N′-dicyclohexcylcarbodiimide (3.14 g, 15.2 mmol) were added. The reaction was allowed to stir at 40 °C for 3 h, concentrated, and added dropwise to ca. 500 mL of petroleum ether. Tet-TSI was precipitated three times in petroleum ether, filtered, and dried (4.29 g, 85.5%). Preparation of Tyrosin-Modified Tetronic (Tet-Tyr). Tet-Tyr containing four Boc-tyrosin end groups was synthesized using standard carbodiimide coupling chemistry as described below (Scheme 3). TetTA (2.71 g, 0.150 mmol) was reacted with N-Boc-L-tyrosin (341 mg, 1.20 mmol), 1-hydroxybenzotriazole (HOBt) (288 mg, 2.10 mmol), and triethylamine (218 mg, 2.20 mmol) in 40 mL of a 50:50 mixture of dichloromethane (DCM) and dimethylformamide (DMF). O(benzotriazole-1-yl)-N,N,N′,N′-tetramethyluronium hexafluorophosphate (HBTU) (461 mg, 1.20 mmol) in 20 mL of DCM was then added, and the coupling reaction was allowed to stir under an argon atmosphere at 25 °C for 1 h. The solution was successively washed with saturated sodium chloride solution, aqueous solution of 5% NaHCO3, dilute hydrochloric acid, and distilled water. The crude product was concentrated under reduced pressure. The residue was dissolved in 20.0 mL of DCM and added dropwise to ca. 800 mL of diethyl ether. Tet-Tyr was precipitated three times in diethyl ether, filtered, and dried (1.56 g, 56.7%). Preparation of Tetra-Tetronic Gel by Cross-Linking Tetronic Macromonomers (Tet Gel). A prescribed amount of Tet-TA and Tet-TSI was dissolved in 0.1 M phosphate buffer, pH 7.4 and 5.8, respectively. Two solutions were mixed and allowed to react for 96 h at 25 °C to complete the cross-linking reaction. The final concentration of the polymer was 25, 30, 35, 40, and 50 wt %. Preparation of Tetra-Tyrosin-Tetronic Gel by EnzymeMediated Cross-Linking Reaction (Tet-Tyr Gel). To form TetTyr gel, horseradish peroxidase and hydrogen peroxide (HRP/H2O2) were added to solutions of Tet-Tyr in phosphate-buffered saline (PBS). Tet-Tyr (1.1 g) in 1.00 mL of 10 mM PBS (pH 7.4) was mixed with HRP solution (0.50 mL of 0.6 mg/mL stock solution) and H2O2

Figure 1. (a) Schematic illustration of the principle for measuring the friction coefficient between a gel network and water. (b) An apparatus used in this study. lower end of a glass tube of 5.5 mm in diameter. The water is pushed by small pressure P. The velocity of the water flow through the gel v is determined by measuring the rate at which water flows out of the upper end of the gel in a steady state. The friction coefficient of the gel f is defined by

f=

P vL

(2)

As mentioned in the Introduction, Tokita and Tanaka designed the precision apparatus to measure the rate of water flows out of the gel precisely.17 In this study, we measured the flow rate under the relatively low hydrostatic pressure to avoid the bending deformation of the gel and the gel shrinking due to the frictional resistance. We, therefore, employed simpler apparatus schematically illustrated in Figure 1b. A capillary is immersed into a large amount of water at a desired depth h0. Then, the height of the water inside the capillary h(t) is measured as a function of time. In this geometry, the hydrostatic pressure P that is applied to the open end of the gel is expressed as follows:

P = ρg[h0 − h(t )]

(3)

Here ρ and g denote the density of water and the acceleration of gravity, respectively. The linear velocity of the fluid in the gel is then written by

v= D

dh(t ) dt

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Macromolecules Substitution of eqs 2 and 3 into eq 1 yields ρg dh(t ) = [h0 − h(t )] dt Lf

(4)

The time course of water flow through the gel is then given by h0 − h(t ) ⎛ t⎞ = exp⎜− ⎟ ⎝ τ⎠ h0

(5)

where the characteristic time τ is written by

τ=

Lf ρg

(6)

The friction coefficient of the gel is therefore determined from the elution time course of water through the gel. All apparatuses are set on an optical table to avoid any mechanical disturbance. The height of the water in the capillary h(t) and the initial depth of the water h0 are measured by the moving microscope staged on a microtranslator. The typical value of h0 is about 20−40 mm depending on the applied hydrostatic pressure. Prior to the measurement, the open end of the gel is kept in contact with the water until the height of the water inside the glass tube become constant. The effects of the pressure change due to the capillary force are minimized. The temperature was controlled to within 0.1 °C of the desired temperature. The gel samples used for friction experiments were prepared between the glass plates with spacers of 4 mm thickness. After equilibration in deionized water at the desired temperature, the gel was cut out in cylindrical shape with 5.5 mm in diameter, the same diameter as that of glass tube, and hold at the lower end of a glass tube.

Figure 2. (a) Equilibrium swelling degrees, W/W25 °C, of 30 wt % Tet gel and 30 wt % Tet-Tyr gel in water are plotted as a function of temperature. (b) Storage moduli (G′) and loss moduli (G″) as a function of frequency for 30 wt % Tet gel and 30 wt % Tet-Tyr gel at 25 °C. A frequency sweep test was conducted with a shear amplitude γ = 1% under an oscillating frequency of 0.1−100 s−1.

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RESULTS AND DISCUSSION Mechanical Properties and Equilibrium Swelling Degree. The storage mudulus G′ and the loss modulus G″ for 30 wt % Tet gel and Tet-Tyr gel at 25 °C showed behaviors typical of the gel samples in that the elastic storage modulus G′ was substantially greater than the viscous loss modulus G″ over the full range of frequency measured (Figure 2a). Clear rubbery plateaus are observed, indicating both Tet gel and Tyr-Tet gel behave like highly elastic body due to the formation of networks with chemical cross-linking. Figure 2b shows the temperature dependence of the swelling ratios, W/W25 °C, of 30 wt % Tet gel and 30 wt % Tet-Tyr gel in water. The volumes of both gels gradually decrease with increasing temperature. The combination of enthalpic and ehtropic changes of the whole system is considered to determine this lower critical solution temperature (LCST) type phase behavior. At lower temperatures, the formation of ether−water hydrogen bonds results in a favorable excess free energy ΔGex consistent with the swollen state in water. Increasing temperature leads to a reduction in favorable ether− water interaction due to breakup of ether−water hydrogen bonding. In addition, the entropically unfavorable structure of waters surrounding hydrophobic moieties (waters of hydrophobic hydration) becomes less ordered bulk water with increasing temperature. As a result, polymer chains lose hydrophobic hydration and increase contacts within the chains. Thus, collapse of gel follows. These changes occurred reversibly, without hysteresis, when the temperature is decreased. Test of Apparatus for Water Flow Measurement. Figure 3 shows the typical experimental results for 30 wt % Tet Gel at 25 °C with different hydrostatic pressure P. The time course of the height of meniscus of water h(t) in a glass tube is given in this figure. The measurements were taken for 3.6 × 105 s to determine accurate flow time course. As shown in Figure 3,

Figure 3. Time course of the position of the meniscus in the glass tube for 30 wt % Tet gel at 25 °C under different hydrostatic pressures.

water can pass through the gel even at these low pressures. The velocity of the water in the glass tube is obtained from the slope of the line shown in Figure 3. The velocity obtained is plotted as a function of the pressure in Figure 4. The relationship between applied pressure and the velocity is linear with a line through the origin. According to eq 5, the relative height change of the water inside the glass tube [h0 − h(t)]/h0 is plotted as a function of time in semilogarithmic scale in Figure 5. The results are well expressed by single-exponential function over the whole time range of the measurements. The friction coefficient, f = 2.15 × 1010 dyn·s/cm4, is obtained from the slope of the straight line given in Figure 5 using the eqs 5 and 6. In order to check the performance of the apparatus, we measured the velocity of water flow through the poly(acrylamide) gel under the same hydrogel concentration and temperature ranges conducted by Tokita and Tanaka17 and E

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Figure 4. Pressure dependence of the velocity of the water in the glass tube for 30 wt % Tet gel at 25 °C. The straight line in the figure is obtained by the least-squares method.

Figure 6. Double-logarithmic plot of the friction coefficient as a function of the total concentration of the gel at 25 °C. The slope of the straight line is 1.5.

Using eqs 1 and 8, we find the concentration dependence of the friction coefficient f ∝ Cp3/2

The experimentally obtained exponent 1.5 is therefore in a good agreement with scaling prediction. The results indicate that frictional property of a gel is mainly controlled by the mesh size of the gel network. Temperature Dependence of the Friction Coefficient. The temperature dependence of 30 wt % Tet gel was measured within a temperature range between 25 and 60 °C. The diskshaped gel prepared between the glass plates was equilibrated in deionized water at the desired experiment temperature. After reaching the swelling equilibrium, the gel was cut out in cylindrical shape with 5.5 mm in diameter and about 4 mm in thickness and was held at the lower end of a glass tube. As has already mentioned, the friction coefficient between the network of a gel and water should be proportional to the viscosity of water passing through the gel and also inversely proportional to the square of the average mesh size of the network. Therefore, in order to discuss the temperature dependence of the correlation length, it should be use the ratio f(T)/η(T) rather than the raw value of the friction coefficient f(T). The temperature dependence of the friction coefficient normalized by the viscosity of water f(T)/η(T) is given in Figure 7. The viscosity of water η(T) is taken from a table. The normalized friction for Tet gel increases with temperature, and the f(T)/η(T) value at 50 °C is about 10 times larger than that at 15 °C. The gel−water friction is primarily determined by the mesh size of the gel network and the viscosity of water. The water viscosity does not show any anomaly in our experiments. When the network is homogeneous, the mesh size is given by the average distance between the nearest polymer−polymer contacts. Therefore, the increase in the normalized friction f(T)/η(T) for Tet gel with temperature attributed to the decrease in the average mesh size of the network due to the dehydration of the chains at higher temperature. Comparison of the Friction Coefficient between Tet Gel and Tet-Tyr Gel. By measure of the similarity between tetra PEG gel and Tet gel, the homogeneous gel is expected to prepare by cross-linking Tetronic macromonomers through activated ester chemistry. We adopted the enzyme-mediated

Figure 5. Relative height change, [h0 − h(t)]/h0 for 30 wt % Tet gel at 25 °C, measured under different hydrostatic pressures is plotted as a function of time.

calculated the friction coefficient between poly(acrylamide) gel and water. The obtained values of friction coefficients for poly(acrylamide) gel under various conditions are in agreement with those reported by Tokita and Tanaka within the range of experimental error (Supporting Information). These data indicate that that hydrogels are held in the flow tube in such a way as to avoid leaks around the hydrogel’s periphery, and it is possible to determine the friction using this simple apparatus. Gel Concentration Dependence of the Friction Coefficient. The concentration dependence of the friction coefficient for Tet gel was measured at 25 °C between the concentration range from 25 to 50 wt %. The results are shown in Figure 6, in which the friction coefficient f is plotted as a function of the polymer concentration Cp in double-logarithmic scale. The data are well represented by a straight line with a slope of 1.5, which indicates that the concentration dependence of friction coefficient is expressed by a power law relationship: f ∼ Cp1.5

(7)

where Cp is the total concentration of gel. The friction coefficient of the network between a gel and water should be proportional to the viscosity of water passing through the gel and also determined by the average mesh size of the gel network, which is assumed to be proportional to the correlation length ξ of a gel. Therefore, we obtain the relationship shown in eq 1. The scaling prediction for correlation length ξ is32

ξ ∼ Cp−3/4

(9)

(8) F

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Figure 7. Temperature dependence of the friction coefficient of the 30 wt % Tet gel normalized by the viscosity of water.

Figure 8. Pressure dependence of the velocity of the water in the glass tube for 30 wt % Tet-Tyr gel along with 30 wt % Tet gel at 25 °C. The straight lines in the figure are obtained by the least-squares method.

cross-linking reaction to prepare the randomly cross-linked Tetronic gel. Tet-Tyr gel was prepared via the HRP-mediated coupling reaction of phenolic moieties in Tet-Tyr under physiological conditions. HRP is a hemoprotein that catalizes the conjugation of phenol and aniline derivatives via decomposed H2O2 molecules. In the presence of HRP and H2O2, phenoxyl radicals are formed by the HRP-catalyzed oxidation of phenols of N-Boc-L-tyrosin moieties at the end of the polymer. Phenoxyl radicals are coupled to each other via a carbon−carbon bond at the ortho position of the phenol groups or via a carbon−oxygen bond between the carbon atom at the ortho position of the phenol groups and the phenolic oxygen. For the permanently cross-linked gel, the equilibrium shear elastic modulus Ge can be predicted by the theory of rubber elasticity first developed by Flory,37,38 which can be expressed by the following equation:39,40 ⎛ ⟨r 2⟩ 2⎞ Ge = ⎜1 − ⎟νeRT 2 ϕ⎠ ⎝ ⟨r0 ⟩

(10)

which allows the number of effective chains per unit volume νe to be estimated. R is the gas constant, T is the temperature, ⟨r2⟩ represents the average square end-to-end distance in the swollen state, and ⟨r02⟩ is the value of ⟨r2⟩ at the end of gelation process. The functionality ϕ is the number of strands linked to a cross-linker. The functionality ϕ of the Tet and Tet-Tyr gels are ϕ = 4. The quantity actually measured was the storage modulus G′ and also the loss modulus G″. The density νe is related to the density of effective junctions ne using the following equality:40

νe =

⎛ϕ⎞ ⎜ ⎟n ⎝2⎠ e

Figure 9. (a) Time course of the positions of the meniscus in the glass tube and (b) relative height changes, [h0 − h(t)]/h0, for 30 wt % Tet gel and 30 wt % Tet-Tyr gel at 25 °C measured under hydrostatic pressures P = 0.294 Pa are plotted as a function of time.

the time course of the height of meniscus of water h(t) in a glass tube for 30 wt % Tet-Tyr gel measured at 25 °C under hydrostatic pressures P = 0.294 Pa. The measurements were carried out under the same condition as that for 30 wt % Tet gel shown in Figure 3. The relative height change of the water inside the glass tube [h0 − h(t)]/h0 for 30 wt % Tet-Tyr gel is plotted as a function of time in semilogarithmic scale together with the result for 30 wt % Tet gel in Figure 9b. The results are well expressed by single-exponential function over the whole time range of the measurements. The friction coefficient for 30 wt % Tet-Tyr gel, f = 1.95 × 109 dyn·s/cm4, is obtained from the slope of the straight line given in Figure 8b using the eqs 5 and 6. The friction coefficient for 30 wt % Tet-Tyr gel is about an order of magnitude smaller than that for 30 wt % Tet gel.

(11)

The equilibrium shear modulus Ge corresponds to the frequency-independent elastic modulus G′ (plateau modulus). Considering from the values of plateau modulus for the gels shown in Figure 2a, the density νe for Tet-Tyr gel is assumed to be identical to that for Tet gel, which makes it possible to directly compare the friction coefficients at same temperature. Figure 8 shows the velocity of the water passing through 30 wt % Tet-Tyr gel as a function of applied pressure along with that for 30 wt % Tet gel at 25 °C. The relationship between applied pressure and the velocity for 30 wt % Tet-Tyr gel is linear within the pressure range applied here. Figure 9a shows G

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network is homogeneous, the mesh size is given by the average distance between the nearest polymer−polymer contacts. Therefore, the increase in the normalized friction f(T)/η(T) with temperature attributed to the decrease in the average mesh size of the network due to the dehydration of the chains at higher temperature. Randomly cross-linked Tetronic gel was prepared by enzyme-mediated cross-linking reaction of tyrosinmodified Tetronic and compared its friction coefficient with that of the homogeneous Tetronic gel. The friction coefficient for the randomly cross-linked gel is about an order of magnitude smaller than that for homogeneous gel. Random cross-linking of the polymer presumably produces the spatial inhomogeneity. In such an inhomogeneous network, water passes through the regions with the less network density avoiding the denser region. This indicates that the friction coefficient is determined by the effective mesh size of the network rather than the distance between the neighboring two chemical cross-links. The results in the present study suggest that the density fluctuations of the polymer network play an important role for the transport properties of the gel. It is of interest to study the correlation between transport property and the microscopic network structure, especially to compare the homogeneous Tetronic gel with the randomly cross-linked Tetronic gel. Our recent small-angle X-ray scattering studies will be reported elsewhere.

The gel−solvent friction is primarily determined by the pore size of the polymer network and the viscosity of the solvent. When the networks of polymer gels have the frozen-in disorder in the connectivity resulting from a random cross-linking, some portions of the gel swell while the other portions shrink maintaining the total gel volume constant. The water passes through the swollen open space avoiding the shrunken regions. This result indicates that water can flow through the Tet-Tyr gel more easily than in homogeneously cross-linked Tet gel. The enzyme-mediated cross-linking reaction of Tet-Tyr polymer occurs nonrandomly due to the existence of various nonidealities such as the conversion and structure dependent reactivities of the functional groups multiple cross-linking reactions. These nonidealities during gelation necessarily result in the formation of polymer gels with a large number of network defects, affecting their physical properties such as swelling, elasticity, transparency, and permeability. One of the network defects is the inhomogeneous cross-link density distribution, known as the spatial gel inhomogeneity, which is closely connected to the spatial concentration fluctuations. It is worthy to mention that the appearance of both Tet gel and the Tet-Tyr gel are transparent. Although the spatial concentration fluctuations in Tet-Tyr gels are considered to be larger than those of Tet gels, the correlation length, that is the extension of inhomogeneities in the Tet-Tyr gels, is relatively small and is less than the wavelength of visible light. These results, therefore, indicate that the friction coefficient is expected to be the good measure of the concentration fluctuation in the gel. It should be mentioned that the friction coefficient for Tet gel obtained in this study is typically of the order of 1010 dyn·s/ cm4, which is about 2 orders of magnitude smaller than that of poly(acrylamide) gel,17 although the concentration of Tet gel is higher by several times. These results indicate that the network structure of the gel determines its transport properties. Despite significant progress in understanding the basic structure−property relationships of networks, much remains to be learned about how the foundational macromolecular building blocks transmit properties across the length scales to the macroscopic sample. Fundamental challenges include understanding the relationship between network structure, dynamics, and mechanical properties. Developing the gel structure−transport property relationships require multiple measurement techniques. Small-angle neutron scattering and small-angle X-ray scattering studies were done on the Tet gels to investigate the network microstructures and relative homogeneity of the networks. Scattering profiles for 30 wt % Tet gel and Tet-Tyr gel were clearly distinguishable, indicating that each gel has different microstructures. More extensive study is needed, however, to identify the microscopic structures of the gels, which will lead to the aid for further confirmation of the gel structure−transport property relationships.

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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.5b01997. Figure S1 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Fax +80-92-802-4118; Tel +81-92-802-4126 (M.A.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was partly supported by a Grant-in-Aid (No. 25288055, 26102534, and 26560243) from the Ministry of Education, Culture, Science, Sports and Technology of Japan.

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REFERENCES

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SUMMARY The friction coefficient between the well-defined network of Tetronic gel and water is measured as a function of the polymer concentration of the gel and the temperature by a simply designed apparatus. The homogeneous Tetronic gel is prepared by cross-linking Tetronic macromonomers through activated ester chemistry. The concentration dependence of the friction coefficient is well described by a power low relationship f ∼ Cpν with the exponent of ν = 1.5, which is in a good agreement with scaling prediction 1.5. The normalized friction coefficient f(T)/ η(T) for Tetronic gel increases with temperature. When the H

DOI: 10.1021/acs.macromol.5b01997 Macromolecules XXXX, XXX, XXX−XXX

Article

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DOI: 10.1021/acs.macromol.5b01997 Macromolecules XXXX, XXX, XXX−XXX