Rheological Behavior of Environmentally Friendly Castor Oil-Based

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Rheological Behavior of Environmentally Friendly Castor Oil-Based Waterborne Polyurethane Dispersions Samy A. Madbouly,†,∥ Ying Xia,† and Michael R. Kessler*,†,‡,§ †

Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, United States Ames Laboratory, US Department of Energy, Ames, Iowa 50011, United States § Department of Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99164, United States ∥ Department of Chemistry, Faculty of Science, Cairo University, Orman-Giza, Egypt ‡

ABSTRACT: Novel biorenewable, waterborne, castor oil-based polyurethane dispersions (PUDs) were successfully synthesized via homogeneous solution polymerization in methyl ethyl ketone followed by solvent exchange with water. Small-amplitude oscillatory shear flow experiments were used to systematically investigate the rheological behavior of these environmentally friendly, biorenewable, aqueous dispersions as a function of angular frequency, solid content, and temperature. In addition, the morphology of the dispersions was investigated at 60 °C for different time intervals using transmission electron microscopy (TEM). The solid content and temperature were found to significantly affect the rheological behavior of the PUDs. The composition dependency of the complex viscosity (η*) was found to be well described by the Krieger−Dougherty equation. Thermally induced gelation was observed for PUDs with a solid content ≥27 wt %. Although the viscoelastic behavior of the PUDs was well described by the time−temperature superposition (TTS) principle in a temperature range lower than the gel point, TTS failed to represent the behavior of the PUDs at temperatures near the critical gel point. The real time gelation behavior was also studied for different solid contents of PUDs under isothermal conditions over a wide range of angular frequencies. Furthermore, both G′ and G″ showed a power law relationship with the angular frequency at the gel point, with critical power law exponents similar to those predicted theoretically by percolation theory. Aggregation and interconnection of the nano-PU particles caused the formation of fractal gels at a critical temperature, as confirmed by TEM.

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INTRODUCTION Conventional, solventborne polyurethane (PU) systems have been widely used in many industrial applications, such as coatings, adhesives, inks, and paints. Formulation and application of solventborne polyurethanes typically involve the evaporation of large amounts of volatile organic compounds (VOCs) into the atmosphere and consequently cause a wide variety of air quality problems. The Environmental Protection Agency and other air quality regulators have stepped up their efforts to eliminate or decrease the amounts of VOCs released into the atmosphere and forced industries to develop environmentally friendly products.1−3 Waterborne polyurethane dispersions (PUDs) have recently emerged as important alternatives to their solvent-based counterparts in various applications as a result of increasing pressure to limit detrimental health and environmental effects. In this approach, the toxic and expensive volatile organic solvents were replaced by water as an environmentally benign solvent used in the formulation of PUDs, resulting in minimal VOC contents.4−12 Continued calls for establishing a low-pollution chemical industry and the unique price advantage of waterborne over solventborne polyurethanes opened the market place for aqueous PUDs. Aqueous PUDs are considered to be the most rapidly developing and active branches of PU chemistry © XXXX American Chemical Society

and technology driven by their versatility and environmental friendliness. PUDs can be tailored to various applications by varying the preparation method and chemical structure of the polyurethane. Waterborne PUDs have been used particularly as coatings for various fibers, adhesives for alternative substrates, primers for metals, caulking materials, emulsion polymerization media for different monomers, paint additives, defoamers, associate thickeners, pigment pastes, and textile dyes.13−25 The early studies of Dieterich et al.26,27 on waterborne PUDs are considered the first and inspired much of the work in this field. Anionic colloidal PUDs consist of different chemical species and can be synthesized by a reaction of diisocyanates, polyol, and a dihydroxy acid, such as dimethylolpropanic acid (DMPA), that incorporates carboxylic functionality in the prepolymer backbone. Tertiary amine (e.g., triethylamine, TEA) is then used to neutralize the carboxylic groups and produce ionic centers to stabilize the polymer particle in water. Waterborne PUDs are stable when the nanosize PU droplets (20−200 nm) persist uniformly in the continuous aqueous phase. Coalescence of PU droplets into bigger aggregates Received: January 29, 2013 Revised: April 26, 2013

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Scheme 1. Elementary Steps for the Synthesis of Castor Oil-Based PUD

normally leads to particle flocculation and consequently unstable dispersions.28−31 Dispersion stability, rheological behavior, and film-forming properties are expected to be strongly dependent on the colloidal state (e.g., particle size and dispersibility), chemical structure (e.g., polyol and diisocyanate), and composition (e.g., ratios of hard and soft segments as well as solid content in dispersion) of the PUD. The rheological properties of PUDs play an important if not a dominant role in controlling the processing conditions and identifying the optimum properties of both dispersions and solid films. Therefore, it is crucial to understand rheological properties of PUDs to design and prepare a new class of stable dispersions with different properties and a wide range of industrial applications in a controlled and reproducible manner. Most plastic materials, including high-performance polyurethane, are produced entirely from petroleum-based products. However, environmental concerns and high crude oil prices have triggered a search for biorenewable feedstocks for the production of PU and PUDs. With the recent effort to establish green chemistry and sustainability, great attention has been devoted to replace petroleum-based polymers by more environmentally friendly biopolymers based on renewable resources. Vegetable oils are abundant, inexpensive, natural materials that can be used to synthesize a wide range of polyols with different chemical structures and functionalities (in particular with different numbers of hydroxyl groups). The different types of vegetable oil-based polyols can be employed

to synthesize bio-based PUDs and PU materials with a wide range of colloidal behavior and physical properties, respectively. Castor oil’s unique structure, with ∼90% of the fatty acid chains in the oil bearing a hydroxyl group, eliminates the need for chemical modification of the triglyceride to produce polyols for PU synthesis. PU materials, including solid films, obtained from solvent-cast waterborne PUDs, can be flexible and rigid, or soft elastomers, or ductile and hard plastics, depending on the different types and concentrations of vegetable oil-based polyols. Vegetable oil-based waterborne polyurethanes have been studied to a much lesser extent in the literature than petroleum-based PUDs. Chemically modified soybean oil (methoxylated polyol) was used with various hydroxyl contents to synthesize aqueous, bio-based PUDs.32,33 The hydroxyl group content had a significant influence on glass transition temperature (Tg) and mechanical properties of the obtained PU films. The strength, stiffness, and toughness as well as the Tg of PU films increased with increasing hydroxyl content. Most literature studies and patents on PUDs are mainly focused on the industrial applications of these important systems. Few systematic studies have been aimed at generating basic data that would provide fundamental insights into the relationships between polymer structure, rheological properties, and coating performance under typical conditions PUDs encounter during use. Slight variations in the solids content, temperature, and particle size in PUDs can lead to significant changes in strength B

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DMPA at 2.0:1.0:0.99, respectively. After adding 100 mL of MEK, the reaction was continued for another 2 h at 78 °C to reduce the viscosity of the reacted mixture and prevent gelation. Subsequently, the mixture was cooled down to room temperature, and TEA (1.2 equiv per DMPA) was added under continuous stirring for 30 min to neutralize the free carboxylic acid groups in the PU chains. Then a given amount of water was added dropwise over 30 min at an agitation speed of 600 rpm to prepare stable dispersions with different solid contents, namely, 16, 18, 20, 23, 27, 29, and 32 wt %. The mixture was then transferred to a rotary evaporator, and the MEK was removed at a partial vacuum of 70 mmHg to afford solvent-free waterborne dispersions. Scheme 1 shows the elementary steps for the synthesis of castor oil-based PUD. Rheological Measurements. The viscoelastic behavior of PUD as a function of its solid content was determined using an AR2000ex rheometer (TA Instruments) with 25 mm diameter parallel plates. A thin layer of low-viscosity silicone oil was applied to the air/sample interface to eliminate water evaporation during the rheological measurements. All viscoelastic measurements using the AR2000ex rheometer were carried out under constant temperature conditions (±0.1 K) using an air/N2 gas convection oven designed with twin element heater guns, a barrel-shaped chamber, and three internal platinum resistance thermometers (PRT). The following rheological experiments were performed: 1. Strain sweep at constant angular frequency and temperature to determine the linear viscoelastic regime of the PUDs. 2. Angular frequency sweep at different constant temperatures (10− 80 °C) in the linear viscoelastic regime to determine master curves for the dynamic shear moduli (storage shear modulus, G′, and loss modulus, G″) using horizontal shifts of the experimental data. The zero-shear viscosities (η0) of the PUDs as functions of solid content and temperature were also calculated by fitting the complex viscosity η* vs ω data to the Carreau−Yasuda model. 3. A time sweep at different constant angular shear frequencies (ω = 0.5−100 rad/s) and temperatures (55, 60, 65, and 70 °C) in the linear viscoelastic regime to evaluate the effect of thermally induced gelation on the viscoelastic characteristic functions (G′, G″, η*, and tan δ). 4. The dynamic shear moduli, G′ and G″, were measured as functions of angular frequency at a given constant temperature for different gelation times in the linear viscoelastic region to test the validity of expressing G′ and G″ vs ω in a power law form with critical exponents based on the percolation theory. Transmission Electron Microscopy (TEM). The morphology of the particles in the dispersion was determined using TEM (1200EX by JEOL, Ltd.). The dispersions were diluted with DI water to ∼0.5 wt %. Approximately 3 μL of the diluted dispersion was then deposited onto a carbon film grid. A thin layer of the liquid sample was formed by removing the excess deposited dispersion on the TEM grid using filter paper. The thin PUD layer was then mixed quickly with aqueous uranium acetate solution (2 wt %) as a negative stain agent for better morphology contrast. Figure 1 shows TEM picture of the morphology for a PUD with 20 wt % solid content as an example. The PUD exhibited dispersed nano-PU particles with a diameter of ∼30 nm. The

and the range of particle interactions, consequently altering the phase behavior, morphology, and rheology. The current work investigates the rheological properties of a well-characterized system of castor oil-based PUDs with various solid contents as functions of temperature, angular frequency, and gelation time. The rheological behavior of these environmentally friendly, bio-based, aqueous dispersions is analyzed using the Krieger−Dougherty equation, time−temperature superposition or WLF principle, and the Carreau−Yasuda model. In addition, thermally induced gelation phenomena observed with these dispersions are explored for different compositions and interpreted based on the Winter−Chambon criterion and percolation theory. The mechanism of thermally induced gelation is determined by studying the morphology of the dispersion using transmission electron microscopy after the samples were annealed for different time intervals at gelation temperature. The systematic rheological investigation of the current bio-based PUDs generated accurate and useful data necessary to guide the synthesis, processing, and modeling of this important class of materials. The current rheological investigation of castor oil-based PUDs is different from our previous studies for petroleumbased PUDs.37 The main difference between the two systems can be summarized as follows: 1. The petroleum-based PUDs have been synthesized via a prepolymer emulsification process with N-methylpyrrolidone (NMP) solvent, while an acetone process was used for the current castor oil-based PUDs. This processing difference leads to different applications; for example, the prepolymer emulsification process is used to prepare PUDs for the coatings industry, while the acetone process is used to prepare PUDs for adhesives applications. 2. For the prepolymer emulsification process, the dispersion normally contains ∼12 wt % NMP as organic solvent to improve the coating performance, but no organic solvent remains in the castor oil-based PUDs prepared via the acetone process, as will be mentioned in the Experimental Section. 3. The petroleum-based PUDs described in our previous work comprise thermoplastic PU particles dispersed in water, while the current castor oil-based PUDs consist of thermoset PU particles dispersed in water (see Scheme 1). 4. For a constant concentration of dimethylolpropionic acid (internal surfactant), the particle size of castor oil-based PUDs is ∼4 times lower than that of the previously described petroleum-based PUDs. This size difference has a significant influence on the viscoelastic behavior and gelation kinetics as discussed later.

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EXPERIMENTAL SECTION

Materials. Castor oil, dimethylolpropionic acid (DMPA), isophorone diisocyanate (IPDI), and dibutyltin dilaurate (DBTDL) were obtained from Aldrich Chemical Co. (Milwaukee, WI), while methyl ethyl ketone (MEK) and triethylamine (TEA) were purchased from Fisher Scientific Company (Fair Lawn, NJ). All materials were used as received without further purification or analysis. Synthesis of Castor Oil-Based PUDs. A 500 mL roundbottomed, three-necked flask equipped with a mechanical stirrer, nitrogen inlet, condenser, and thermometer was used as a reactor vessel for the polymerization reaction; its temperature was controlled by a constant temperature oil bath. 20.0 g of castor oil, 12.46 g of IPDI, 3.72 g of DMPA, and 1 drop of DBTDL as catalyst were mixed in the reactor at 78 °C for 1 h. The weights of the reactants were calculated accurately to keep the mole ratio between the NCO groups of the IPDI, the OH groups of the castor oil, and the OH groups of the

Figure 1. PUD and its TEM nanostructure morphology for 20 wt % solid content. C

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effect of temperature on the morphology of the PUD with 27 wt % solid content was also investigated using TEM after annealing the sample at 60 °C for various time intervals (every 50 min) up to 150 min. After each time interval at 60 °C, TEM specimens were prepared using the procedure mentioned above.

|η*| = η0[1 + (τηw)a ](n − 1)/ a

(1)

where τη defines the location of the transition from Newtonian to shear-thinning behavior as mentioned above, while n and a are material constants. The zero shear viscosity, η0, can be calculated from eq 1 as a fitting parameter to the experimental results using nonlinear regression analysis. The lines in Figure 2 were computed from eq 1, while the symbols represent the experimental data.34,35 Obviously, the model fits the experimental data well. Using the Krieger−Dougherty equation (eq 2), the dependency of the dimensionless viscosity, ηr (zero shear viscosity normalized by the solvent viscosity), of the dispersions on volume fraction (ϕ) can be used to calculate the critical volume fraction (ϕc) at which the viscosity of the dispersions increased significantly36,37

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RESULTS AND DISCUSSION Effect of Solid Content on the Viscoelastic Behavior of PUDs. Dynamic rheology has been widely used as an accurate technique to investigate viscoelastic behavior of thermoplastic and thermosetting polymers, polymer dispersions, and polymer composites.44−57 In this section, the effect of solid content on the rheological properties of castor oil-based PUDs will be investigated. Figure 2 shows the dependency of

−kϕc ⎛ ϕ⎞ ⎜ ⎟ ηr = ⎜1 − ⎟ ϕc ⎠ ⎝

(2)

with ηr =

η0D ηs

(3)

where k is a shape parameter, η0D is the zero shear viscosity of the dispersions, and ηs is the solvent (water) viscosity. Figure 3

Figure 2. Angular frequency dependence of complex viscosity, η*, for PUDs with different solid contents. The lines are calculated from eq 1, while the symbols represent experimental data.

the complex viscosity of castor oil-based PUDs on angular frequency for different solid contents at 20 °C using a doublelogarithmic scale. It is clear that the solid content of PU had a significant effect on the viscosity of the dispersions. The viscosity increased systematically, and the dispersions changed from Newtonian behavior (frequency independent) for PU ≤ 18 wt % to non-Newtonian (frequency dependent) for PU ≥20 wt % at 20 °C. This behavior is attributed to the fact that the number of particles increases with increasing solid content, which leads to a significant decrease in the percentage of free water because each particle adsorbs a thin layer of bound water, thereby reducing the volume fraction of unbound free water even further. It must also be mentioned here that for a constant concentration of dimethylolpropionic acid (internal surfactant) the particle size of castor oil-based PUDs is ∼4 times lower than the corresponding value of petroleum-based PUDs.37 This finding was found to have a significant influence on the viscoelastic behavior. For example the complex viscosity of castor oil-based PUD with 32 wt % solid content is about 5 orders of magnitude higher than the corresponding value for the petroleum-based PUD.37 This is again due to the fact that the smaller the particle size the lower the free water and the larger the viscosity. The complex viscosity η* was frequency independent as long as the angular frequency (ω) was sufficiently smaller than the reciprocal of the characteristic relaxation time (τη) of all modes. However, the decrease of η* with frequency indicated that some modes had reciprocal of the characteristic relaxation time (1/τη) smaller than ω. Complex viscosity η* as a function of angular frequency at a constant temperature can be well described by the Carreau−Yasuda model,53 as seen in eq 1:

Figure 3. Dependency of reduced viscosity, ηr, at 20 °C on volume fraction. The line passing through the experimental data is the fitting line of eq 2 determined by nonlinear regression analysis.

shows that the experimental values are in good agreement with eq 2. The symbols represent experimental data while the line was calculated using k and ϕc as fitting parameters. The calculated value of ϕc based on the above regression analysis was 0.35. It is well established that eq 2 works well for hardsphere dispersions with volume fractions lower than 0.55 and that ϕc is lower for small, monodispersed particles than large ones as well as ϕc increases with increasing polydispersity.37 The relationship displayed in Figure 3 is governed by the interaction between the repulsive force of similar charges surrounding the surface of each particle and hydrodynamic interaction. The charge density on the particle surface controls the interaction potential between the particles. As mentioned in the Experimental Section and presented in Scheme 1, all PUDs of different solid contents were prepared using a constant amount of DMPA; i.e., all particles should have similar charge density regardless of the change in solid contents. Therefore, the repulsive forces between particles should be constant for all PUDs of different solid contents. The increase in viscosity with D

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increasing solid contents is directly related to the increase in the number of particles and the decrease in the particle−particle distance that cause a significant increase in hydrodynamic interactions between the particles. In addition, each particle in the dispersion is adsorbed with a thin layer of water due to the presence of hydrophilic −COO−HN+(C2H5)3 groups on the surface of the particle, leading to a decrease in the concentration of free water (continuous phase) in the dispersion and consequently to an increase in viscosity. It appears that the interaction potential generated by the repulsive forces between similar charged particles is significant at low concentrations. At high concentrations, both interparticle distance and interaction potential decrease, rendering hydrodynamic interaction the only factor responsible for the observed increase in PUD viscosity. The normalized relative viscosity (ηr/η0) of PUDs can be described by the equation38,39 ηr = f (τ0ω) η0 (4)

Figure 5. Angular frequency dependence of dynamic viscosity for PUD with 32 wt % solid content at different constant temperatures. The solid lines are calculated from eq 1.

where τ0 is a shift factor and f(τ0ω) is a universal function, independent of molecular weight, concentration, and temperature. Based on eq 4, the complex viscosity of PUD as a function of solid content (Figure 2) can be used to construct a master curve of dynamic viscosity over a wide range of angular frequencies, as seen in Figure 4. Here, Newtonian behavior

(T ≥ 60 °C), the complex viscosity increased significantly. In addition, the η* vs ω at different temperatures for this PUD is in good agreement with eq 1, as shown by the fitting lines passing through the experimental points. The significant increase in viscosity with increasing temperature in the high temperature range (T ≥ 60 °C) may be attributed to the thermally induced gelation of this dispersion. It was observed only for PUDs of solid content ≥27 wt %. The thermally induced gelation was also confirmed by heating the dispersion in a tightly closed glass bottle (i.e., eliminating the possibility of water evaporation) to around 60 °C in a water bath for 3 h, after which the liquid dispersion changed to a solid gel. The gelation process and its kinetics for these castor oil-based PUDs and their dependency on temperature, time, and solid content will be considered in more detail in the next section. Figure 6 shows the temperature dependence of η0 for a PUD with 32 wt % solid content obtained from fitting the data in

Figure 4. Master curve of normalized viscosity, ηr/η0, at 20 °C for PUDs with different solid contents.

(viscosity independent of angular frequency) is followed by strong shear thinning behavior (viscosity decreases greatly with increasing angular frequency) in both low and high frequency ranges. This master curve of dynamic viscosity provides an important result that should be very useful in predicting the behavior of PUDs, particularly under deformation and flow conditions that are experimentally inaccessible (i.e., very wide angular frequency range). Effect of Temperature. Temperature has a significant effect on the viscoelastic behavior of PUDs. We selected PUDs with 32 wt % solid content as one viscous example to study the effect of temperature on the rheological properties of these biobased aqueous dispersions. Figure 5 shows the complex viscosities of PUDs with 32 wt % solid content as a function of angular frequency at different temperatures. The complex viscosity of this dispersion decreased systematically with increasing temperature up to 50 °C. At higher temperatures

Figure 6. Temperature dependence of zero-shear viscosity for PUDs with 32 wt % solid content. The dotted line indicates the sol−gel transition temperature.

Figure 5 to the Carreau−Yasuda model (eq 1). Here, η0 decreased linearly with increasing temperature up to 50 °C. In this temperature range the dispersion exhibited liquidlike, viscoelastic behavior. At higher temperatures the viscosity increased significantly with increasing temperature, and the dispersion exhibited a solidlike, viscoelastic behavior. The E

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polymeric materials, such as block copolymers near the order−disorder transition and polymer blends at the liquid− liquid transition.40−42 Arrhenius and/or WLF equations (eqs 6 and 7, respectively) can be used to investigate the temperature dependence of the shift factor:43

dotted line in Figure 6 indicates the sol−gel transition temperature for this dispersion. The thermally induced gelation of PUD at high temperatures may cause a deviation from the time−temperature superposition principle (TTS) represented by the Williams− Landel−Ferry model (WLF) . Therefore, the angular frequency dependence of the dynamic shear moduli (G′ and G″) of PUDs with 32 wt % solid content was investigated over a wide range of temperatures, even exceeding the gel temperature, i.e., up to 65 °C to verify the validity of the WLF superposition principle. On the basis of thermorheological simplicity, the master curves for the dynamic shear moduli, G′ and G″, can be constructed by horizontal shifts along the x-axis (frequency axis) according to the equation G′(ωaT , T0) = G′(ω , T0)

log aT =

Ea ⎛ 1 1⎞ ⎜ − ⎟ 2.303R ⎝ T T0 ⎠

(6)

log aT =

−c1(T − T0) c 2 + (T − T0)

(7)

where Ea is the flow activation energy, R is the universal gas constant, and c1 and c2 are the WLF parameters. The shift factor aT for the data in Figure 7 as a function of temperature is shown in Figure 8. Here, the solid line was calculated from the

(5)

where aT and T0 are the horizontal shift factor and reference temperature, respectively. The accessible frequency window for the linear viscoelastic experiment of PUD can be greatly extended by the TTS principle. This principle applies to stable materials without any physical or chemical reaction during the dynamic measurements, and only the effect of temperature on the relaxation process is considered.37 Therefore, the principle works well when the stress-sustaining structure in the system does not change with temperature and relaxation times of all modes of this structure change with temperature by the same factor.37 The master curves of G′ and G″ for PUDs with 32 wt % solid content at T0 = 25 °C are depicted in Figure 7. The

Figure 8. Temperature dependence of shift factor aT for a PUD with 32 wt % solid content. The inset plot demonstrates the Arrhenius-type plot for the temperature dependence of aT.

WLF equation using c1 and c2 as fitting parameters. The experimental data are well described by the WLF equation up to a temperature below the Tgel, i.e., T < 60 °C. The temperature dependence of the shift factor aT deviates significantly from the WLF equation (shown by the solid curve in Figure 8) at higher temperatures, as seen in Figure 8. Similar behavior was observed using the Arrhenius equation (shown by the solid line in the inset plot of Figure 8) for the same experimental data.. The value of Ea calculated from the slope of the straight line of the Arrhenius-type plot (inset plot of Figure 8) was approximately 71 ± 3 kJ/mol. Real-Time Measurements. Monitoring the changes in viscoelastic material characteristics G′, G″, and tan δ as functions of curing time at gelation temperature for PUDs with different solid contents provides rheological insight into the kinetics of thermal-induced gelation. Figure 9 shows collective diagrams for the time dependence of G′ and G″ for a 29 wt % PUD at 60 °C and different constant shear frequencies. During the early stage of the gelation process and before the formation of a three-dimensional elastic gel, G′ was slightly lower than G″ at different angular frequencies. Both G′ and G″ increased rapidly with increasing gelation time, and the magnitude of the increase was dependent on angular frequency. In addition, the magnitude of the increase in G′ was higher than the increase in G″ at a given gelation time and angular frequency under the same experimental conditions. In more detail, G′ was lower than G″ in the early stage of the gelation process but became ∼1 order of magnitude higher than G″ at the end of the gelation process (see Figure 9). This behavior can be attributed to the fact that the stress induced in the system by branching and the formation of a three-dimensional

Figure 7. Master curves of storage and loss moduli at a reference temperature of 25 °C for a PUD with 32 wt % solid content.

WLF principle proved valid for temperatures up 55 °C and failed for T ≥ 60 °C (similar to the increase in dynamic viscosity with increasing temperature at high temperatures; see Figure 5). At T ≥ 60 °C, clear deviations from the terminal slopes of G′ and G″ were observed (see Figure 7). This deviation (lack of superimposability of the viscoelastic response at low frequencies) is attributed to the fact that the sample underwent gelation at elevated temperatures (i.e., the contribution of the longest relaxation mode to the viscoelastic material function at the onset of gel formation). Deviations from the WLF principle have been observed for other F

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fractal structure is macroscopically percolated. After reaching the gel point, tan δ decreases gradually with time because the magnitude of increase in G′ is higher than that in G″. On the basis of the preceding discussion, it is apparent that the Winter−Chambon criterion is applicable to the thermally induced gelation of PUD over a wide range of frequencies (as shown in Figure 10), indicating that there is a self-similar structure (or critical gel) at the gel point. Similar timedependent behavior of G′, G″, and tan δ for a 29 wt % PUD at 70 °C and different constant angular frequencies is shown in Figure 11. Here, the tgel obtained from the crossover point of G′

Figure 9. Time dependence of G′ and G″ for a 29 wt % PUD at 60 °C and different constant angular frequencies (the arrow indicates the gel time). The inset plot shows the time dependence of G′ and G″ for only 1 and 100 rad/s angular frequency.

gel is primarily elastic in origin. The gel point (tgel), obtained from the crossover point of G′ and G″ (shown by the arrow in Figure 9), was at approximately 20 ± 2 min. The calculated value of tgel is almost frequency independent, as seen in the inset plot of Figure 9, where the value of tgel at 1 and 100 rad/s angular frequency is almost constant. The tgel can be accurately evaluated using the time dependence of tan δ at different angular frequencies according to the Winter−Chambon approach. Based on this method, tgel can be identified as the instant in time at which the moduli scale in an identical fashion with time; i.e., G′ and G″ show the following power law behavior:37,44,45 G′ ∼ G″ ∼ ωn

Figure 11. Time dependence of G′, G″, and tan δ for a 29 wt % PUD at 70 °C and different constant angular frequencies (the arrow denotes the gel time).

and G″ (or from the time at which tan δ is angular frequency independent) is shorter at higher temperatures than at lower temperatures (approximately 5 and 21 min at 70 and 60 °C, respectively). In addition, the rate of the increase in G′ and G″ and their values at the end of the gelation process increase significantly with increasing gelation temperature. Figure 12a shows the effect of the solid contents in PUDs on the crossover point of G′ and G″ at 60 °C and 1 rad/s angular frequency. The tgel obtained from the crossover point of G′ and G″ increased significantly with decreasing solid content of the PUD. In addition, the values of G′ and G″ at any constant gelation time increased dramatically with increasing solid content of the PUD. This result suggested that with higher solid content of the PUD the number of particles increased, which in turn increased the viscosity and consequently the rate of the gelation process. This data also confirmed that the gelation behavior of castor-oil-based PUDs can be observed for samples with solid content as small as 27 wt %. However, on the other hand, no gelation behavior has been observed previously for our petroleum-based PUDs of solid content less than 40 wt %37 due to the significant difference in the particle size and particle−particle interaction as already mentioned above. The temperature dependence of tgel for PUDs with different solid contents can be described by the equation37

(8)

where n is the relaxation exponent which can be linked to microstructural parameters. For all materials following the above relation over a wide range of angular frequencies, the loss tangent, tan δ = G″/ G′, can be given by the equation46 ⎛ nπ ⎞ tan δ = tan⎜ ⎟ ⎝ 2 ⎠

(9)

According to this equation, tan δ is independent of angular frequency at the gel point. This criterion has been used successfully for a variety of chemically and physically crosslinking systems. Figure 10 shows that tan δ for a 29 wt % PUD at 60 °C is frequency independent at tgel = 21 min, indicating that the system has reached the gel point and the cluster of the

ln(tgel) = constant +

Ea RT

(10)

where Ea is the apparent activation energy and T is the absolute isothermal gelation temperature. The value of Ea can be obtained from the slope of the linear relationship between ln(tgel) and the inverse of the absolute isothermal gelation temperature for PUDs with different solid contents, as described in Figure 12b. The value of Ea was 190 ± 5 kJ/ mol, independent of the different solid contents of the PUD.

Figure 10. Time dependence of tan δ for a 29 wt % PUD at 60 °C and different constant angular frequencies (the arrow denotes the gel time). G

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occupy the total volume of the dispersion. Therefore, they have to move cooperatively in order to rearrange their spatial configuration substantially, which becomes increasingly unlikely near the gel point.48 This gelation process is irreversible, and once the particle aggregates have formed, they are not easily disrupted when the dispersion is cooled down to room temperature. Figure 13 shows typical TEM photographs for PUDs with 27 wt % solid content after annealing the specimens in tightly closed glass bottles at 60 °C for different time intervals. The results explain the mechanism of thermally induced gelation of PUDs. During the early stage of the gelation process, the nanodispersed PU particles (∼30 nm) form aggregates. During the intermediate stage, the aggregated particles interconnected and formed cluster structures (see TEM photographs at 100 min). This interconnection step is quite different from the preceding aggregation step in that the aggregates do not diffuse randomly but directly experience their nearest neighbors. The resulting clusters were irregular but statistically self-similar. As the aggregation and interconnection processes continued with annealing time at 60 °C, larger clusters formed and interdiffused to form larger aggregates. They are examples of mass fractals.49 Although the examined PUDs exhibited gelation behavior after heating at 60 °C for up to 150 min (see Figures 12a and 13, respectively), the specimens did not completely convert to a solid material; rather, they formed very viscous dispersions that could be diluted to prepare the TEM samples for morphology analysis. A solid elastic gel was formed at the late stage of the gelation process (after ∼300 min annealing time). Figure 14a demonstrates the frequency dependence of G′ at different time intervals for 29 wt % PUD at 60 °C. The value of G′ increased strongly with increasing angular frequency and gelation time. During the late stage of the gelation process, G′ was no longer frequency dependent and reached an equilibrium value (Geq) due to the formation of an elastic fractal gel. Similar

Figure 12. (a) Time dependence of G′ (solid symbols) and G″ (open symbols) for PUDs with different solid contents at 60 °C and 1 rad/s angular frequency. The arrows indicate the gelation times for each PUD. (b) Dependence of tgel on the absolute inverse temperature, 1/ T, of the gelation process for PUDs with different solid contents.

The gelation behavior of PUDs is in good agreement with the kinetic modeling of aggregation and gel formation in quiescent dispersions of polymer colloids postulated by Lattuada et al.48 According to this model, in aqueous dispersions the gel is formed through fractal aggregations that

Figure 13. TEM photographs of PUDs with 27 wt % solid content at 60 °C for different annealing times. H

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percolation theory (n = 2/3).50−54 At very long times, the values of n′ and n″ decreased and became as low as 0.08 and 0.2, respectively, indicating the formation of an elastic fractal gel. The values of the exponents n′ and n″ should be temperature dependent because of the different degrees of gelation accomplished at different temperatures. The values of G′ and G″ as functions of angular frequency for a 29 wt % PUD at different constant temperatures in the vicinity of the gel point are shown in Figure 16. The slopes of G′ and G″ vs ω (n′ and

Figure 14. (a) Variation of G′ as a function of angular frequency for a 29 wt % PUD at 60 °C for different constant gelation times. (b) Variation of G″ as a function of angular frequency for a 29 wt % PUD at 60 °C for different constant gelation times.

Figure 16. Dynamic shear moduli, G′ and G″ (solid and open symbols, respectively), for a 29 wt % PUD as a function of angular frequency at different constant temperatures. The x-axis is extended by a factor a, ranging from 1 to 1014, to obtain a valid comparison.

behavior was observed for the frequency dependence of G′ for different gelation times; i.e., G″ increased rapidly with time and frequency and attained a nearly constant value during the late stage of the gelation process, as seen in Figure 14b. The variations of G′ and G″ with angular frequency can be calculated using the power law of eq 8. This behavior is applicable over the entire frequency range. The values of the exponents n′ and n″, obtained from the slopes of the curves G′ and G″ vs ω, respectively, are gelation time dependent. Figure 15 shows the time dependence of n′ and n″ at 60 °C for a PUD with 29 wt % solid content. The values of the two exponents decreased exponentially with time and became identical at the gel point; i.e., at tgel, n′ = n″ = 0.36. The values of the exponents were slightly lower than those obtained for different systems reported in the literature and predicted theoretically using

n″, respectively) were temperature dependent, as expected. In this figure, both G′ and G″ were shifted horizontally by a temperature-dependent factor a to provide a clear comparison of the data and avoid overlap over a wide range of temperatures. G′ (solid symbols) was lower than G″ (open symbols) at T ≤ 60 °C, and both were strongly dependent on angular frequency (i.e., exhibited liquidlike behavior). At T = 65 °C, G′ and G″ overlapped, and at higher temperatures G′ increased more rapidly than G″ (solidlike behavior); both moduli became less dependent on angular frequency, indicating the formation of a fractal gel structure. The exponents n′ and n″ at different constant temperatures can be evaluated from the slopes of each curves of G′ and G″ vs ω, respectively. Figure 17 depicts the temperature dependence of n′ and n″ for a 29 wt % PUD; these values were obtained from the slopes of the curves in Figure 16. One can see that the exponents n′ and n″ decrease strongly with temperature and cross over at the Tgel = 63 °C. At Tgel, both n′ and n″ are identical and equal 0.4, which is slightly lower than the value predicted theoretically from the percolation theory (n = 2/3).50−54

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CONCLUSION Viscoelastic properties of biorenewable, waterborne, castor oilbased polyurethane dispersions (PUDs) were extensively investigated for the first time as functions of solid content, angular frequency, and temperature using small-amplitude oscillatory shear flow experiments. The complex viscosity of the PUDs increased dramatically at a critical volume fraction of polyurethane, ϕc = 0.35, below which the viscosity increased slightly with composition. At this critical concentration the

Figure 15. Exponents n′ and n″ as a function of gelation time for a 29 wt % PUD. The arrow indicates the gel time, tgel. I

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REFERENCES

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Figure 17. Exponents n′ and n″ as a function of temperature for a PUD with 29 wt % solid content. The arrow indicates the gel temperature, Tgel.

particles were very crowded, and the viscosity increase was caused by the hydrodynamic interaction between the different particles. Thermally induced gelation was observed only for PUDs with solid contents ≥27 wt % (here, a dramatic increase in the viscoelastic material characteristics (G′, G″, and η*) at gelation temperature was observed. The kinetics of thermally induced gelation behavior of PUDs was investigated analyzing the real-time evolution of G′, G″, η*, and tan δ at constant temperatures (55, 60, 65, and 70 °C) and angular frequencies for different solid contents. Following the Winter−Chambon model, the value of tgel was determined for PUDs of different solid contents at different constant isothermal temperatures utilizing the point at which all curves of tan δ coincided and were independent of angular frequency. The value of tgel obtained using this method was almost identical to the value determined by the crossover point of G′ and G″ at different angular frequencies. At the early stage of the thermally induced gelation process, the nanodispersed PU particles (∼30 nm) were aggregated. During the intermediate stage of the gelation process, the aggregated particles became interconnected and produced a cluster structure. As the aggregation and interconnection processes continued with annealing time at gelation temperature, larger clusters were formed and interdiffused to form big aggregates, as confirmed by TEM at different gelation times. This gelation process was irreversible, and once the particle aggregates were formed, they were not easily disrupted when the dispersion cooled down to room temperature. The values of the exponents n′ and n″, obtained from the slopes of the curves G′ and G″ vs ω, respectively, were dependent on gelation time and gelation temperature. The values of the two exponents decreased exponentially with time; they were identical at the gel point, i.e., at tgel, n′ = n″ ∼ 0.4, which is slightly lower than the value predicted theoretically using percolation theory (n = 2/3). These biorenewable PUDs exhibited rich and complex viscoelastic behavior and can serve as excellent model systems for more detailed explorations of rheology and macromolecular structure under flow and deformation conditions for other PUDs.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.R.K.). Notes

The authors declare no competing financial interest. J

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