Effect of Index on Curing Kinetics and Viscoelastic Properties of Polyurethane Gels

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1 Effect of Index on Curing Kinetics and Viscoelastic Properties of Polyurethane Gels Lifeng Wu* and Rafael E. Camargo *Contact information: Lifeng Wu, Ph.D. Sr. Technical Specialist Huntsman Polyurethanes 219 Executive Hills Blvd. Auburn Hills, MI USA Tel: Fax: Date of presentation: September 11, 26 "Presented at a meeting of the Thermoset Resin Formulators Association at the Hyatt Regency Montreal in Montreal, Quebec, Canada, September 11 through 12, 26. This paper is presented by invitation of TRFA. It is publicly distributed upon request by the TRFA to assist in the communication of information and viewpoints relevant to the thermoset industry. The paper and its contents have not been reviewed or evaluated by the TRFA and should not be construed as having been adopted or endorsed by the TRFA.

2 Introduction Soft gels have fascinated people for decades due to their unique viscoelastic properties. 1 A gel can be described as a colloidal system with liquid like characteristics. The combination between solid and liquid characteristics in gels leads to various applications, such as energy absorbers, dampers, and adhesives. In particular, they have been used as shoe inserts, bicycle seat cushions, computer keyboard and mouse pads, and some clinical applications. Chemically crosslinked gels can be made from water swelled acrylate polymers, plasticized poly(vinyl chloride), lightly crosslinked silicone fluids, and polyurethanes (PU). Due to the rich selectivity of chemistry, PU gels can be prepared with various schemes: (1) hydrogel, e.g., poly(ethylene oxide) network swelled with water; (2) plasticizer gel, e.g., PU network plasticized with phthalates; (3) polyol gel, e.g., lightly crosslinked PU network with excess multifunctional polyols; and (4) monol gel, e.g., polyol mixture of diol and monol crosslinked with multifunctional isocyanates. 2,3 We focused on polyol gel in this work. The formulation can be simplified as only two components: a multifunctional polyol and a difunctional or multifunctional isocyanate. The index (r) of formulation is defined as the ratio of [NCO]/[OH], where [NCO] and [OH] denote molar concentrations of isocyanate groups and hydroxyl groups, respectively. Viscoelastic properties of polyol gel greatly depend on index, which should be high enough to form a network matrix, and low enough to have many unreacted dangling polyol chains for liquid like relaxation behavior. The index window of polyol gel depends on the functionalities of both polyol and isocyanate. In this paper, we chose a system consisting of difunctional isocyanate (A 2 ) and trifunctional polyol (B 3 ), and studied the effect of index on curing kinetics and viscoelastic properties of cured gels. Experimental Section Materials. Jeffol G31-55, Rubinate 129, and Jeffcat TD-33A were supplied from Huntsman Corporation. Jeffol G31-55 is a trifunctional poly(propylene oxide-b-ethylene oxide) polyol with a total molecular weight of 36. Rubinate 129 is a prepolymer based on diphenylmethane diisocyanate (MDI). Its functionality is slightly higher than 2 and NCO value is The formation of urethane links was catalyzed with.5 wt% of Jeffcat TD-33A for all formulations in this study. Rheology. Curing kinetics was measured on a TA AR-2 rheometer for systems with r = Jeffol G31-55, Jeffcat TD-33A and Rubinate 129 were mixed together for 2 seconds at room temperature, and loaded onto 25 mm diameter parallel plates at 5 C. Storage modulus (G ), loss modulus (G ) and phase angle (δ = tan -1 (G /G )) were immediately monitored at 5 C with 1% strain (γ) and 1 rad/s frequency (ω). The curing time ranges from 2 hours to 5 hours. For each cured sample, dynamic frequency sweeps (.1 6 rad/s) were conducted with 1% strain at 3 C, 5 C and 7 C, respectively. Master curves were built at a reference temperature of 5 C by horizontally shifting isothermal frequency sweep data. 2

3 Results and Discussion 1. Curing kinetics The formulation with r =.4 leads to a viscous liquid, while gels or soft elastomers were obtained for systems with higher indices. This is in a good agreement with branching theory, 4,5 which predicts that the lower limit of index is.5 for an A 2 + B 3 system to form a gel. Figures 1a-f show curing kinetics for r =.5,.6,.7,.8,.9 and 1., respectively. They all exhibit the following similar features. At the beginning of curing reaction, storage modulus (G ) was much lower than loss modulus (G ) such that phase angle δ (= tan -1 (G /G )) was about 9, indicating liquid characteristics of original reaction mixtures. G increased initially and started to level off at about 2 minutes. The initial increase of G reflects the growth of molecular weight. In contrast, G started to grow at about 6 minutes with higher growth rate and crossed over with G before it leveled off. The gel point can be identified by G = G (or δ = 45 ) based on previous experimental works. 6-1 As a result, δ dropped from 9 at about 6 minutes and then leveled off at a certain value, which depends on the index of formulation. For r =.5, δ reached 45 (i.e., G = G ) at the steady state. This behavior can be associated with the formation of critical gel. 1 For r >.5, the system passed the gel point at a certain instant and showed a solid like behavior (small δ) at the steady state. In addition, for r =.9 and 1., G showed a second stage growth after 4 minutes; the mechanism will be discussed later. The evolution of viscoelastic properties from liquid to gel to solid-like behavior agrees well with the formation of network. To understand molecular mechanism of rheological responses during curing, we need to correlate the curing time to reaction conversion (p), which is defined as ([NCO] - [NCO])/[NCO]. [NCO] and [NCO] denote original molar concentration and molar concentration at time t, respectively, for isocyanate groups. A simple kinetic model for the formation of urethane can be expressed as: Solving this equation yields or, d[nco] = k[nco][oh]. (1) dt 1- rp ln( ) = k[oh] (1 r)t, (2) 1- p p e e k[h] (1 r)t = k[h] (1 r)t 1. (3) r Branching theory predicts a critical conversion (p c ) at gel point by index and functionalities (f A and f B ) of components A and B as: p c 1 =. (4) r(f 1)(f 1) A B 3

4 1.E+7 (a) r = E+7 (b) r = E+1 1.E E+1 1.E E E E+7 1.E+1 (c) r = E+7 1.E+1 (d) r = E+ 1.E+ 1.E E E+7 (e) r = E+1 1.E+ 1.E E+7 (f) r = E+1 1.E+ 1.E Figure 1. Time evolution of storage modulus (G ), loss modulus (G ) and phase angle (δ) at indices of (a).5, (b).6, (c).7, (d).8, (e).9 and (f) 1. during curing. For each index, the critical conversion was calculated using Equation (4), while gel time was determined from curing data in Figure 1. As shown in Figure 2, these data fit very well to Equation (2) with k[oh] =.28 min -1. Therefore, we can calculate time evolution of reaction conversion by Equation (3) and, furthermore, the growth of weight average molecular weight (M w ) with time based on Macosko-Miller prediction. 11 Viscosity before gel point plays an important role in processing of gels. Figure 3 compares the initial growth of G at various indices. G nearly overlaps for all systems below 5 minutes; moreover, log(g ) is approximately proportional to time at this initial stage. Because reaction mixtures displayed liquid response (δ = 9 ) at this stage, the zero shear viscosity η = G /ω, where ω = 1 rad/s for all curing measurements in this work. Therefore, the initial viscosity 4

5 4 Ln[(1-rp)/(1-p)] k[h] =.28 min (1-r)t Figure 2. Data fitting of gel time to Equation (2). Solid circles denote gel times determined from Figure 1. Solid line represents the fitting result. (Pa) 1.E+1 r =.5 r =.6 r =.7 r =.8 r =.9 r = 1. r = 1. 1.E+1 (Pa) 1.E+ 1.E+ 1.E E-1 Figure 3. Initial growth of G at various indices. G with r = 1. was also shown as solid squares for comparison. 5

6 grew exponentially with curing time, nearly independent of index. When G started to build up at about 6 minutes, G curves diverged from each other; G grew faster for high index systems. Figure 4 illustrates the initial growth of weight average molecular weight at various indices calculated using Macosko-Miller theory. The time evolution of molecular weight at different indices is consistent with that observed for G. Moreover, as shown in Figure 4, the slope of G is about twice of that for M w, leading to a simple scaling of G (or η ) ~ M w 2. Note that η ~ M for unentangled polymer melts and η ~ M 3.4 for entangled polymer melts. The entanglement molecular weight is about 8 for poly(propylene oxide). For r =.5 1., the initial molecular weight was around 26; the molecular weight passed the entanglement molecular weight at about 4 minutes. Therefore, initial curing data are located in the transition region, where the molecular weight dependence of viscosity changes from 1 to 3.4. The scaling factor of 2 from our limited data is consistent with this transition. Moreover, molecular entanglements can account for the upsurge of G after 6 minutes. Mw (g/mol) 1 1 r =.5 r =.6 r =.7 r =.8 r =.9 r = 1. r = (Pa) Figure 4. Initial growth of weight average molecular weight (M w ) at various indices. G with r = 1. was also shown as open squares for comparison. Note that the scale of G is different with that for M w. The late stage curing is also of interest. For formulations with r =.9 and 1., G data showed a second stage growth (Figures 1e,f), which was not observed for r <.9. The appearance of this post-cure feature can be attributed to high crosslink density. Miller and Macosko predicted, for a system of diisocyanate and triol, that crosslink density (µ) follows the relationship: µ = [OH] (2 ). (5) 2 rp 6

7 Hence, the crosslink density increases with increasing index and conversion. The time evolution of crosslink density was calculated and shown in Figure 5. G data for r =.9 and 1. were also shown for comparison. The late stage growth of G was only observed when the crosslink density was beyond.4.5 mol/l for this curing system. The mechanism will be discussed in terms of relaxation behavior in the next section. 1.8 r =.6 r =.7 r =.8 r =.9 r = 1. r =.9 r = 1. µ.6.4 (Pa).2 1.E+1 1.E Figure 5. Time evolution of crosslink density (µ) at various indices. Curing data of G with r =.9 and 1. were also shown as open triangles and open squares, respectively, for comparison. 2. Viscoelastic properties Figures 6a-f show frequency sweep data at a reference temperature of 5 C for r =.5,.6,.7,.8,.9 and 1., respectively. For all indices, master curves were constructed by horizontally shifting isothermal frequency sweep data at 3 C and 7 C with shift factors (a T ) of 3.6 and.34, respectively. For r =.5.8, frequency scan data at various temperatures superpose very well; whereas time-temperature superposition breaks down for r =.9 and 1.. Based on different viscoelastic properties, cured samples can be classified into three categories: (1) Critical gel for r =.5. G and G show typical relaxation behavior of critical gels: G G ~ ω.5. Critical gels can be characterized by gel stiffness (S) and relaxation exponent (n) as follows: 1 G (ω) = G (ω)/tan(nπ/2) = SΓ(1-n)cos(nπ/2)ω n, (6) where Γ(1-n) is gamma function. For this system, relaxation exponent n =.5, which is consistent with previous studies for some PU gels; 6-1 gel stiffness S is about 35 Pa-s.5, 7

8 indicating that this critical gel is very soft. Both n and S can be further tuned by varying formulation index, molecular weight of precursors or adding non-reacting solvent. 1 (2) Soft gels for r =.6.8. G exhibits a plateau at low frequency regime, indicating the formation of network. The plateau modulus (G ) increases with increasing index, associated with the increase of crosslink density. Interestingly, G data remain nearly unchanged for r =.6.8; these three samples show the same scaling of G ~ ω.5. This indicates that cured samples in this category exhibit the same ability to dissipate energy, even though more crosslinks formed with increasing index. The applied energy can be partially dissipated through the motion of unreacted dangling chains in the network. (a) r = (b) r = (c) r = (d) r = C 7 C 3 C 5 C 7 C 3 C (e) r = (f) r = Figure 6. Master curves of G and G for cured samples at indices of (a).5, (b).6, (c).7, (d).8, (e).9 and (f) 1. at a reference temperature of 5 C. For each index, shift factors (a T ) were 3.6 and.34 for data collected at 3 C and 7 C, respectively. 8

9 (3) Soft elastomers at r =.9 and 1.. Frequency sweep data, especially of G, do not superpose for these two samples. A plateau of G around 2 kpa was observed at 3 C and 5 C in the low frequency region, while, at 7 C, G relaxes faster at high frequencies and then shows a plateau at about 1 kpa at low frequencies. Hence, the frequency dependence of G is very sensitive to temperature at high crosslink densities. The plateau of G can be attributed to much less dangling chains in the network and thus more solid characteristics. However, it is unclear why high index systems show distinct relaxation pattern at different temperatures. More work is required to understand this behavior. Therefore, index plays a very important role in viscoelastic properties of cured samples. The effect of index on rheology can be associated with crosslink density (µ). For this trifunctional crosslinker system, the plateau modulus (G ) of G depends linearly on µ as follows: 1 G = µrt. (7) 2 where R is gas constant and T is temperature. Figure 7 compares the experimental data and theoretical prediction for G at various indices. The theory captures the effect of index on G very well; the prediction follows the same pattern as the experimental data with increasing index. The lower experimental values of G might result from imperfect network structure. 1.E+7 G (Pa) r Figure 7. The effect of index on plateau modulus (G ) of G for cured samples. Solid circles denote experimental data of G, determined from Figure 6. Solid line represents the theoretical prediction based on Equation (7). 9

10 1.E+7 r = 1. 3 min_ 3 min_ 9 min_ 9 min_ 3 min_ 3 min_ Figure 8. The transition of relaxation behavior during curing for r = 1.. On the other hand, the relaxation behavior of G shows a strong dependence of crosslink density at high crosslink densities. Besides the viscoelastic properties illustrated in Figures 6e,f, this behavior was also demonstrated by a second growth process of G in curing kinetics (Figures 1e,f). Figure 8 shows frequency sweeps conducted at different curing times, i.e., different crosslink densities, for r = 1.. At t = 3 min, both G and G exhibit nearly the same relaxation behavior as observed for the cured gel at r =.8 (Figure 6d). Interestingly, the crosslink density was calculated as.34 mol/l at this instant for the r = 1. system, very close to the crosslink density of.36 mol/l for the r =.8 cured sample. As curing time reached 9 min (µ =.64 mol/l), the plateau modulus of G increased while G displayed less frequency dependence than G measured at low crosslink densities. Combined with the curing kinetics shown in Figure 1f, we attributed the second stage growth of G to the reduction of frequency dependence of G at high crosslink densities. As discussed before, the change of G relaxation can be associated with the decrease of dangling chains as crosslink density increases. The sample was further cured for 3.5 more hours (t = 3 min and µ =.76 mol/l), G was nearly unchanged, while G raised up by 2 times. This also indicates that G is more sensitive to the post-cure process than G at high crosslink densities. Conclusion Curing kinetics was rheologically studied for an A 2 + B 3 PU model system with indices r = The initial viscosity grows exponentially with time, nearly independent of the index. After gel point, crosslink density plays an important role in viscoelastic properties. The plateau modulus of G is proportional to crosslink density, while the relaxation behavior of G shows a strong dependence of crosslink density at high crosslink densities. Crosslink density can be 1

11 easily controlled by index (Equation 5). As index increases, cured samples exhibit distinct viscoelastic properties from critical gel, to soft gels, and to soft elastomers. Reference (1) Winter HH, Mours M, Adv. Polym. Sci., 1997, 134, 165 (2) Arendoski CA, US patent 6,98,979, 25 (3) Bleys GJ, Geukens DAE, Verbeke HGG, US patent 6,914,117, 25 (4) Flory PJ, J. Am. Chem. Soc., 1941, 63, 383 (5) Stockmayer WH, J. Chem. Phys., 1943, 11, 45 (6) Chambon F, Winter HH, Polym. Bull., 1985, 13, 499 (7) Winter HH, Chambon F, J. Rheol., 1986, 3, 367 (8) Chambon F, Petrovic ZS, MacKnight WJ, Winter HH, Macromolecules, 1986, 19, 2146 (9) Winter HH, Morganelli P, Chambon F, Macromolecules, 1988, 21, 532 (1) Muller R, Gerard E, Dugand P, Rempp P, Gnanou Y, Macromolecules, 1991, 24, 1321 (11) Macosko CW, Miller DR, Macromolecules, 1976, 9, 199 (12) Miller DR, Macosko CW, Macromolecules, 1976, 9, 26 11

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