In situ curing kinetics of moisture reactive acetoxysiloxane sealant

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Kinetics, Catalysis, and Reaction Engineering

In situ curing kinetics of moisture reactive acetoxysiloxane sealant Jennifer M. Knipe, Justin Sirrine, April M. Sawvel, Harris E. Mason, James P. Lewicki, Yunwei Sun, Elizabeth A. Glascoe, and Hom N. Sharma Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b03396 • Publication Date (Web): 20 Aug 2019 Downloaded from pubs.acs.org on August 28, 2019

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Industrial & Engineering Chemistry Research

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In situ curing kinetics of moisture reactive acetoxysiloxane sealant Jennifer M. Knipe, Justin Sirrine, April M. Sawvel, Harris E. Mason, James P. Lewicki, Yunwei Sun, Elizabeth A. Glascoe, Hom N. Sharma*

Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, California 94550, United States Corresponding Author: *[email protected] Abstract Moisture diffusion and reaction chemistry in polymeric materials affect the mechanical properties, chemical compatibility, and durability of the materials. The ability to model reaction kinetics within materials can facilitate material selection and predict long-term performance. In this study, low field nuclear magnetic resonance (NMR) T2 relaxometry and magnetic resonance imaging (MRI) were used to measure the curing kinetics of a commercially available water-reactive silicone adhesive material. Relaxation times were measured at four different temperatures from 25–60 °C and three different water vapor concentrations. The single-step autocatalytic Sestak-Berggren (S-B) reaction model was used to model the reaction kinetics. An activation energy of 3.7 kJ/mol was estimated using the S-B model and confirmed by isoconversional analysis. The cure rate was found to vary with water vapor concentration, and an empirical linear relationship between water vapor concentration and the kinetic rate constant was determined. MRI was used to corroborate the autocatalytic reaction model. Introduction Room-temperature vulcanizing (RTV) silicones are polymers that undergo crosslinking, or curing, upon exposure to ambient temperature and humidity. They are commonly used as sealants, adhesives, coatings, and molds1–4 and the water vapor sorption and curing kinetics are of interest to many industries including electronics, automobile, and aerospace. The reaction kinetics can be complex due to dynamic change in material morphology and property during the curing process. Such variation can impact the kinetics of the actual reaction (for example: diffusional limitations due to cured material5,6). A deeper understanding of moisture diffusion and reaction kinetics within RTV

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2 materials is critical to understanding performance of these materials in a wide variety of applications7,8 and may also be instrumental in predicting curing time, aging effects, and long-term performance of the material. Kinetic data are particularly advantageous if it is collected in situ in relevant reaction conditions without destroying the sample. Recently, there have been some studies utilizing in situ techniques to understand moisture reactions involving diffusion through polymers. In one example, Selim et al. investigated the reaction kinetics of the degradation of water-soluble carotenoids from saffron, a spice with many culinary and therapeutic applications, that were encapsulated in amorphous polymers.8 The degradation was monitored as a function of water activity by using UV-Vis spectroscopy to periodically measure the absorbance of the material. Since the experimental conditions matched those typical of storage and shelf life, the data were directly translatable to assessments of the product stability over time. In a different study, Bauer et al. evaluated the moisture-reactive cure of polysilazanes, preceramic polymers, over several hours using FT-IR to elucidate the effect of temperature, relative humidity, and catalyst concentration.9 Non-destructive and non-perturbative analysis methods such as FTIR and UV-Vis are valuable techniques because they can produce a comprehensive data set as a function of time. In this work, we investigate the curing of a commercially available moisture-reactive alkoxysilane silicone, RTV 734. As RTV 734 cures, the acetoxy groups react with water to form a crosslinked silicone network and release acetic acid as a by-product according to Figure 1.

Figure 1: Schematic of silicone with acetoxy groups undergoing hydrolysis with water vapor, followed by condensation reactions to form a crosslinked silicone polymer network, or gel. Though researchers have investigated the curing thickness as a function of time by sacrificing samples at periodic timepoints10,11, this reaction lends itself well to in situ experiments as the curing takes place on the order of hours to days at ambient temperature and humidity conditions.


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3 Here, we use low field nuclear magnetic resonance (NMR) T2 relaxometry, a rapid, non-destructive technique that has previously been used to study sol-gel kinetics during in situ polymerization and curing12 to quantify the curing kinetics of RTV 734. Magnetic resonance imaging (MRI) is an imaging application of T2 relaxometry that provides non-destructive, spatial visualization of the internal structure and processes of materials13–15; we utilized this technique to monitor the curing front progression through RTV 734 over time. Experimental Section Materials All reagents were used as received without further purification. Potassium sulfate (≥ 99.0 %), sodium chloride, and magnesium chloride were purchased from Sigma Aldrich. Dow Corning® RTV 734 Flowable Sealant (Dow Chemical, Midland, MI) was purchased from Grainger. Wilmad 10 mm 7” Time-Domain NMR tubes with flat bottom were purchased from Wilmad-LabGlass (Vineland, NJ). Hygrochron® iButton Temperature/Humidity Loggers, a USB-to-1-wire RJ11 adapter, and a 1-wire network cable were purchased from Maxim Integrated (San Jose, CA). The OneWireViewer software package was downloaded from the Maxim Integrated website. Controlled Humidity The humidity for these experiments was controlled by flowing air equilibrated at room temperature with various saturated salt solutions, shown in Figure 2. The relative humidity (RH) and air flow rate were calibrated by flowing the humidified air into a 20 mm outer diameter (OD) NMR tube and using Hygrochron® iButton Temperature/Humidity Loggers placed in the vapor phase of the saturated salt solution chamber and in the tube to measure and record the temperature and humidity every 2 minutes, with a temperature-humidity correction applied as specified in the DS1923 Hygrochron® manual. Prior to the experiments, the RH of the vapor phase of each salt solution and the temperature was measured at 23.3 °C (room temperature) with air flow through the headspace. The measured relative humidity of the saturated solution vapor phase of K2SO4 was 88.2% RH, NaCl was 72.7% RH, and MgCl2 was 35.3% RH at, corresponding to water vapor concentrations of 1.00, 0.75, and 0.40 mol/m3. Since the RH may fluctuate during experiments of this duration or vary from experiment to experiment, the humidity data



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4 from the room temperature (23°C) vapor phase of the solutions collected every two minutes during experiments was used to calculate the average water vapor concentration for each solution across all experiments as well as the standard deviation from the mean during a single experiment and between all experiments for each salt solution. The average water vapor concentrations of K2SO4, NaCl, and MgCl2 were 1.010, 0.756, and 0.398 mol/m3, respectively; the standard deviations within a single experiment were 0.008, 0.007, and 0.009, respectively; and the standard deviations between experiments using the same salt solution were 0.005, 0.030, and 0.040, respectively. These concentrations are very close to those calculated from the RH of the salt solution vapor phases prior to the curing experiments. The standard deviation from the average during a single experiment is quite low as we would expect, while there is slightly greater variability in the concentration from experiment to experiment. The RH measurements in the vapor phase of the salt solution and in the tube typically matched within ±0.2%, indicating that the air flow rate was sufficient to equilibrate the tube with the saturated salt solution water vapor density. The time to reach equilibration was typically less than 5 minutes; we expect the equilibration to be even faster within a 10 mm OD tube although we could not verify this as the iButton loggers did not fit in the smaller tube.

Figure 2: A schematic of the experimental setup. The humidity was controlled by flowing air through the headspace of a saturated salt solution, then down into the NMR tube containing the sample. The sample was inserted into a Bruker Minispec to take the T2 measurements as a function of cure time. The temperature was controlled within the Minispec by an attached circulating water bath. NMR Sample Preparation


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5 To set up the T2 relaxometry experiments, RTV 734 sealant was injected into the NMR tube using a syringe and flexible plastic tubing. Care was taken to deposit the sealant at the bottom of the tube without contaminating the sides of the tube, while also minimizing bubbles in the sealant. The same new tube of sealant RTV 734 was used in all experiments. To ensure the water content of the sealant was minimized, ~1 ml of the material near the opening of the sealant tube was discarded prior to injecting the sealant into the syringe. After sealant deposition, the NMR tube with the sample of RTV 734 was inserted into the NMR spectrometer sample chamber such that the sample (~5 mm in height) was centered in the coil, and then allowed to equilibrate at the analysis temperature for 2 min. Temperature control for the sample chamber was provided by an attached Julabo F32 circulating water bath. Then the NMR tube was uncapped and tubing flowing the air humidified by room temperature saturated salt solution was placed into the glass NMR tube, leaving a ~ 0.5 cm gap between the tubing and the sealant-air interface. The top of the glass NMR tube was only loosely capped in order to allow the air flow out and dissipate the generated acetic acid. Low Field NMR T2 Relaxometry A low field Bruker mq20 Minispec™ (Billerica, MA) permanent magnet 1H NMR spectrometer provided spin-spin relaxation (T2) measurements as a function of time. The instrument employed the Carr-Purcell-Meiboom-Gill (CPMG) spin echo method.16 The 90° - 180° pulse separation (τ) was set to τ = 0.5 ms and other acquisition parameters were tuned automatically with the Minispec software using a 10 mm time-domain NMR tube with ~ 1 cm of completely cured RTV 734 sealant at the bottom; these values include 90° pulse length of τP = 2.16 μs and recycle delay of 2 s and were held constant across all experiments. The number of data points used for fitting each measurement was set at 1000 to provide a good fit for the entire T2 decay curve range. T2 values were obtained by fitting the series of decay curves with a biexponential fit. T2 measurements were the taken at variable time intervals (from 30 seconds to 30 minutes) over a total time period of 24 hours. The T2 measurements were taken at sample temperatures of 25, 30, 40, and 60 ±0.1 °C and water vapor concentrations of 1, 0.75, and 0.4 mol/m3. The relative humidity in the vapor phase of the saturated salt solution



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6 was measured every 2 minutes throughout the experiment using an Hygrochron® iButton Temperature/Humidity Logger. The saturated salt solutions were maintained at room temperature (23 ± 1.2 °C), allowing highertemperature T2 measurements to be obtained at constant water vapor density. Therefore, the measured 88.2 % RH at 23.3 °C in the vapor phase of the saturated K2SO4 solution corresponds to 82.8% RH at 24.3 °C, 59.8% RH at 30.1 °C, 35.0% RH at 40.6 °C, and 14.9% RH at 60.5 °C assuming a constant water vapor density of 18.4 g/m3. The RH within the 20 mm OD tube was also measured at the various temperatures used in the experiments and was found to be in good agreement with theoretical values at 84.2% RH, 55.6% RH, 35.6% RH, and 13.2% RH, respectively. Spatially-resolved T2 (MRI) experiments were performed on a Bruker (Billerica, MA) Avance 400 MHz spectrometer equipped with a high-resolution Micro2.5 microimaging system with a 25 mm RF coil. Twodimensional T2 weighted images were collected using the multi-slice multi-echo (MSME) protocol from Bruker. The field of view (FOV) was 15 mm by 15 mm with a resolution of 0.167 mm/pixel by 0.167 mm/pixel. The slice thickness was 0.5 mm. A total of 24 echo times were measured ranging from 3.43 ms to 82.34 ms. A repetition time of 3 s was used, and four averages were collected for a total time of 18 min. Results & Discussion Relaxometry Analysis of Siloxane Cure RTV 734 is a commercially available moisture-reactive acetoxysilane sealant that cures within hours to days at ambient temperature and humidity.17 The curing reaction is shown schematically in Figure 1. The crosslinked silicone network forms by a two-part reaction: first the hydrolysis of the acetoxy groups followed by the condensation of the hydrolyzed species. Generally, the hydrolysis reaches completion before condensation occurs as the fully-hydrolyzed species are typically much more reactive than partially-hydrolyzed species.18 Thus, the polycondensation is expected to be the rate-limiting step of the curing reactions. During the curing process, the RTV 734 sealant changes physically from a viscous solution (sol) to a crosslinked gel. As shown in Figure 3A, the curing progresses away from the sealant-air interface. The reaction quickly occurs


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7 at the interface of the sealant and the water vapor, creating a cured layer or “skin” that the water vapor must then diffuse through to reach unreacted sealant. Additionally, the condensation reaction produces both water and acetic acid products that may catalyze the reaction. This chemistry creates a complex diffusion-reaction process for which it is difficult to separate the two mechanisms experimentally.

Figure 3: A) As the RTV 734 curing reaction progresses, the material changes from a sol to a gel and water vapor must diffuse through the layer of cured gel to react with the uncured sol underneath. B) Representative plot of relaxation decay curves for a single sample as cure time progresses. As the material cures from sol to gel the relative



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8 amplitude decreases more sharply. C & D) Representative graphs of the biexponential fit (dashed line) of the relaxation decay curve (solid line) at C) cure time=0 and D) cure time=24 hours. In this study, low field nuclear magnetic resonance (NMR) T2 relaxometry was used as a rapid and non-destructive technique to probe the curing kinetics of RTV 734 in-situ. The relationship between T2 relaxation time and polymer dynamics is well-established19,20 and low field relaxometry has been used to quantify changes in elastomer dynamics as a function of curing, thermal and irradiative aging, and mechanical stress21–24. In the techniques used here, an initial radio frequency (rf) pulse is applied followed by a train of pulses that refocus the magnetization into a series of echoes. The intensity of these echoes decays over time with a time constant T2 as magnetization is transferred to neighboring spins via residual 1H-1H dipolar couplings that arise from the restricted motion of topologically constrained polymer chains.21 In elastomeric materials the transverse relaxation time, T2, is directly proportional to segmental chain dynamics with longer, more mobile chain segments resulting in longer T2 relaxation times.25 When the mobility of a system changes as a function of time, as in the case of increased chemical and physical crosslinking during RTV 734 curing, the T2 response will reflect the global change in motional dynamics within the system. Thus, T2 relaxometry can be used to measure polymer degree of curing as a function of cure time. It can also be used in a similar way to indicate network structure such as cross-link density and defects26, making it a useful in situ tool for understanding the effect of water vapor on reaction kinetics as well as mechanical properties. An example of a set of typical relaxation decay curves for a single sample obtained over 24 hours of cure time is shown in Figure 3B. Changes in T2 can be rendered two-dimensional with T2-weighted magnetic resonance imaging (MRI), resulting in spatial visualization of the internal structure and processes of materials13–15. Complex samples, such as a partially cured material, often result in a distribution of relaxation times within a single sample. The result is a multi-exponential relaxation decay curve that reflects the heterogeneous distribution of relaxation rates within the system. In the biexponential fit of the relaxation curves plotted here, we observed a rapid relaxation decay that occurs between 0 and 2 ms in addition to a much slower relaxation decay that occurs between 40-200 ms, depending on the cure time. The rapid decay is attributed to coupled network chains with restricted motion such as those that are physically or chemically cross-linked, while the longer decay times are attributed to


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9 uncoupled, rapidly rotating chains such as those from unreacted chain groups or dangling chain end defects that persist after chemical cross-linking occurs. These T2 relaxation times are in good agreement with literature values, with reported T2 of cured polymers being on the order of 0.1-1 ms27,28 (the rapid relaxation decay) and reported T2 of uncured sols being on the order of 100 ms (slower relaxation decay).29 As the curing reaction proceeds the contribution of the longer relaxation decay component decreases significantly with relaxation decay curves at the reaction end-point approaching mono-exponential relaxation behavior. To quantify changes in the T2 relaxation times as a function of cure time of the RTV 734, we empirically applied a biexponential fit to each decay curve, where one exponential represents the uncured solution contribution and one exponential represents the cured, crosslinked polymer network contribution, as shown in Equation 1. Although this oversimplifies the contributions to the relaxation decay curves during the complex RTV 734 curing process, the biexponential model fits the data quite well, suggesting that the relaxation times are dominated by the sol-gel contributions. Therefore, we feel that our analysis validates these assumptions and this biexponential analysis and assignment of sol and gel parts has been used by other researchers to model the relaxation times during polymer crosslinking29,30 Furthermore, we investigated other relevant models and the fitting information is provided in Supporting Information.

𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 = 𝑦0 + 𝐴1exp

[ ]

[ ]

―𝑡 ―𝑡 + 𝐴2exp 𝑇2,1 𝑇2,2

(1) The pre-exponential terms A1 and A2 represent the fraction of the sol and gel components, respectively, T2,1 and T2,2 are the relaxation times of the sol and gel components, and t is the decay time of the curve. Note that in our notation the subscript 1 represents the uncured solution and subscript 2 represents the cured gel. We also assumed that the sol and gel components of the biexponential fit comprised 100% of the T2 contributions and thus fixed the sum of the pre-exponential parameters to 1, shown in Equation 2 where

𝐴1 + 𝐴2 = 1


(2)


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10 All fits of the decay data had R2 values greater than 0.98 suggesting that these assumptions were valid and the biexponential fit represented the data well. An example of fitted data is shown in Figures 3C and 3D and a representative plot of residuals is shown in Figure S2. However, the mean squared error (MSE) of the residuals changes as the cure time progresses, indicating that different models may fit the data better at various points in the curing reaction. Typically, we saw MSE range from ~0.03-0.40 at 25 °C, ~0.02-0.5 at 30 °C, ~0.02-0.5 at 40 °C, and ~0.1-1 at 60 °C, and in general the MSE was smallest at short cure times, increased as the cure point was approached, and then slightly decreased at longer cure times past the cure point. Vargas et al. noted that the best fit may shift from biexponential at shorter cure times to mono-exponential at longer cure times, and therefore used a stretched exponential fit to account for the distribution of relaxation times during the curing process.31 The stretched exponential model did not converge for our long cure time data unless the exponential term was fixed to 1, reducing it to a mono-exponential fit that was worse than a biexponential fit (R2 ~0.7-0.8 and MSE ~1-2, see representative data in Figure S3). Thus, we feel that for our data the biexponential function is an appropriate model to extract the relaxation times from the decay curves. The weighted average of the sol and gel T2 values from the biexponential fit was then calculated for each timepoint during the curing time according to Equation 3.

𝑇2,avg = 𝐴1𝑇2,1 + 𝐴2𝑇2,2

(3)

The parameters from the biexponential fit of a representative sample condition (1 mol/m3 water vapor concentration, 25 °C) are shown as a function of cure time in Figure S1. T2 can then be converted to the degree of cure, α, of the sealant by assuming a linear dependence between α and the relaxation rate, 𝑇2―1, and normalizing according to ―1 ―1 ―1 Equation 4, where 𝑇2,min is the minimum value of 𝑇2,avg (i.e., at the start of the reaction) and 𝑇2,max is the maximum ―1 value of 𝑇2,avg (i.e., at the end of the reaction).

―1 ―1 𝑇2,avg ― 𝑇2,min

𝛼 = 𝑇 ―1

2,max

― 𝑇2,―1min

(4)


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11 Figure 4A shows plots of the weighted average 𝑇2,avg at four different reaction temperatures as a function of cure time, and the fitted preexponential parameters A1 and A2 are plotted as a function of cure time in Figure 4B. Experimental data points are not shown on these plots because the curves are an average of three data sets; the standard deviation of 𝑇2,avg is shown by the dotted lines in Figure 4A. Since the deviation was quite small it was not shown on all plots for the sake of clarity but is shown in Figure S1. As expected, we observed a dramatic decrease in 𝑇2,avg from 70-50 ms (depending on reaction temperature) at the start of the reaction to a final 𝑇2,avg converging at a value of ~8 ms for all reaction temperatures. The preexponential parameters A1 (dashed lines) and A2 (solid lines), which represent the sol and gel fraction, respectively, begin around 60%/40% and plateau at approximately 10%/90%. We would not expect the RTV to reach 100% gel since there will be dangling unreacted chains, dissolved reaction products, filler, and possibly artifacts such as internal T2 gradients at polymer-filler interfaces that will affect the final 𝑇2,avg in the cured material.[22-24] As the biexponential fit of the decay curves and the corresponding two-component sol/gel interpretation is a simplified analysis of a likely much more complex system, it was encouraging that the fitted parameters agree reasonably with what we would physically expect in a sol/gel system, justifying our method of analysis. Figure 4C shows the reaction progress in terms of the degree of cure. The cure point is defined as the point in time when the RTV 734 sealant has reacted sufficiently to form a crosslinked, gel network during the curing process12, represented graphically by the point in time when the slope of 𝑇2,avg versus cure time approaches 0 or the degree of cure reaches 1. As shown in Figure 4D, for all reaction temperatures the cure point is between 17-19 hours. The cure point shows a small (approximately 2 hours) but noticeable increase at elevated temperatures. However, this may be an artifact of increased molecular mobility causing longer T2 times. Other researchers have also observed an apparent increase in the cure point with temperature in relaxation time data of condensation polymerization reactions, and have used calorimetry to monitor and explain this observation as an artifact that arises from increased molecular mobility of the molecules at higher temperatures.12 Temperature has competing effects on the relaxation time: higher temperature causes faster curing that decreases the relaxation time, but it also increases the mobility of the protons, thereby increasing the relaxation time. It is not possible to deconvolute these competing effects from



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12 relaxation time data alone, but we would expect the effect of temperature on mobility to dominate in condensation polymerization reactions nearly until the cure point is reached, and the cure point is known to occur at a high degree of cure (>0.9) for this type of polymerization. The degree of cure, , is calculated here as normalized, average T2 values in an attempt to account for molecular mobility changes that occur at elevated temperature. Although it is possible that the observed increased cure time is an artifact, our normalized data suggests that the slight increase in cure time as a function of temperature is a real phenomenon; however, calorimetry experiments are necessary to definitively determine the effect of temperature on the cure point.


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13 Figure 4: A) The weighted average NMR relaxometry time T2, B) the preexponential terms A1 (dashed) and A2 (solid) and C) the degree of cure α as a function of cure time for RTV 734 cured at four different temperatures and D) the cure point as a function of temperature. Kinetic Model of Moisture-Reactive Cure The kinetic parameters of the curing reaction can be determined by fitting the data to a generalized rate equation. It should be noted that this is an approximation where a sole single-step kinetics equation, Equation 5, is used to describe a complex set of kinetic equations32; in the case of RTV sealant curing, the hydrolysis and condensation kinetic equations are approximated by this single-step kinetics equation

𝑑𝛼 = 𝑘app(𝑇)𝑓(𝛼) 𝑑𝑡

(5)

where dα/dt is the cure rate, kapp is an Arrhenius-type apparent kinetic rate constant that varies with temperature and f(α) is a function that represents the reaction mechanism. We attempted fitting our data using various kinetic models for f(α) commonly cited in literature, including 1D, 2D, and 3D diffusion models, the Prout-Tompkins model, the Johnson-Mehl-Avrami model, and the Sestak-Berggren model.33–35 We found that the two-parameter Sestak-Berggren (S-B) autocatalytic kinetic model given by Equation 636 was the only model that represented the shape of the cure rate versus degree of cure curves, shown in Figure 5A. This model is used to describe reactions for which the maximum rate of cure occurs at a degree of cure greater than zero because one or more of the reaction products act to further propagate the reaction,37,38 as is the case for our data. In this model, m and n are fitted parameters that represent the initiation reaction order and the propagation reaction order, respectively. It should be noted that this is a semi-empirical model and gives no mechanistic insight into the reaction steps. The S-B autocatalytic model has been used to describe the kinetics of many curing reactions, including crosslinking of vinyl-terminated PDMS 37, curing of a polyester resin 31, curing of an epoxy resin33,39,40, and crosslinking of carboxyl-terminated poly(acrylonitrile-co-butadiene). 41



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14

d𝛼 𝑛 = 𝑘app𝛼𝑚(1 ― 𝛼) d𝑡 (6) The kinetic parameters 𝑘app, m, and n were calculated by nonlinear regression analysis of d𝛼/dt versus 𝛼. The fitted curves are shown as the dashed lines in Figure 5A and represent a good fit to the experimental data, with R2 > 0.99 for all temperatures. The 30°C data was omitted from the plot for the sake of clarity as it so closely matched that of 25°C. As expected, the rate of cure increases with temperature while the induction period, or the time until the minima in cure rate between degree of cure 0-0.1 is reached, decreases. 31 Prior to the induction point, the cure rate is higher at lower temperatures but following the induction point the cure rate is higher at higher reaction temperatures. This again highlights the complexity surrounding mobility, temperature, and relaxation times, with the induction point indicating a shift in the relaxation time from mobility-dominated to reaction-dominated. At very high degree of cure (>0.9) the cure rates begin to converge, as the reaction is dominated by the crosslink density and gelation of the sealant and temperature no longer has an effect.

Figure 5: A) Cure rate versus the degree of cure of RTV 734 sealant at three different reaction temperatures. B) The Arrhenius plot of the natural log of the kinetic rate constant versus 1/T shows a linear relationship; the energy of activation of the reaction was calculated from the slope of this plot.


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15 Since changing the values of m and n shift the peak of the cure rate left and right while 𝑘app shifts the amplitude of the peak, based on our experimental data it seemed that m and n are likely to be constant or nearly constant while the value of 𝑘app varies with temperature. Fitting the model to our data confirmed that m and n varied slightly over the range of temperatures tested, as shown in Table 1. The order m varied by ±2% from the mean while n varied by ±1.5% from the mean, both of which are relatively small ranges. Using this autocatalytic model, other researchers have observed that m and n were temperature-dependent for curing of vinyl polysiloxanes

37

and curing of a

polyester resin31 by free-radical polymerization, and varied as much as 30% from the mean. However, Cho et al assumed that n was constant with temperature over a range of 25 ― 100 °C, and found that 𝑘app and m increased with temperature for the UV-initiated cationic photo-polymerization of cycloaliphatic diepoxide.38 In our analysis, m and n varied so little with temperature that they may be assumed to be constant and good fits of the data to the autocatalytic model are still obtained; this is reasonable because we would not expect the reaction order n to vary with temperature, although it is possible that the reaction order m could vary with temperature. Table 1: Fitted parameters of RTV 734 sealant cured at three temperatures with constant water vapor concentration (1 mol/m3) Fitted Parameter

25 °C

40 °C

60 °C

(value ± S.D.)

(value ± S.D.)

(value ± S.D.)

𝑘app

0.632 ± 0.006

0.685 ± 0.003

0.739 ± 0.006

m

1.781 ± 0.011

1.727 ± 0.005

1.719 ± 0.009

n

0.512 ± 0.004

0.518 ± 0.002

0.529 ± 0.004

R-Square

0.994

0.997

0.992

Isoconversional Analysis The apparent kinetic rate constant 𝑘app varied with temperature and follows a linear Arrhenius relationship, as shown in Figure 5B.



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16

𝑘𝑎𝑝𝑝 = 𝐴exp

―𝐸𝑎

[ ] 𝑅𝑇

(7)

where A is the preexponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature, and Ea is the reaction activation energy. From the slope of the line in Figure 5B, the activation energy was calculated to be 3.7 kJ/mol. The activation energy was corroborated using the Friedman method of isoconversional analysis, which is independent of a reaction model under the assumption that the extent of conversion is a function of temperature only.35,42 In this analysis, the cure rate depends on the rate constant, k, which is a function of temperature, T, and some unknown function of the degree of cure, f(α), shown in Equation 5. The equation can then be written in terms of the activation energy, Ea, according to the Arrhenius relationship given in Equation 7 to arrive at Equation 8. Equation 9 is reached by taking the natural log of Equation 8, and by plotting ln

( ) d𝛼 d𝑡

versus

1 𝑇

the activation

energy can be determined from the slope of the resulting line at each value of the degree of cure, α. Thus, we obtained Figure 6, showing the activation energy as a function of the degree of cure, or α. As expected, the activation energy depends on the degree of cure but is generally within the range of 3 ― 8 kJ/mol, which is in good agreement with the fitted reaction model analysis. ―𝐸𝑎 d𝛼 = 𝑓(𝛼)𝐴exp 𝑅𝑇 d𝑡

[ ]

ln

𝐸𝑎 1 d𝛼 = ln [𝑓(𝛼)] ― ∙ 𝑅 𝑇 d𝑡

( )


(8)

(9)

Page 17 of 29

17 Equation Plot

Activation Energy, Ea (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Weight

12

Intercept

10

Activation Energy, \i(E\-(a)) No Weighting -34.55813 ± 1.50928

B1

483.61126 ± 20.70701

B2

-1955.32072 ± 101.16303

B3

3514.31051 ± 224.58101

B4

-2941.11842 ± 230.5898

B5

942.02169 ± 88.8328

Residual Sum of Squares

8

y = Intercept + B1*x^1 + B2*x^ 2 + B3*x^3 + B4*x^4 + B5*x^5

1031.51581

R-Square(COD)

0.74658

Adj. R-Square

0.74502

6 4 2 0 -2 -4 0.0

0.2

0.4

0.6

0.8

1.0

Degree of Cure ()

Figure 6: Activation energy of the RTV 734 curing reaction as a function of the degree of cure as determined by Freidman isoconversional analysis. The red dashed line is a fifth order polynomial fit to guide the eye. Effect of Moisture Concentration We also conducted isothermal experiments while varying the water vapor concentration at the interface with the RTV 734 sealant. When comparing the reaction at different water vapor concentrations, there is a noticeable difference in the T2 during the cure. Figure 7 shows T2, A1, A2, and degree of cure as a function of cure time of three reactions carried out at 60 °C with three different water vapor concentrations; as the water vapor concentration increases the cure point decreases, shown in Figure 7D.



Page 18 of 29

18

Figure 7: A) The weighted average NMR relaxometry time T2, B) the inverse T2-1, and C) the degree of cure α as a function of cure time for RTV 734 sealant cured at 60 °C with three different water vapor concentrations and D) the cure point as a function of temperature. The cure rate versus degree of cure of isothermal experiments is shown in Figure 8A, and the data again suggested that m and n are nearly constant while the maximum cure rate increased dramatically with water vapor concentration. Again, we would not expect the reaction order n to vary with water vapor concentration but it is possible that water vapor concentration could affect the reaction order m if water induces the autocatalytic effect, though our results indicate the influence of water vapor concentration on m is likely negligible. The model fits, shown by the dashed lines, again resulted in values of m and n of ~1.7 and ~0.52, respectively, and varied only


Page 19 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


19 slightly with water vapor concentration as shown in Table 2. The apparent kinetic rate constant k varied approximately linearly with water vapor concentration as shown in Figure 8B. Therefore, an empirical relationship for the true rate constant, k, may be given by kapp/CH2O,0, where CH2O,0 is the water vapor concentration and thus the slope of kapp versus CH2O,0 is equal to k. This results in the autocatalytic model taking the form shown in Equation 10, where k= 0.756 ±0.076 m3/mol-1hr-1over the range of concentrations tested at 60 °C. Similar results are shown for data taken at 25 °C in Figure S2.

d𝛼 𝑛 = 𝑘𝐶H2O,0𝛼𝑚(1 ― 𝛼) d𝑡 where 𝑘 = 𝐴exp

―𝐸𝑎

[ ] 𝑅𝑇

(10)

Figure 8 A) Isothermal cure rate versus the degree of cure of RTV at three di

fferent water vapor concentrations. B) A plot of the apparent kinetic rate constant versus water vapor concentration shows a linear relationship, suggesting a diffusion component dependent on the water vapor concentration.



Page 20 of 29

20 Table 2: Fitted parameters of RTV 734 sealant cured at three water vapor concentrations at constant temperature (60 °C) Fitted Parameter

1.00 mol/m3 water vapor



(value ± S.D.)

(value ± S.D.)

(value ± S.D.)

kapp

0.738 ± 0.006

0.590 ± 0.023

0.296 ± 0.002

m

1.716 ± 0.009

1.710 ± 0.036

1.711 ± 0

n

0.528 ± 0.004

0.510 ± 0.017

0.520 ± 0.005

kc=kapp/CH2O,0

0.738

0.787

0.722

R-Square

0.992

0.994

0.979

However, since the kinetic rate constant should only be a function of temperature, the dependence of kapp on water vapor concentration indicates that the reaction is limited at some point by diffusion of the water vapor, which is expected given the necessity of water vapor diffusion through cured material shown in Figure 3A. Therefore, we examined the incorporation of a diffusion component kdiff as well as a kinetic component kchem into the rate constant term kapp, shown in Equation 11. According to this expression, when the reaction rate is much faster than the diffusion rate and kchem >> kdiff, kapp ≈ kdiff and diffusion is limiting.

𝑘app =

𝑘chem𝑘diff 𝑘chem + 𝑘diff

(11)

The term kdiff is a function of the degree of cure, α, since as the curing progresses the increased crosslink density and viscosity of the sealant affect the diffusion rate. Chern and Poehlein derived from polymer free volume theory a relationship to describe kdiff as a function of the degree of cure5, shown in Equation 12, and Cole et al.6 subsequently combined this with Equation 10 to arrive at the expression for kapp shown in Equation 13, where kchem is dependent on temperature according to the Arrhenius relationship given in Equation 7.

𝑘diff = 𝑘chemexp[ ―𝐶(𝛼 ― 𝛼c)]


(12)

Page 21 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


21

𝑘app =

𝑘chem 1 + exp[ ―𝐶(𝛼 ― 𝛼c)] (13)

In the Cole-Poehlin model for kapp given by Equation 13, the diffusion component of the rate constant is activated once a certain degree of cure 𝛼c, is reached such that the chain entanglements or crosslinks reach a density that impacts the diffusion coefficient. The term C is a constant that depends on the material properties, structure, and curing temperature.43 This model has been used to describe the curing kinetics of epoxy amine resins6 and polyester resins31, and a similar approach derived by Russell and Kardos44 from the dependence of viscosity on cure time to model the dependence of kdiff on α during the curing of polyimides.45 However, for all of our data the fits indicated that the constant C, a measure of the dependence on the diffusion term, went to zero with large error or did not converge at all. Thus, the fits of this model to the data are inconclusive and the semi-empirical model given by Equation 10 remains the best representation of our data. Transient NMR Imaging Although there is a known dependence of T2 relaxation time on elastomer cross-link density, bulk T2 relaxation times are also influenced by factors such as changes in the dynamic order parameter (Sb) and internal magnetic susceptibility and internal T2 gradients that arise from changes at polymer-filler interfaces and/or void spaces in the polymer matrix.22,46,47 In-situ T2-weighted MRI was used to visualize the reaction front progression through the sample and to verify the presence of two distinct T2 relaxation regimes within RTV 734 sealant while curing in ambient temperature and relative humidity conditions (Figure 9A). A video of the cure progression over time can be viewed in the Supporting Information. The panel of images represent a vertical cross-section (0.5 mm slice) through the center of a 10 mm diameter sample taken at various times throughout the curing process. A total of 12 vertical slices were collected at each time point to cover the entire cross-section of the sample and the center slice shown here was determined to be representative of the curing profile present in the entire sample. For a condensation reaction, it is well known that the transition from solution to gel is very sudden and distinct. This is consistent with the T2-weighted MRI images shown here which display a sharp contrast between the cured portion of the sealant (blue) and the uncured portion of the sealant (yellow/red). The uncured portion of the material has a T2 relaxation



Page 22 of 29

22 time of 40-45 ms while the cured portion has a T2 relaxation time of 12 ms, which is comparable to the T2 values obtained from the NMR experiment at 25 °C. We note that the MRI experiment was run at ambient temperature and humidity, so we expect the cure rate to be much slower than the NMR experiments in which humidity was provided. The clear presence of a slow T2 regime related to the gel portion of the network and a fast T2 regime related to the solid portion of the network in the MRI data validate our assignment of two T2 values used in the fitting of our bulk T2 data above. This experiment is also an excellent example of the utility of spatially-resolved T2 relaxometry as a tool to monitor the progress of curing reactions over time, and its advantage over other experimental techniques, such as manually measuring the thickness of cured samples, which may be subject to error introduced by compression by calipers or nonuniform curing and artifacts during curing, as some reports have noted.48 Since there is no gradient of T2 values between the cured and uncured RTV sealant, we can infer that there is little change in the molecular mobility (related to the chain length and crosslinking density) until the sample reaches the gel point at a high degree of cure. Thus, we would expect that for this type of polymerization the diffusion constant would not be greatly affected until the gelation point is reached, which may explain why the model incorporating a diffusion component into the reaction rate constant (Equation 14) failed to result in a good fit to our data.


Page 23 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


23 Figure 9: A) T2-weighted MRI images of RTV 734 taken in-situ; the panel of images shows the representative center cross-section of the sample at four timepoints during the curing experiment (t = hours of cure time); B) Thickness of cured portion of sample versus (cure time)1/2 determined from the spatially resolved T2 data. From the spatially resolved T2 data, we measured and plotted the thickness of the cured silicone sealant as a function of the square root of cure time, shown in Figure 9B. According to the curing model for moisture-cured siloxanes reported by Comyn et al., shown in Equation 14, a linear relationship is expected between cured thickness, z, and time1/2 in a diffusion-limited reaction where the rate of hydrolysis and condensation reactions, once moisture reaches the polymerization front, is much faster than the rate of moisture diffusion through the cured portion of the sealant.10 The slope of cured thickness versus t1/2 is thus (2VPp)1/2, where the volume of sealant that reacts with one mol of water, V, is not dependent on temperature and the permeability of water in the cured sealant, P, is slightly dependent on temperature. However, it should be noted that the partial pressure of water, p, is strongly dependent on temperature for a given vapor density, or mass of water per unit volume of air (i.e., g/m3). 1

𝑧 = (2𝑉𝑃𝑝𝑡)2

(14)

While a linear relationship between z and t1/2 has been reported in studies involving the curing of moisture-reactive acetoxysiloxane sealants10 and isocyanate adhesives48, we were surprised to find from our spatially resolved T2 data in Figure 9B that the relationship was linear only up until ~300 s1/2, then increased nonlinearly until the sample was completely cured at ~400 s1/2. This result was reminiscent of the T2 relaxation time data in Figure 4C, in which the rate of degree of cure progression increased dramatically after about 12 hours of cure time. In a later report, Comyn et al. noted that in fact the relationship between z and t1/2 changes sharply from linear to increasingly positive during the curing of an alkoxysilicone sealant, and this had not been seen in previous studies because the samples were thick enough and/or the cure time not long enough to reach the “kink” in the plot.11 The authors attribute this nonlinear increase to the counter-diffusion of macromolecules such as crosslinking or adhesion agents that may react with water at the diffusion front and inhibit the curing reaction. Therefore, when the diffusion front reaches a sample depth where the concentration of this molecules is depleted, the cure rate increases non-



Page 24 of 29

24 linearly. We posit that this nonlinear increase in cured sample thickness could also be due to autocatalysis of this reaction; since water and acetic acid are produced during the curing, the formation of these reaction products may eliminate the diffusion limitation as the reaction progresses by increasing the local water concentration at the reaction front and/or increasing chain mobility due to plasticization or local exothermic heating. It is also possible that the production of acetic acid decreases the local pH and catalyzes the reaction. Thus, we feel that the best model for the moisture-reactive curing of RTV 734 alkoxysiloxane sealant is the autocatalytic single-step model with an empirical first-order dependence on the initial (constant) water vapor concentration, shown in Equation 10. Conclusions T2 relaxometry was used to measure the reaction progress of silicone sealant RTV 734 curing in the presence of water vapor at various temperatures and water vapor concentrations. The T2 relaxation times were converted to degree of cure, α, and the rate of cure was then fitted with a reaction model. Additionally, we used T2-weighted MRI imaging to spatially resolve the progression of the curing front as a function of cure time. From the images, we extracted and plotted the cure thickness of the sealant as a function of cure time to compare to curing models proposed in the literature. It was found that the single-step autocatalytic S-B model was the best fit to the experimental data. While semiempirical, this autocatalytic model makes physical sense as the reaction products, water and acetic acid, may indeed serve to further promote the reaction by increasing local water concentration, increasing chain mobility, creating local exothermic heating, or decreasing the local pH. Using this kinetic model, an Arrhenius relationship was found for the apparent rate constant, k, and from this relationship the activation energy of the reaction was found to be 3.7 kJ/mol. Interestingly, the apparent rate constant also exhibited a linear dependence on water vapor concentration, which suggests a dependence on rate of water vapor diffusion although the data could not be fit to diffusion models reported in the literature. The spatially resolved T2 data enabled us to determine that the sealant curing was in fact only diffusion-limited for the first portion of the curing, at which point the autocatalytic effect presumably dominates and overcomes diffusion limitations. This may be because water is a product of the curing reaction and


Page 25 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25 as the reaction enters the autocatalyzed regime, the local concentration of water increases and eliminates diffusion limitations. Therefore, the best model for the moisture-reactive curing of RTV 734 alkoxysiloxane sealant is the autocatalytic single-step model with an empirical first-order dependence on the water vapor concentration for the condition where the water vapor concentration remains constant. Acknowledgements This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The authors would like to acknowledge the Joint DoD /

DOE Munitions Technology Development Program (JMP) for funding to perform this work.

This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes. Competing interests The authors declare no competing interests. Supporting Information Figure S1: Parameters from the biexponential fit of a representative sample condition (1 mol/m3 water vapor concentration, 25 °C) Figure S2: Representative biexponential fit and residual plot (60 °C and 2.9 hours of cure time)



Page 26 of 29

26 Figure S3: Representative stretched exponential fit and residual plot (60 °C and 25 hours of cure time) Figure S4: Best fits with kinetic models commonly used in literature (1 mol/m3, 25 °C data) Figure S5: S-B autocatalytic model fits to isothermal data taken at 25 °C and three different water vapor concentrations Video S6: In-situ T2-weighted MRI of RTV 734 cure progression References (1) (2) (3) (4) (5) (6)

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29 Table of Contents (TOC)/Abstract graphic


In situ curing kinetics of moisture reactive acetoxysiloxane sealant

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