Solvent Effects in Polyurethane Cure: A Model Study - ACS Publications

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Solvent Effects in Polyurethane Cure: A Model Study Stephen Monaghan and Richard A. Pethrick* WestCHEM, Department of Pure and Applied Chemistry, University of Strathclyde, Thomas Graham Building, 295 Cathedral Street, Glasgow G4 32QQ, U.K.

ABSTRACT: The effect of change of solvent type on the rate of cure of a polyol with an isocyanate was measured using a range of different techniques. The initial stages of the cure process were followed using viscosity and Fourier transform infrared spectroscopy [FTIR] measurements. The gelation point was observed using viscosity measurements and depends on the solvent used. FTIR measurements confirm that both acceleration and inhibition of the polyurethane formation occurs with change of solvent. Comparative studies carried using mixtures of ethyl acetate/toluene and n-butyl acetate/xylene are reported. Intrinsic viscosity measurements revealed that the size of the polyol changes with temperature in a different manner depending on the solvent used. In part, the size of the polyol influences the ability for reaction to occur. Measurements of the permittivity, refractive index and solution viscosity indicates that these solvent mixtures deviate from ideality. A model to describe the observed solvent effects is proposed which includes the influence of polarity on the transition state and viscosity on the diffusion of the reactants. Using the measured viscosity and permittivity data for the mixtures, it was possible to obtain a good fit of the experimental data. This study illustrates how the polyurethane reaction is sensitive to the type of solvent used and indicates how the reactivity may be influenced by change in solvent.

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INTRODUCTION Two component (2K) polyurethane [PU] aqueous and solvent based coatings are widely used in the automobile, aircraft and white goods industry. The solvent is selected on the basis of its ability to dissolve the polyurethane components, evaporate from the coating and form durable films. Concerns over the release of volatile organic compounds (VOC’s), have led to the use of various solvent blends and the development of aqueous based systems.1,2 Solvent blends which are environmentally friendly potentially can replace the environmentally more harmful single solvent systems. In a previous paper, the possible effects of solvent on the cure of PU’s were identified.3 The rate of reaction of isocyanate and polyol in mixtures of methyl ethyl ketone [MEK] and toluene [TOL] varied with composition, being slowest in toluene. Cure of PU systems have been extensively investigated for both aqueous and solvent based systems; however, the sensitivity of the cure kinetics to changes in solvent blends has not been fully addressed.1−7 In this paper, we examine the influence of solvent with different hydrogen bonding indices [HBI] on the PU cure process. The solvent is usually selected on the basis of its ability to dissolve the components and evaporate from the mixture to form a film. The solubility parameter (δ) is a numerical representation of the solvency characteristics of the liquid and © 2012 American Chemical Society

provides a simple basis for solvent selection. The solubility parameter is defined as the square root the cohesive energy density and represented as δ=

ΔEv Vm

(1)

where ΔEv is the energy of vaporisation and Vm is the molar volume for the solvent or the mixture. Ideally the value of δ should be selected to be close to that of the component being dissolved. For polar liquids, a three parameter model describes the solubility parameter and involves adding to eq 1 a fractional polarity parameter, p, together with a net hydrogen bond accepting index, θA, commonly known as the hydrogen bond index, HBI.8 The additional terms allow for specific interactions between molecules in the system and have been used to explore polymer−solvent interactions.9,10 Solvents can be split into four main categories: non-hydrogen bonding (aliphatic hydrocarbons), hydrogen bond acceptors (esters and ketones), donors (chloroform) and donor/acceptors (alcohols). The HBI, θA, is calculated from the following equation Received: March 13, 2012 Revised: April 13, 2012 Published: April 25, 2012 3928

dx.doi.org/10.1021/ma300514e | Macromolecules 2012, 45, 3928−3938

Macromolecules θA = Ksγ

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(2)

where γ is the spectroscopic value of hydrogen bonding obtained by Gordy11 and Ks is a weighting factor taken as −1 for simple alcohols, 0 for glycol ethers, and +1 for esters, ketones, and all other solvents. Ephraim et al., have studied the reaction of phenyl isocyanate with alcohols in various solvents and proposed the formation of complexes between the solvent and the OH groups on the alcohol.12 Freeman et al.,13−15 and Alfassi et al.,16 investigated the reactivity of electrons with ions in propanol/water and butanol/water mixtures and found that the rate constant for the reaction between solvated electrons and nitride ions in water is 48 times larger than in 1-butanol at 298 K. However the rate constant of the reaction of solvated electrons with ammonium, NH4+, ions in water is 104 times smaller than in 1-butanol and attributed the observed variations to viscosity and dielectric effects. Studies of the addition reaction of Cl2•− radicals indicated that solvent polarity and specific solvation of the ionic reactants and products was influencing the course of the reaction.. Lesar et al.,17 monitored the reaction between 1,5napthalene diisocyanate and polycaprolactone in toluene, ethyl methyl ketone and ethyl acetate and found that the rate of reaction strongly depended on the reaction medium, being fastest in the nonpolar toluene and slower in ethyl methyl ketone and ethyl acetate. The uncatalyzed and catalyzed polymerization of a hydroxyl-terminated polybutadiene with toluene diisocyanate has been studied in toluene, benzene, chlorobenzene dioxane and nitrobenzene.18 The reactivity varied with solvent, but the dielectric constant, the electron donor number or the hydrogen bonding index of the solvents individually appear to have no effect on the rate however significant variations were observed with variation of the solvent. In this study we examine the effects of various solvents and solvent mixtures on the rates of reactions of a simple model isocyanate and a diol. The polyol used is similar to that used in paint formulations and is a styrene-acrylic copolyol. The isocyanate used is a trimeric form of hexamethylene diisocyanate, the isocyanate group being unconjugated with the rest of the molecule simplifies the nature of the interactions which can influence the formation of the reaction intermediate. Changes in temperature and solvent can have a profound effect on the ability of the isocyanate to react with the polyol. Changes in temperature will not only change the ability for the reaction to occur but can also change the conformation of the polyol. This study attempts to consider the various factors which can influence the rate of cure and help develop a model by which the variations in rate can be predicted. In this study, the possible effects of evaporation are avoided by performing the cure measurements in sealed systems. The initial study explores the effects of change in solvent on a fully formulated 2K PU system, which contains processing aids and catalysts. In order explore whether the solvent effects are associated with the catalysts or processing aids, an FTIR study was conducted without catalysts or processing aids. For long cure times which are found with uncatalyzed, curometer measurements are difficult and a study of the viscosity changes during cure was carried out on catalyzed systems. Finally, the eliminate some of the possible contradictory effects a study was carried out using solvent mixtures on catalyzed systems. A subsequent paper will explore the effects of solvent evaporation on the cure process.

Article

EXPERIMENTAL SECTION

Materials and Reaction System. The polyol, Joncryl 569 obtained from BASF UK, was a styrene-acrylic copolymer. Gel permeation chromatography indicated polyol had a Mn 1310 and Mw 2420. Using a combination of nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy and elemental analysis,

Figure 1. Structures of isocyanate and styrene acrylic copolyol. it was found the structure was as shown in Figure 1 with “n” being approximately 6. The isocyanate, Tolonate HDT LV was obtained from Perstorp UK and is a cyclic trimeric form of hexamethylene diisocyanate, Figure 1. The reaction was catalyzed by dibutyl tin dilaurate [DBTDL] which was added at levels between 0.1 and 0.5%. In a typical formulation, 8.2 g of Joncryl 569 was reacted with 4.4 g of Tolonate HDT LV dispersed in 10 g of solvent. The solvent used were AR grade where appropriate and were obtained from Aldrich Chemical Co., U.K. The xylene used in this study was 99% p-xylene. For the initial viscosity studies two processing aids were added: Tinuvin 292, bis(1,2,26,6-pentamethyl1−4piperidnyl)sebacate, and Tinuvin 1130, [3-[3-(2H-benzotriazol-2-yl)5-(1,1-dimethylethyl)-4-hydroxyphenyl]-1-oxopropyl]-ω-[3-[3-(2Hbenzotriazol-2-yl)-5-(1,1-dimethylethyl)-4-hydroxyphenyl]-1oxopropoxy]poly(oxy-1,2-ethanediyl), with n typically 6−7. The compounds were obtained from BASF, Europe. These compounds impart UV stability of the PU coatings. Viscosity and Curometer Measurements. Shear viscosity measurements were carried out on the solvents and the solutions using either a Haake Rotovisco RV3 operating at shear rates between 64 and 724 rpm or a Haake Viscotester VT5-L operating at a fixed shear rate to monitor cure. The instruments were equipped with solvent trap to avoid evaporation of solvent. The cure−viscosity profiles were measured using the Strathclyde vibrating probe curometer operating at a frequency of 1 Hz. An analysis of the amplitude and phase allows determination of the gelation and vitrification points.19 The curometer used a paraffin film to avoid evaporation of the solvent. The viscosities of the dilute polymer solutions and the solvent mixtures were measured using an Ubbelohde suspended level viscometer thermostated in a water bath to ±0.1 °C.20 The viscosity was measured using the standard method and the flow time was recorded electronically to better than ±2 s, and the values were an average of five measurements. Fourier Transform Infrared Measurements. A Nicolet Impact 410 FTIR spectrometer equipped with a temperature controlled solution cell, using KBr windows and PTFE spacers was used to investigate the change in the intensity of the −NCO, −NH, and −OH stretching vibrations as a function of cure time. The band intensities were determined by integration of the peak over a fixed window. Corrections were made for instrumental drift by using the C−H stretch as an internal reference and the variation of the OH, NH and OH stretching band intensities monitored with time. The samples were monitored for ∼570 min, with FTIR spectra taken at 30-min intervals. Density, Dielectric Permittivity and RefractiveIindex. The density was measured using a Antoon Paar D60 Density Meter with a Antoon Paar D601 density measuring cell thermostated at 25 °C. The dielectric permittivity was measured using a Teradyne C357 1kHz Capacitance Bridge and a solution cell thermostated at 25 °C. The 3929


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refractive index was measured with an Abbe refractometer operating with a sodium lamp and thermostated at 25 °C.

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RESULTS AND DISCUSSION Preliminary Investigation of Solvent Effects. As a preliminary to a more detailed studies, the initial stage of the cure reaction between the polyol and the isocyanate were explored used the Haake Rotovisco RV3 for a range of solvent systems, Figure 2. For this initial study two processing aids;

Figure 2. Variation of viscosity with time for various solvent systems at 25 °C for a catalyzed system which also contains processing aids and was catalyzed with 0.01% DBTDL.

Tinuvin 292 and Tinuvin 1130 were added to the formulation and was catalyzed with 0.01% DBTDL. The solvents used were amyl acetate [AmAc], acetone [Ac], ethyl 3-ethoxypropionate, [EEP], ethoxy propyl aceatate [EPA], ethyl acetate [EtAc], methyloxy acetyl ketone [MAK], methyl isobutyl ketone [MiBK], methoxy propyl acetate, [MPA], n-butyl acetate [nBAc], toluene [TOL], and p-xylene [XYL]. At 25 °C significant differences are observed in the rate at which cure occurs, as indicated by the increase in viscosity with time. Surprisingly, acetone is the slowest system to cure, whereas amyl acetate and ethyl propyl acetate exhibit high rates of cure. Toluene cures faster than xylene which is significantly faster than ethyl 3-ethyoxypropionate. Small changes in the chemical structure of the solvent are having profound effects on the rate of cure and could be influencing the ability of the isocyanate to access the hydroxyl groups of the polyol or to achieve activation to the transition state for the reaction. The additives Tinuvin 292 and Tinuving 1130, which both contain polyether and piperidnyl groups, have the potential to interact with the tin catalysts and hence influence the cure process. FTIR Studies of the Rate of Cure. The cure characteristics for the various solutions were determined by observing the changes in the intensity of the −NCO, −NH, and −OH stretching vibrations as a function of cure time, Figure 3. In this study, the processing aids and catalysts were omitted to remove the possible effects which these might have on the cure process. FTIR measurements were performed in triplicate to obtain reliable kinetic data. Different rates of cure are observed, which implies that the mechanism of reaction changes with the solvent. The FTIR observations do not parallel those of the viscosity, Figure 2 and these differences can in part be attributed to the absence of the processing aids in the FTIR study. In the FTIR study acetone and ethyl acetate show an

Figure 3. FTIR plots for the cure in amyl acetate at 25 °C (A); variation of the % isocyanate with time for the various solvent systems studied (B); variation of the rate constant with the hydrogen bonding index [HBI] (C). This system was uncatalyzed and did not contain processing aids.

initial period of inhibition followed by relatively high rates of reaction. Amyl acetate, and methyloxy acetyl ketone all show high reactivity, whereas methoxy propyl acetate, methyl isobutyl ketone, Ethyl 3-ethoxypropionate show relatively low rates of reactivity. One possible explanation of the apparent inhibition of the reaction in the case of acetone and ethyl acetate could be the formation of a complex which suppresses the polyurethane reaction. An alternative hypothesis could be that the solvent is influencing the size of the polyol and hence the accessibility of the reactive OH functions. Plots of ln(isocyanate) consumption against time, excluding the initial inhibition period, give fairly linear plots from which rate constant may be calculated. In the case of acetone, ethyl 3930


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presented in Table 1. A value of 100 Pa s was arbitrarily chosen and is ∼104 times larger than that of the solvent. The addition

acetate and amyl acetate, after the initial inhibited period, exhibit high rates of reaction. Strathclyde Curometer studies. During cure the viscosity can change over five decades or more and the vibrating probe method provides a useful method of following the cure process. Measurements of the various solution systems were performed at 25 °C using a vibrational frequency of 1 Hz. A typical plot is shown in Figure 4A. The damping coefficients p′2 (real,

Table 1. Effect of Catalysts and Solvent on the Times to Reach a Viscosity of 100 Pa s for Measurements Carried out at 25 °C time (min) to reach 100 Pa s

amplitude) and p″2 (imaginary, phase) are related to the viscosity η measured at a frequency ω by the relations and

p″2 = (p1 ηωC /k)/(1 + (ηωC /k)2 )

DBTDL 0.05%

DBTDL 0.01%

acetone amylacetate ethyl 3-ethoxypropionate, ethoxy propyl aceatate ethyl acetate methyloxy acetyl ketone methyl isobutyl ketone methoxy propyl acetate n-butyl acetate toluene xylene

12.5 8.2 11.5 10.3 8.4 9.0 10.5 10.5 8 4.2 4.5

50 60 35 40 50 50 50 35 40 50 40

130 110 200 75 245 175 165 115 90 115

of catalysts to the reaction has changed the rates of the reaction but also the sensitivity to solvent. While the relative order of reaction between solvents of similar type remains, i.e., xylene being slower than xylene, the ketone based solvents which are capable of interacting with the catalysts DBTDL, are exhibiting a different order of reaction to that observed with the FTIR measurements. Increasing the dibutyltin laurate [DBTDL] catalysts from 0.01 w/w% to 0.05% w/w% produces a significant decrease in the time which is required to achieve a viscosity of 100 Pa s. Measurement of the rate at which the viscosity increases, Table 1, demonstrates the expected proportionality between the rate and catalysts concentration. The rate of cure is typically 1000 Pa s/min for a catalyzed system with 0.05% DBTDL and 300 Pa s/min for 0.01% DBTDL, whereas the uncatalyzed systems cure in the region of 25 Pa s/min. The differences in the rates of cure can be attributed to differences in the effective activity of the catalysts changing with solvent polarity. The curometer data parallels that from the viscosity studies showing large differences in activity between the ketonic solvents and significant differences in reactivity between toluene and p-xylene, however the presence of catalysts has changed the order of the reaction in some cases. The data presented in Table 1, indicates that there is no simple correlation between the rate at which cure occurs and the hydrogen bonding index [HBI]. In order to gain further insight in the relative importance of the factors which might influence cure, a study was undertaken of the size of the polyol in various selected solvents. For this study, acetone, ethyl acetate, n-butyl acetate, toluene, and xylene were studied. Size of the Polyol in Solution. Changes in the intrinsic viscosity reflect variation dimensions of the polyol with temperature. The size of a polymer molecule in solution is characterized by its intrinsic viscosity [η], defined in terms of the Kraemer’s equation:21−28

Figure 4. Curometer plots for the polyol−isocyanate reaction in ethyl acetate at 25 °C: (A) viscosity time plots for various solvent systems cured at 25 °C; (B) catalyst with 0.01% DBTDL.

p′2 = p1 /(1 + (ηωC /k)2 )

solvent system

H bonding index

(3)

where p1 is the amplitude of the undamped probe motion, C is a geometric factor related to the probe/material contact area, and k is an instrument contact. These latter terms are obtained by calibration with fluids of known viscosity. In the FTIR studies, no catalyst was used and the cure times were consequently very long, however the effect of solvent on the cure process was very evident. In order to avoid the possible effects of evaporation, the curometer test were performed on catalyzed systems. The curometer allows the viscosity to be measured from the initial solution values up to values of the order of 4 × 105 Pa s. The viscosity profiles of the solutions are shown in Figure 4B. Measurements were undertaken with two different level of catalyst; 0.05% and 0.01% of dibutyl tin laurate DBDTL]. The times to react a viscosity of 100 Pa s are

ln[ηr ]/c = [η]K − kK [η]K 2 c

(4)

where ηr is relative viscosity of a polymer solution with concentration c, and kK is the Kraemer’s constant. The intrinsic viscosity is directly proportional to the average root-mean3931


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square distance between the chain ends ⟨r−2⟩1/2, which itself will reflect the strength of the interaction between polymer and solvent.29 Equation 4 has been used for oligomeric species but strictly speaking requires modification for low molecular weight species to allow form specific solvent interactions.29 In this study, the intrinsic viscosity is used to compare dimensions and not to determine absolute values. The Ubbelhode viscometer was used to determine the variation of the viscosity with concentration over a range from 0.1 to 30 w/w%. The intrinsic viscosity was determined from the initial linear plots of ln[η]r/c versus concentration. Measurements were undertaken for five different solvents; acetone, ethyl acetate, n-butyl acetate, toluene and xylene at four temperatures, 25, 30, 35, and 40 °C. The values of the intrinsic viscosity, Figure 5A varied both with temperature and H bonding index.

The polarity will also influence the tendency for hydroxy group to interact with the carbonyl function to which it is attached. The reverse is true for acetone and n-butyl acetate, where increase in temperature is associated initially with an increase in size, however once more a collapse of the polyol size is observed on further increase in temperature. In the case of toluene and ethyl acetate, the size once more increases at 40 °C reflecting increased solvent interactions opening up the polyol possibly through enhanced collisional dipole - π interactions. The cure characteristics of the various solvents, Figure 2, show that the polyol in acetone has the most compact structure and are initially the least reactive. The PU reaction is faster in toluene than xylene and this is reflected in the smaller dimensions of the polyol in xylene than in toluene. However, the PU reaction in n-butyl acetate is exhibiting a higher reactive than ethyl acetate which does not scale with the dimensions at 25 °C. In these solvents, the polyol is showing a very different temperature dependence of the size, which may explain the observed variations. The size variations may be expected in part to reflect the accessibility of the reactive functions on the polyol and hence, in part, help to explain the variations seen in Figures 2,3, and 4. Studies of Solvent Mixtures. In order to gain further insight into the details of the solvent effects, two mixtures of solvents were studied: ethyl acetate/toluene and n-butyl acetate/xylene. These combinations was selected as the intrinsic viscosities in the two solvents exhibited similar characteristics, the cure rates were different, polarities of the solvents are different but they have similar evaporation rates. Comparison of the behavior in these mixtures explores the effects of polarity on the polyurethane reaction. FTIR studies. The change in the isocyanate concentration was monitored for the first 570 min for mixtures of ethyl acetate/toluene100/0, 90/10, 80/20, 70/30, 60/40, 50/50, 40/ 60, 30/70, 20/80, 10/90, and 0/100 at 25 °C. The measurements were carried out in triplicate. The rate constants for the reaction of isocyanate with polyol have been shown by a number of workers to follow second order kinetics.29−33 Plots of the 1/[isocyanate] against time, yielded good linear fits and the variation of the rate constants with composition of the solvent are presented in Figure 6. The rate constant for the reaction in ethyl acetate is higher than that in toluene and if simple additivity were to operate,

Figure 5. Variation of the intrinsic viscosity [A] and ratio of the radius relative to the value in acetone at 25 °C [B] with temperature and solvent for the polyol in acetone, n-butyl acetate, ethyl acetate, toluene, and xylene.

A clearer picture emerges of the behavior of the polyol if the values are referenced to value of acetone at 25 °C, Figure 5B. The polyol contains polar acrylic and nonpolar styrene moieties and hence its interaction with the solvent will be complex, reflecting the ability to achieve favorable interactions with various elements of the chain. Toluene is better able to solvate the phenyl moiety than the more sterically hindered p-xylene. Increasing temperature causes a decrease in size for toluene, pxylene and ethyl acetate reflecting the effects of increased occupancy of higher energy gauche conformations of the chain leading to a decrease in size and a more compact structure being formed.

Figure 6. Rate constants as a function of composition for ethyl acetate/toluene mixtures at 25 °C. 3932


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then a linear variation with composition might be anticipated. The addition of ethyl acetate to toluene leads to enhancement of the rate of reaction, reaching a maximum at a composition of 40% ethyl acetate. However with further addition of ethyl acetate the rate drops reaching a minimum at 70% ethyl acetate, before once more increasing. The rate constants were investigated as a function of temperature for ethyl acetate/toluene mixtures of 100/0, 75/ 25, 50/50, 75/25, and 0/100w/w% composition at 25, 35, 45, and 55 °C. Using the Arrhenius equation k = A exp( −Ea /RT )

(5)

the Arrhenius activation energies [Ea] and pre-exponential factor [A] determined, Figure 7. The activation energy for the Figure 8. Variation of the second order rate constants with composition for n-butyl aceatete/xylene mixtures at 25 °C.

xylene. This is in contrast to the behavior of ethyl acetate/ toluene where the addition of ethyl acetate initially increases the rate. Measurements were performed in n-butyl acetate/ xylene mixtures of 100/0, 75/25, 50/50, 75/25, and 0/100w/w % composition at 25, 35, 45, and 55 °C and the Arrhenius activation energies [Ea] and pre-exponential factor [A] measured, Figure 9. In the case of n-butyl acetate/xylene the variation of the activation energy, Figure 9A, reflects the variation in the rate constants, Figure 8, increasing and then

Figure 7. Variation of the activation energy [A] and pre-exponential factor [B] for the polyurethane reaction in mixtures of ethyl acetate/ toluene.

reaction in toluene is higher than that for the reaction in ethyl acetate and the variation with composition parallels that observed for the rates of reaction with composition. The preexponential factor A exhibits a similar variation to that for the activation energy, Figure 7B. The A factor is an indication of the mechanism of reaction and changes in this value imply that the detail of the mechanism of reaction may be changing with solvent. A parallel study was undertaken of mixtures of n-butyl acetate and xylene. The variation of the isocyanate concentration was monitored as a function of time, change in mixture composition and temperature. The variation of the isocyanate concentration was found to fit a second order rate equation and the variation as a function of concentration is shown in Figure 8. The rate is dependent on solvent and shows a minimum at approximately a 60/40 w/w% mixture of n-butyl acetate and

Figure 9. Variation of the activation energy [A] and pre-exponential factor [B] for the polyurethane reaction in mixtures of n-butyl acetate/ xylene. 3933


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where ai and γi represent the activity and activity coefficient, respectively, of species I which may be the reactants [A, B], products or transition state [C]. The activity coefficient is a quantitative measure of the change in interaction energies resulting from the process of dissolution of the species in the solvent. The rate of consumption of the reactant, A, has the form

decreasing. A parallel variation is also observed for A with composition, Figure 9B. Chang et al.30 studied the effect of solvent on the reaction of phenyl isocyanate with n-butanol using IR spectroscopy and found that the second order rate constant for this reaction in an unsolvated system is 6.67 × 10−4 L mol−1 s−1 at 25 °C. The same reaction was carried out in various solvents including ethyl acetate, toluene, xylene and n-butyl acetate, the rate constants for these reactions were found to be 3.00 × 10−6, 1.53 × 10−4, 1.83 × 10−4, and 4.00 × 10−6 L mol−1 s−1 at 25 °C, respectively. It is clear that there is a 50-fold increase in the rate constant when moving from ethyl acetate as the solvent to toluene. Kogon31 used IR spectroscopy to investigate the reaction of 2,4-and 2,6- TDI with ethanol and found the rate constants to be 1.08 × 10−3 and 2.46 × 10−4 L mol−1 s−1, respectively. Matthews1 quotes activation energies for the reaction of MDI and 2,4- TDI with diethylene glycol adipate polyester in chlorobenzene and found these to be 43.89 kJ mol−1 for MDI and 52.67 and 38.87 kJ mol−1 for the 2 and 4 position isocyanate groups on 2,4-TDI, respectively. Davis et al.32 calculated the activation energy of phenyl isocyanate with methanol in di-n-butylether to be 38.9 kJ mol−1 and for the same reaction in benzene the activation energy is 25.9 kJ mol−1. Baker et al.33 quotes values for the activation energy of phenyl isocyanate with 1- and 2- butanol as 33.86 and 41.38 kJ mol−1, respectively. The values obtained in this study are comparable to those of other workers who have observed solvent effects using different isocyanate - polyol systems. A Model for Solvent Effects. The solvent is having more than one effect on the rate of the polyurethane reaction,1−9. If we assume that the transition state is bimolecular, Figure 10 applies.

− dA = k1ABγAγB − k −1CγC dt

(7)

where k1 and k−1 are respectively the rate constants of the forward and reverse reactions, A,B, and C are the concentrations of reactants and product. At equilibrium −dA/ dt = 0, it follows that; k1ABγAγB = k −1CγC

and

Ke =

CγC k1 = k −1 ABγAγB

(8)

If we consider that transition state or more correctly the activated complex, designated by ±, then we introduce its activity as, γ±, and rewrite eq 7 in the form k −1CγC k1ABγAγB − dA = − dt γ± γ±

(9)

At equilibrium, the activity coefficient, γ±, cancels in order to satisfy the equilibrium expression. Thus, the rate constant, k, can be expressed as, k=

kBT ± K h

(10)

where K± is the concentration of the transition state which is influenced by the effects of solvent and kB is Boltzmann’s constant, T is the temperature, h is Planck’s constant. kBT exp( −ΔG±/RT ) and h kT k = B exp(ΔS ±/R − ΔH ±/RT ) h

k=

(11)

The values of ΔG, ΔH, and ΔS are dependent on the solvent system. For a bimolecular process k=

The initial reactants and transition state will be solvated to a greater or lesser extent. In the PU reaction it will be assumed that the barrier for the reverse process is very high compared with that for the forward reaction. The solvent molecules may form a “cage” around the reacting pair aiding reaction or may inhibit reaction by forming complexes with the reacting species. The effective activity of the isocyanate and polyol should be included in the kinetic equation for the formation of the transition state. The equilibrium constant, Ke, for the distribution between the reactants, products and transition state can be written in the form aC C ⎛ γC ⎞ ⎜⎜ ⎟⎟ = aAaB AB ⎝ γAγB ⎠

(12)

The transition state involves electrons and partial charge generation and a change in the dipolar contribution to the total free energy. The activation energy, EA, will have an electrostatic contribution due to dipole interactions, Ee, as well as a contribution from nonelectrostatic effects, En, and can be expressed in the form

Figure 10. Schematic of the reaction between polyol and isocyanate.

Ke =

kBT ± γAγB K h γ±

EA = En + Ee

(13)

where Ee includes electrostatic contributions in terms of the dipole moments of the reactants, μA and μB, and must include a function, f(θA, θB) which reflects their mutual orientation described by their angles of inclination, θA and θB, the dielectric permittivity of the solvent, ε, and the distance apart of the dipole centers in the reactive complex, rAB μμ Ee = A B3 f (θA , θB) ε rAB (14)

(6)

which leads to a contribution to the overall rate of reaction 3934


Macromolecules ⎛ ⎞ μμ k e = A e exp⎜ − A B 3 f (θA , θB)⎟ ⎝ RTε rAB ⎠

Article

(15)

where Ae is the pre-exponential factor for the electrostatic contribution to the activation energy. The above theory considers only the effect of solvent on the formation of the transitions state. In solution the reactants have to diffuse through the solvent in order to be able to react and this process is described by the Smouluchowski equation k2 =

2000NAkBT ⎛ r ⎞ r ⎜2 + A + B ⎟ 3η rB rA ⎠ ⎝

(16)

where rA and rB are respectively the sizes of the reactants, η is the viscosity, NA is Avogadro’s number. If the two molecules are of similar size, i.e., rA ≈ rB, the radii cancel and the rate constant is approximately independent of the species involved k2 ≈

8000NAkBT 8000RT = 3η 3η

(17)

and is dependent on the solvent viscosity. In the initial stages of the polymerization it is reasonable to assume the reactants having similar size. As the reaction proceeds additional terms require to be added to allow for the growing polymer chain, however for low molecular weight species prior to gelation it is reasonable to assume that the rate scales with the viscosity. Combining the diffusion control and electrostatic contributions yields; kobs = a

⎞ ⎛ μμ RT + Ae exp⎜ − A B 3 f (θA , θB)⎟ η ⎠ ⎝ RTε rAB

Figure 11. Dielectric permittivity as a function of solvent composition for ethyl acetate−toluene mixtures with and without polyol-A present [A] and for n-butyl acetate−xylene mixtures with and without polyol-A present. [B].

(18)

Equation 18 is appropriate for an uncatalyzed reaction. The catalyst will influence the nature of the transition state which will in turn influence the activity of the transition state. If we assume that the reactions can be considered to be concurrent, then the observed rate constant will have the general form

xylene was performed. If the mixtures were ideal a linear relationship between the composition of the mixture and the various parameters would be expected. The dielectric permittivity shows a good linear variation with composition for both the solvents and the mixture containing the polyol for both mixtures. The variation in the case of the ethyl acetate−toluene mixture is larger in the case of the more polar ethyl acetate than the less polar n-butyl acetate. In the case of the n-butyl acetate/xylene, the polyol adds a slightly higher increment than in the case of the ethyl acetate/toluene mixtures. The refractive index variation shows a linear variation except that in this case the refractive index drops with the addition of the polar molecule, Figure 12. A drop in refractive index implies that the atom density is decreasing and would reflect an opening of the liquid structure. The refractive index is increased with the addition of the polyol. The increase in the permittivity, Figure 11 is a direct measure of the increased dipole content in the solution and Figure 11B shows a distinct increment directly associated with the addition of the polyol. The magnitude of the dipole moment will be the difference between the square of the refractive index and the permittivity measured at low frequency. As expected the dipole moment increase with the concentration of ethyl acetate or nbutyl acetate. The densities of the mixtures and the mixtures plus the poloyl were measured and the results are shown in Figure 13. Interestingly, ethyl acetate addition causes an increase in the density, which would reflect an increase in the packing and the peak in the deviation from a simple linear mixing law occurs in

kobs = k′ + kc[catalyst]n

where k′ is the rate constant for the uncatalyzed reaction, kc is the rate constant, and n is the order of the catalyzed reaction. Therefore, the overall expression for the second order rate constant of a catalyzed bimolecular reaction will have the form kobs = a

⎞ ⎛ μμ RT + Ae exp⎜ − A B 3 f (θA , θB)⎟ η ⎠ ⎝ RTεrAB

+ kc[catalyst]n

(19)

The observed rate constant will be expect to depend on the inverse of the viscosity of the media, the exponential of the dipole moment of the two reacting species, the dielectric permittivity of the solvent and a function of the distance apart of the dipole centers in the transition state and on the catalysts concentration. For a particular case, the values of μA, μB, and the function f(θA,θB) will be assumed to be approximately constant. In practice, this will not be correct if the solvent either forms a cage or undergoes specific interaction however eq 19 provides a first step to modeling these complex systems. Comparison of the Model with Experimental Data. A study of the change in dielectric permittivity, Figure 11, refractive index, Figure 12, and density, Figure 13, of the mixtures of ethyl acetate with toluene and n-butyl acetate with 3935


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Figure 13. Density as a function of solvent composition for ethyl acetate−toluene mixtures with and without polyol-A [A] and n-butyl acetate−xylene mixtures with and without polyol-A [B].

Figure 12. Refractive index as a function of solvent composition for ethyl acetate − toluene mixtures with and without polyol-A present [A] and for n-butyl acetate−xylene mixtures with and without polyol-A present [B].

The non ideality of the mixing is once more clearly evident. However we can see the additional contribution arising from the polyol to the total dielectric permittivity in both the ethyl acetate−toluene and the n-butyl acetate−xylene mixtures. The additional contribution to the permittivity arising from the formation of the mixture is easiest observed in xylene when it makes a contribution of ∼0.16D. Interaction of the polyol with the polar n-butyl acetate appears to reduce this increment at high concentrations of n-butyl acetate. In the case of ethyl acetate, non ideal mixing leads to a non linear variation of the effective dipole in the solvent mixture and the increment after the addition of the polyol is smaller than in the case of the nbutyl acetate. This data indicates that significant dipole interactions are occurring and these may be expected to influence the reactivity of the polyol−isocyanate reaction on the transition state. The other important factor influencing the reaction is the viscosity. The viscosities of the solvent mixtures were measured and both systems showed a complex behavior which reflects the non ideality of the mixing in these systems, Figure 15. The rate data, Figures 6 and 8 can be fitted to an equation of the form

the same region as a deviation from linearity of the refractive index against composition curve, Figure 12A. In both cases, the addition of the polyol leads to an increase in the density, the polyol having a distinct effect on the formation of structure in the liquid mixture. Deviations from ideal mixing behavior have been reported for a number of esters/aromatic hydrocarbon mixtures and the data reported here are comparable to those published elsewhere.34−38 Deviations from ideal mixing in these systems are attributed to disruption of the local structure which exists in the pure liquids and the creation of new interactions as a consequence of dipole − induced dipole interaction between the permanent dipole on the esters and the polarizable π electron structure of the aromatic rings. The deviations from ideality are greater in the case of the ethyl acetate/toluene than in n-butyl acetate/xylene mixtures. The “effective” dipole moment of the mixture can be calculated using the Clausius−Mossotti equation N ⎛ μ2 ⎞ M ⎛ εr − 1 ⎞ ⎜ ⎟ = A ⎜α + ⎟ 3kT ⎠ ρ ⎝ εr + 2 ⎠ 3εo ⎝

(20)

kobs =

where M is the molecular weight, ρ the density, εr is the relative permittivity, NA is the Avogadro Number, α is the polarizability, and εo is the permittivity of free space, μ is the dipole moment, k the Boltzmann constant and T the absolute temperature. The high frequency limiting value of the permittivity is εr ≈ n2. This equality neglects collision polarization and the contributions from infrared absorptions and therefore the “effective” values are an overestimate of the true values, Figure 14.

⎛ μ⎞ A + B exp⎜ −C ⎟ + D ⎝ η ε⎠

(21)

where A is a constant incorporating R and T, B is Ae, C is a constant incorporating R, T, rAB and a contribution from the dipole moment of the isocyanate and polyol, and D is a constant associated with the catalyst. The value for the viscosity, η, is taken from the experimentally measured value, ε is the measured dielectric permittivity of the solvent systems. 3936


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Figure 14. Dipole moment as a function of composition for ethyl acetate−toluene mixtures with and without polyol-A [A] and n-butyl acetate−xylene mixtures with and without polyol-A [B].

Figure 15. Viscosity of reaction media as a function of composition for ethyl acetate−toluene system [A] and for n-butyl acetate−xylene system [B].

Table 2. Values of the Calculated Constants for the Two Solvent Systems

The dipole moments for −NCO and −OH were taken from the literature.39 The value of the constant D in eq 20 can be calculated by comparison of the uncatalyzed and catalyzed systems. The rate constant for the uncatalyzed reaction in ethyl acetate was found to be 2.719 × 10−5 ± 3.799 × 10−6 L mol−1 s−1 and the rate constant for toluene was found to be 4.950 × 10−6 ± 6.520 × 10−7 L mol−1 s−1. Subtracting the uncatalyzed from the catalyzed rate constant produced values for D of 7.447 × 10−5 and 7.396 × 10−5 L mol−1 s−1 respectively for ethyl acetate and toluene solutions. Values of A, B, and C were obtained by using a computer program to fit the experimental and predicted data using minimization of the sum of squares of the functions. The parameter obtained, Table 2 are a both a reflection of the solvent used and unique for that pair of solvents. Plots of the model predictions and the experimental data are shown in Figure 16. The inclusion of the viscosity, dipole moment and dielectric constants in the theory as scaling parameters allows the description of the variation of the rate constant for these complex systems. In particular it is quite surprising to find that in the case of the ethyl acetate/toluene system the dip in the region of 70% ethyl acetate is replicated in the model predictions. In the case of the n-butyl acetate/xylene the model is also allowing the minimum in the rate constant in the region of 60% n-butyl acetate to be predicted. Equation 21, although relatively simple in form allows inclusion of the main factors which are influencing the rate of polyurethane formation in this model system. This equation does however not allow for the possible effects of evaporation, and this will be considered in a subsequent paper.

■

system

A

B

C

EtAc/toluene nBuAc/xylene

7.33 × 10−3 8.60 × 10−3

7.14 × 10−4 2.01 × 10−3

3.43 5.79

CONCLUSIONS The effect of solvent on the cure of a polyol and an isocyanate is clearly demonstrated from a combination of a series of different observations. Consideration of the various steps involved in the reaction leads to the proposal of an expression of the form of eq 20 to describe the effects of change of solvent. Using measured values of the permittivity, viscosity and dipole moment of the mixtures it is possible to fit the experimental variation of the rate constant for this model system. The sensitivity of the rate of cure to the polarity of the media as indicated by eq 21 is consistent with the mechanisms proposed by Krol40 and Oprea41 who have proposed. The rates of reaction observed in this study are comparable with those reported for measurements on pure PU systems.42−49 The detailed of the PU reaction kinetics are complex and it is not surprising that change in solvent can have a profound effect on the rate of cure. Differences in the ability to hydrogen bond between elements of the polymer chains which are formed can have significant effects on the ability to develop physical properties in the final films.50 This study indicates the using solvent blends to replace single solvents in solvent based 2K PU systems can be used to accelerate or alternatively retard the polymerization process. The rates of reaction are dependent on the solvent systems 3937


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Figure 16. Experimental and model values for the rate constant in ethyl acetate/toluene mixtures [A] and n-butyl acetate/xylene [B].

used and combinations of solvents exhibit characteristics which are not simply the additive combination of the behavior of the PU in the pure solvents. Certain solvents are able to form complexes which can inhibit the cure process, whereas other solvents are able to promote the PU reaction.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS S.M. thanks BP Chemical Hull for the support of a studentship during the course of this research. REFERENCES

(1) Matthews, K. H.; Pethrick, R. A. Eur. Polym. J. 1991, 27 (9), 867− 873. (2) Randall, D., Lee, S. The Polyurethane Book; John Wiley & Sons: New York, 2002. (3) Woods, G. The ICI Polyurethane Book, 2nd ed.; John Wiley & Sons: New York,1990. (4) Szycher, M. Polyurethanes; CRC: Boca Raton, FL, and London, 1999. (5) Yahkind, A. L.; Paquet, D. A., Jr.; Parekh, D. V.; Stine, C. L.; van der Ven, L. G. J. Prog. Org. Coat. 2010, 68 (1−2), 28−36. (6) Carroy, A.; Hintermann, T.; Baudin, G.; Bauer, D.; Contich, P.; Dietliker, K.; Faller, M.; Steck, R. Kohli; Lordelot, C.; Misteli, K. Prog. Org. Coat. 2010, 68 (1−2), 37−41. (7) Jindal, K..; Bhattacharya, D.; Francis, L. F.; McCormick, A. V.; Germinario, L. T.; Williams, C. Prog. Org. Coat. 2010, 67 (3), 296− 301. (8) Nebioglu, A.; Teng, G. H.; Soucek, M. D. J. Appl. Polym. Sci. 2006, 99 (1), 115−126. 3938


Solvent Effects in Polyurethane Cure: A Model Study - ACS Publications

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