Experimental Study and Modeling of Nylon Polycondensation in the

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Ind. Eng. Chem. Res. 2003, 42, 2946-2959

Experimental Study and Modeling of Nylon Polycondensation in the Melt Phase Mark A. Schaffer, Kimberley B. McAuley,* and Michael F. Cunningham Department of Chemical Engineering, Queen's University, Kingston, Ontario, Canada K7L 3N6

E. Keith Marchildon DuPont Canada Inc. Research and Business Development Centre, 461 Front Road, P.O. Box 5000, Kingston, Ontario, Canada K7L 5A5

The melt-phase kinetics and equilibrium of nylon polycondensation and the mass transfer of water under conditions of high temperature and low water concentration were investigated by experimental study and mathematical modeling. Nylon 612 was used as a more thermally stable alternative to nylon 66 in a novel reactor system. The water concentration in the melt was varied by altering the composition of a steam/nitrogen mixture bubbled through the stirred molten polymer. Experimental data for the time evolution of carboxylic acid and amine end-group concentrations, water concentration, and inherent viscosity of the polymer samples were collected and compared with the predictions of two mathematical models from the literature. A simplified mathematical model describes the experimental data as well as or better than the literature models and accounts for the solubility of water in the nylon melt, the mass transfer of water, the rate of reaction, and the variation of the apparent equilibrium constant with the water concentration. 1. Introduction Nylon 66 is an aliphatic polyamide, produced industrially from the condensation polymerization of hexamethylenediamine and adipic acid, with diverse applications as a fiber, a film, and a plastic resin.1 The meltphase polycondensation reaction of amine and carboxylic acid end groups to form amide bonds and water has been studied in the past, but most of the experimental kinetic and equilibrium data are from studies of nylon 6;2-12 very few nylon 66 data have been published.13,14 Nylon 66 is the most commercially important of a class of polyamides made from a diamine and a diacid, commonly referred to as AABB polyamides. Analysis of kinetic data for the hydrolytic polymerization of lactams to form AB nylons such as nylon 6 is more complicated than for the polymerization of AABB nylons. Polycondensation occurs in both systems, but in AB nylons, the occurrence of other reactions involving ring opening by water and direct lactam addition to end groups (polyaddition) must also be considered. The majority of the available literature data for all nylons were collected under conditions of high water content and low temperature; relatively few data have been reported for conditions of low water content and high temperature that are typically used for final processing of nylon 66. Because nylon 6 melts in a lower temperature range than nylon 66, the few nylon 6 results available at low water content must often be extrapolated outside the temperature range in which they were collected so that they can be applied to nylon 66 melt systems. Past efforts13 to study polycondensation at high temperatures using nylon 66 have been hindered by simultaneous thermal degradation reactions, which * To whom correspondence should be addressed. Tel.: 613-533-2768. Fax: 613-533-6637. E-mail: mcauleyk@ chee.queensu.ca.

alter the concentrations of reactive end groups and prevent accurate estimations of rate and equilibrium constants. Some of these degradation reactions arise from cyclization of adipic acid residue segments within and at the ends of chains.15 Because nylon 6 and some AABB nylons (such as nylons 68, 610, and 612) are not polymerized from adipic acid monomer, they are less susceptible to thermal degradation than nylon 66. The objective of this study is the development of quantitative knowledge on the kinetics and equilibrium of the polycondensation reaction in nylon 66 at high temperatures and low water contents. More specific goals are to evaluate the predictions of existing mathematical models by comparison with new experimental data, to develop a new model (if required), to determine the effect (if any) of the water concentration on the apparent equilibrium constant, and to distinguish whether the polycondensation reaction obeys secondorder or third-order kinetics. A secondary goal is to evaluate the performance of a custom-designed and -constructed batch reactor system using a lower-melting and more thermally stable polymer than nylon 66. Nylon 612 was used, not only because thermal degradation reactions are expected to be negligible for this polymer, but also because it is an AABB nylon, so none of the additional reactions associated with AB nylons need be considered. As in previous studies,16-20 we assume that the lengths of the aliphatic portions of the polymer repeat unit do not affect the end-group reactivity, so that the kinetics of the polycondensation reaction are comparable for most aliphatic polyamides. This approach allows separation of polycondensation and thermal degradation phenomena, so that information from the present work can be used to account for the contribution of polycondensation in ongoing studies of the thermal degradation of nylon 66 with the same experimental apparatus. Although we assume that

10.1021/ie021029+ CCC: $25.00 © 2003 American Chemical Society Published on Web 05/09/2003

Ind. Eng. Chem. Res., Vol. 42, No. 13, 2003 2947

nylon 612 is an adequate model system for the polycondensation of nylon 66, it is possible that differences in viscosity and other physical quantities that affect reaction kinetics and mass transfer might exist between the two systems. In this study, we present new experimental results from a novel batch reactor system. Downward and upward adjustments to the humidity of a sparge gas bubbled through a nylon 612 melt effect a net polycondensation and a net hydrolysis, respectively, in the polymer. The responses of the end-group and water concentrations and the inherent viscosity to these changes are measured by collection and analysis of polymer samples at various times during each experimental run. The data are compared with the predictions of two literature mathematical models, and parameters are estimated for a new model that accounts for the apparent kinetics and equilibrium of polycondensation and the mass transfer of water. The experimental conditions used in this study correspond to those used industrially at the conclusion of batch polymerization processes for nylon production and in the final process units (called finishers) of continuous processes.16 The experimental and modeling results presented here have practical industrial importance because they allow for the design of improved operating strategies and process equipment for the final stages of melt-phase polymerization of nylon.

where the concentrations of the various species are those that are attained at equilibrium. The apparent equilibrium constant can also be regarded as the ratio of the apparent polycondensation rate constant, kp, to the apparent hydrolysis rate constant, kh. In contrast, the thermodynamic equilibrium constant is a ratio of activities rather than concentrations and is a function of temperature only. Expressing the activity of each species as the product of the concentration and an activity coefficient gives the following relationship between the thermodynamic and apparent equilibrium constants

2. Mathematical Framework

Conflicting reports exist in the literature on the kinetic order of the polycondensation reaction. Some researchers9,14,17-20 contend that overall second-order kinetics (first order in both amine and acid end groups) adequately describe experimental data collected at both high and low water concentrations, whereas others23-28 suggest that, at low water concentrations, the reaction rate is described by overall third-order kinetics involving catalysis of both polycondensation and hydrolysis by the carboxylic acid end group. Third-order kinetics have been assumed by some researchers for the entire water concentration range,29 whereas other researchers30,31 have used a combination of both types of kinetics, simultaneously estimating an uncatalyzed rate constant (ku) and an acid-catalyzed rate constant (kc) and then calculating a composite rate constant

hypothesis21

Assuming that the Flory equal-reactivity is valid, the reactivities of the polymer end groups are chain-length-independent, and polycondensation in nylon polymers is a reversible reaction between amine end groups (A) and carboxylic acid end groups (C) to produce amide linkages (L) and water (W)

R1-COOH + H2N-R2 h R1-CONH-R2 + H2O (1) A L C W End-group concentrations, [C] and [A], are commonly measured by titration22 and are often expressed in units of equivalents per million grams (equiv Mg-1) of polymer. The water concentration, [W], can be measured using a variety of techniques, perhaps most commonly by Karl Fischer titration.22 The amide link concentration can be calculated from a mass balance. For example, for nylon 612

[L] )

106 - 115.15[C] - 58.10[A] - 18.02[W] 155.23

(2)

As it is generally accepted that cyclic oligomers are present only at low concentrations (approximately 1-2 wt %)22 in AABB polyamides, we neglect cyclic species for the purposes of this investigation, and consider all molecules in the reaction mixture to be linear. The attainment of high extents of reaction and high molecular weights depends on the removal of water from the reaction mass to minimize the rate of the reverse reaction of amide link hydrolysis to end groups. The apparent equilibrium constant for polycondensation is defined23 as

Ka )

[L]eq[W]eq [C]eq[A]eq

)

kp kh

(3)

Kt )

( )

( )

γLγW [L]eq[W]eq γLγW ) K γCγA [C]eq[A]eq γ Cγ A a

(4)

Because activities are more difficult to determine than concentrations, often only the apparent equilibrium constant is calculated and used. If the liquid reaction mixture is nonideal, the activity coefficients of some of the species differ from unity and might be compositiondependent, so that, in this case, the apparent equilibrium constant depends on both temperature and composition. The temperature dependence of the thermodynamic equilibrium constant can be expressed using the relationship

(

Kt ) exp -

∆H ∆S + RT R

)

(5)

kp ) ku + kc[C]

(6)

If purely second-order kinetics are used, kc ) 0 and kp ) ku, whereas if purely third-order kinetics are used, ku ) 0 and kp ) kc[C]. The temperature dependence of the polycondensation rate constants can be described using an Arrhenius expression

( )

kj ) Bj exp -

Ej RT

where j ) u, c

(7)

Changes of the species concentrations with time in a molten nylon/water system in a well-mixed batch reactor can be described by the following differential equations

-

( )

)

d[C] [L][W] d[A] )) kp [C][A] dt dt Ka

(

[L][W] d[W] - km([W] - [W]eq) ) kp [C][A] dt Ka

(8)

(9)

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Ind. Eng. Chem. Res., Vol. 42, No. 13, 2003

Table 1. Literature Values for Kinetic and Thermodynamic Parameters for Nylon Polycondensation

author(s)

nylon type(s)

temp (°C)

water content (wt %)

Fukumoto5 Ogata13

6 66

235-272 0.09-0.5 275-300 0.04-0.15 -

Ogata14

66

200-220 3.5-40.8

exp

Giori and Hayes9 Reimschuessel and Nagasubramanian30 Tai et al.31 Tai et al.31 Jones and White17 Roerdink et al.19 Blondel et al.20 Steppan et al.27

6, 7 6

240, 260 0.1-9.5 220-265 unknown

8.687 × 106

6 6 68 46 11, 12 6, 66

230-280 230-280 245-290 180-230 220-310 200-265

1.894 × 107 2.224 × 107 1.122 × 105 5.926 × 105 1.242 × 104 depends on [W] and [C]

Mallon and Ray29

6, 66

200-280 0.2-40.8

1.5, 2.1 0.8 unknown 7-14 unknown 0.2-40.8

Eu (kcal mol-1)

Bu (Mg equiv-1 h-1)

-

(

30.17 -13.82 W00.025

-

where km is the volumetric mass-transfer coefficient for the transport of water between the melt and vapor phases, which is also the product of the mass-transfer coefficient and the interfacial area per unit volume. At chemical equilibrium and vapor-liquid equilibrium, the time derivatives in eqs 8 and 9 are zero because eq 3 is satisfied and [W] ) [W]eq. The water content of the nylon melt at both chemical and vapor-liquid equilibrium, [W]eq, is difficult to measure reproducibly (particularly at low water contents) because hygroscopic nylon samples absorb water from the atmosphere. However, [W]eq can be estimated for nylon 612 samples from the temperature, T; the partial pressure of water in the gas phase, Pw; and the vapor pressure of water, Psat w , using a correlation32 based on Flory-Huggins theory

[W]eq ) 5.55 × 104(Pw/Psat w ) exp(-9.624 + 3613/T) (10) For nylon 66, the corresponding expression for [W]eq is

[W]eq ) 5.55 × 104(Pw/Psat w ) exp(-6.390 + 2258/T) (11) 3. Background 3.1. Experimental Studies. The kinetics and equilibrium of polycondensation have been reviewed previously,16,17,23-29,33,34 so only the most relevant contributions in terms of the present work are described. Estimates of the parameters in eqs 5-7, the nylon used, and the conditions of temperature and water content employed in several published studies are summarized in Table 1. Early studies2,5,6 of nylon 6 polymerization showed that polycondensation is exothermic and Ka decreases as the forward reaction becomes less favorable with increasing temperature. Ka was also observed2,6 to decrease with increasing water concentration. However, at very low water concentrations (0.09-0.5 wt %), Fukumoto5 found Ka to be roughly constant. In analogy with the polyaddition reaction, early investigators3,4 speculated that polycondensation might be catalyzed by carboxylic acid end groups, although their data were not sufficient to test this hypothesis. The only experimental data reported for the kinetics and equilibrium of the polycondensation reaction in molten nylon 66 are from two studies by Ogata.13,14 In a high-temperature/low-water-content equilibrium study,13 the experimental end-group concentrations data

)

Bc (Mg2 equiv-2 h-1)

Ec (kcal mol-1)

∆H (kcal mol-1)

∆S (kcal mol-1 K-1)

-

-

-6.841 -26.54

-1.373 × 10-3 -3.807 × 10-2

22.10

-

-

22.55

2.337 × 104

20.67

depends on [W] see Figure 1 -6.140

depends on [W] see Figure 1 9.300 × 10-4

23.27 23.60 17.34 19.39 14.97 21.40

1.211 × 104 8.455 × 101 -

20.67 16.18 -

-5.946 -6.029 0.000 depends on [W]

9.437 × 10-4 9.132 × 10-4 1.123 × 10-2 depends on [W]

0.404

1.250 × 10-2

-

exp

-10.19) (40.72 RT

8.58

give indications that significant thermal degradation occurred, and Ka was calculated using intrinsic viscosity and water content measurements, rather than from the end-group concentrations. This approach is problematic27 because it assumes that degradation does not affect the intrinsic viscosity of the samples, which might not be true if appreciable polymer chain branching had occurred. The Ka values calculated by Ogata appear to increase with water content at a given temperature, but Ogata ignored this effect and simply averaged the Ka values he obtained. Ogata’s ∆H value from this work is 4 times larger than those from most other studies. In a second study14 of both equilibrium and kinetics at lower temperatures and higher water concentrations, Ogata found that polycondensation was endothermic (in contrast to earlier nylon 6 studies), that Ka decreased with increasing initial water content (in accord with earlier studies), and that both ∆H and ∆S varied with the initial water content. When calculating Ka, Ogata assumed that [A]eq ) [C]eq, and estimated the equilibrium linkage concentration from the difference between the final and initial water concentration measurements, making his results susceptible to the effects of experimental errors. Ogata found that his rate data obeyed second-order kinetics and he developed an empirical correlation for ku as a function of W0, the initial molar ratio of water to nylon salt. This correlation is given in the form of eq 7 in Table 1. Giori and Hayes9 observed that Ka for nylon 6 exhibited exothermic behavior at low water contents and showed a strong dependence on the water concentration, as shown in Figure 1. The linear decrease in Ka as the water content decreases below 0.4 wt % was ascribed to a water-content dependence of the end-group activity coefficients arising from changes in the dielectric constant of the medium, which, in turn, can affect the extent of end-group ionization. Wiloth11 claimed that the Ka values of Giori and Hayes were too low because a period of only 20 h was permitted to elapse, whereas he observed higher Ka values after waiting for 80 h under the same conditions. A less substantial rise in Ka with water content is also apparent in Wiloth’s data.11 In both studies, the equilibrium water concentration was not measured directly, but estimated from the known initial water concentration and the measured equilibrium end-group concentration measurements. Long times were required to reach equilibrium because the starting material in these studies was a mixture of


Figure 1. Experimental data of Giori and Hayes9 for polycondensation equilibrium constant of nylon 6 as a function of water concentration and temperature: (b) 240 °C, (O) 260 °C.

the monomer caprolactam and water. Shorter times to reach equilibrium are expected when the starting material has a higher degree of polymerization, as in the present study. In a further study10 of vapor-liquid equilibrium using molten nylon 6, Giori and Hayes accounted for the decrease in Ka above 2 wt % water by changes in the activity coefficient of water. At water contents lower than 1.5 wt %, γW varied little, and the effect of temperature on Ka was smaller. Giori and Hayes9 used second-order kinetics and found that the effect of the water content on the reaction rate could be attributed to the water concentration dependence of Ka. Unfortunately, only two temperatures were investigated in these experiments, so attempts to estimate the parameters in eqs 5 and 7 from these data would not be very meaningful. Reimschuessel and Nagasubramanian30 developed rate and equilibrium correlations for nylon 6 polymerization, but did not present their experimental data or reveal their methodology, so it is difficult to discern the water contents at which their data were collected. The composite kinetic formulation of eq 6 was used. Their values for E agree well with that of Ogata,13 and their ∆H value agrees well with that of Fukumoto,5 although the ∆S values do not agree, as they have opposite signs. Tai et al. performed nylon 6 polymerization experiments12 at six temperatures and three intermediate initial water concentrations. Using the composite kinetic formulation, they estimated rate and equilibrium constants31 and obtained values consistent with those of Reimschuessel and Nagasubramanian.30 The fitted parameters varied with the initial water concentration, so all of the data could not be adequately represented by a single set of constants. As illustrated by the Bc values in Table 1, the relative contribution of kc to kp in eq 6 decreases with decreasing initial water content, indicating primarily second-order kinetics at low water contents, in agreement with the results of Giori and Hayes.9 The kinetics and equilibrium of polycondensation have also been studied using several less-common nylons: nylon 68,17 nylon 46,18,19 nylon 11,20 and nylon 12.20 Some of these studies were performed at high water contents18,19 typical of the low conversion stage of nylon polymerization processes, so the results are outside of the range of interest of the present study. In other studies,17,20 the water content of the samples is

not reported at all, making it impossible to estimate Ka from the available data. The kinetic and equilibrium parameters that can be obtained from these studies are included in Table 1. 3.2. Mathematical Models. Several authors have fit mathematical models for polycondensation to the available literature data, using various approaches to account for the dependence of the apparent equilibrium constant, Ka, and the apparent rate constant, kp, on the water content, temperature, and end-group concentration. Kumar et al.35 fit an empirical correlation to Ogata’s Ka data14 as a function of W0, the initial molar ratio of water to salt. Steppan et al.27 pointed out the unsuitability of this expression and the kinetic expression of Ogata14 for modeling of continuous polymerization processes because it is far more plausible that Ka and kp are functions of the instantaneous water content rather than the initial water content. Steppan et al.27 fit a thermodynamically consistent empirical model to some of the literature data for equilibrium6,9,14,17,24 and kinetics.14,30 They obtained correlations for Ka and kp across broad ranges of temperature and water concentration that are mathematically equivalent to eqs 5 and 7, but with ∆H and ∆S expressed as empirical functions of the water content; Eu set equal to 21.4 kcal mol-1; and Bu expressed as a function of the concentration of both water and carboxylic acid end groups, so that there is a transition from apparent third-order to second-order kinetics with increasing water concentration near 1.5 wt %. The mathematically complicated composition dependencies of Ka and kp were attributed to nonideality of the liquid reaction mixture and changes in the ionic character of the reaction medium due to end-group ionization. Other researchers have used the correlations of Steppan et al. in reactor models for nylon 66 polymerization in autoclaves,36 flasher tubes,37 and extruders.38,39 Mallon and Ray29 used a more fundamental modeling approach to fit literature data.6-9,12-14 Based on the objections of Wiloth11 to the results of Giori and Hayes,9 Mallon and Ray considered Ka to be constant (rather than decreasing with decreasing water content as in Figure 1) at low water concentrations. They focused on the decrease of Ka with increasing water content. It was assumed that water exists in two states in nylon melts (free water and water hydrogen-bonded in “bridges” between carbonyl groups) and that only free water can participate in reaction 1. Mallon and Ray estimated parameters for the temperature dependencies of the equilibrium constants of the hypothesized water bridge formation reaction and the polycondensation reaction with only free water participating. The model accounts for the experimentally observed decrease in Ka with increasing total water concentration due to an increase in the relative proportion of free water. The dependence of kp on the water content and the shift in apparent kinetics from third to second order was explained by adding a reversible “salting-like” prereaction step to reaction 1. This mechanism involves ionization of acid and amine end groups, their subsequent association with each other, and reaction of the associated pair to form an amide link. Acid catalysis (overall third-order kinetics) was assumed under all conditions. Mallon and Ray proposed that, because the “salting-like” reaction involves charge transfer, the equilibrium constant of this reaction (and hence the overall rate of reaction)

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Table 2. Literature Values for Volumetric Mass-Transfer Coefficient in Molten Nylon/Water Systems authors Nagasubramanian and Reimschuessel43 Jacobsen and Ray44 Russell et al.36 Giudici et al.39

km (h-1) 8 78 87 324

km (original units)

temp (°C)

0.15 g cm-2 h-1 atm-1

265

0.18 kmol h-1 KPa 25000 g h-1 psi-1 0.09 s-1

280 225-280 260-300

would decrease as the dielectric constant of the reaction medium, , increased with increasing water content. The dielectric constant was incorporated into an expression for the overall polycondensation rate constant from this mechanism. An expression for Bc as a function of and T equivalent to Mallon and Ray’s expression and their Ec value are shown in Table 1. A mixing rule incorporating the dielectric constants and weight fractions of bound water, free water, and polymer was used to estimate . The polymer dielectric constant was assumed to follow a decaying exponential relationship with temperature, and the constants in this relationship were estimated using data for low-molecular-weight amides. The model predicts that, at low water contents, is approximately equal to 4, but recent measurements40,41 of the dielectric constant of molten nylon 6 at 228 °C are near 90. This discrepancy remains unresolved, but ongoing research involving the use of process tomography42 to measure quantities related to the dielectric constant in melt-phase nylon reactors under a variety of conditions might help to clarify this issue. The model of Mallon and Ray shows good agreement with literature nylon 6 data and agrees with the rate data of Ogata13 for nylon 66 at 220 °C slightly better than the model of Steppan et al.27 does. The predominant feature that emerges from an examination of the experimental and modeling studies is that the water concentration has a profound effect on nylon polycondensation equilibrium and kinetics. This variation has been explained in terms of medium effects on the activity coefficients of the reacting species and by addition of other reactions, such as ionization of end groups and formation of water bridges (as proposed by Mallon and Ray29). The kinetic order of the reaction and the possibly catalytic role of carboxylic acid end groups is uncertain, and various approaches have been used, including overall second-order kinetics, overall third-order kinetics, a composite rate constant, and the dielectric constant approach of Mallon and Ray.29 3.3. Gas-Liquid Mass Transfer. Very little information is available in the literature regarding mass transfer of water in molten nylon systems.34 The few available estimates of km, the volumetric mass-transfer coefficient defined in eq 9, are summarized in Table 2. Values originally reported in terms of a gas-phase concentration driving force were converted to values in terms of a liquid-phase concentration driving force to permit comparison. Nagasubramanian and Reimschuessel43 collected experimental data for the devolatilization of water and caprolactam from a nylon 6 melt in an unstirred reactor vessel at 265 °C using a helium carrier gas. Russell et al.36 and Jacobsen and Ray44 used similar values for km in their analyses of nylon 66 polycondensation in various types of reactors, but the methods or data used to obtain these values were not described. Giudici et al.39 estimated a much larger value for km by fitting their experimental data for nylon 66 polycondensation under vacuum in a vented twin-screw ex-

truder. As might be anticipated, km varies considerably between different types of reactors with potentially different gas-liquid contacting patterns and values of the interfacial area per unit volume. Other researchers have estimated mass-transfer parameters using correlations. Roos45 used a correlation for bubbles and liquid in laminar flow to estimate the mass-transfer coefficient in a gas-liquid contacting reactor in which nitrogen was sparged through a nylon 6 melt. Woo et al.46,47 used penetration theory to estimate mass-transfer coefficients for polycondensation byproducts in sparged-gas reactors for poly(ethylene terephthalate) and polycarbonate melts. Several other quantities such as byproduct diffusivity, bubble diameter, rise velocity, gas-liquid contact time, and fractional gas holdup must be estimated using various correlations to use this approach. In the present study, rather than using correlations, km is estimated from the experimental data. 4. Experimental Section 4.1. Materials. Additive-free nylon 612 polymer pellets were used as received from DuPont Canada, Inc. Steam was generated from water that had been deionized by reverse-osmosis treatment. Oxygen-free nitrogen was used as received from Praxair Canada. 4.2. Reactor System. The operation of the reactor system is similar to the operation of systems described by Roos45 and Woo et al.46,47 in that a sparge gas is bubbled through a polymer melt. The reactor itself is similar in design to finisher reactors described in several patents48-51 that are used industrially as the final stage in continuous nylon 66 polymerization processes. Although the reactor internals were described in a previous mixing study,52 many features of the reactor system that permit operation with molten polymer have not been previously described. Figure 2 shows a schematic diagram of the reactor system. The reactor itself is a 5-L stainless steel stirred tank, with two intermeshing helical impellers entering from the bottom. The impellers were constructed by twisting circular rods into helices. The reactor vessel has a figure-eight cross section to accommodate the range of motion of the impellers and to give a close clearance between the vessel wall and the impellers. A twin-screw extruder section at the bottom of the vessel pumps the polymer melt through a recirculation channel bored through the wall of the vessel and back into the reactor interior. A valve can be opened to divert the recirculating flow out of the reactor, so that multiple samples of the polymer can be taken at various times during each experimental run. The impellers and the extruder screws are driven by a variable speed drive with torque and speed sensing capability. The reactor system is heated electrically using four separate heating zones: the reactor head flange, the reactor vessel, the extruder barrel, and the sample valve. Each heating zone is equipped with a resistive temperature detector (RTD) embedded in the heated part, one or more electric heaters, and a temperature controller that adjusts the power output to the heater(s) to maintain a set-point temperature. The melt temperature is measured using an RTD inserted into the center of the melt pool, in an open vertical space through which neither impeller moves as it rotates. A key feature of the equipment is a system to generate steam, mix it with nitrogen, and deliver the mixture to the reactor vessel as a preheated sparge gas. Reverse-


Figure 2. Schematic drawing of the experimental apparatus: (1) reactor vessel, (2) impellers, (3) recirculation channel, (4) extruder section, (5) sample valve, (6) gearbox, (7) motor and drive, (8) reactor heating zones, (9) melt RTD, (10) water tank, (11) scale, (12) water seal, (13) pump, (14) steam-generating heaters, (15) N2 cylinders, (16) regulator, (17) N2 metering valve, (18) rotameter, (19) N2 preheater, (20) final heater, (21) sparger tubes, (22) glass coil condenser, (23) condensate tank, (24) buret, (P) pressure gauge, (T) temperature sensor, (TC) temperature controller, (F) mass flowmeter, (R) RPM sensor, (TQ) torque sensor, (D) drain, (V) vent.

osmosis-deionized water is contained in a 20-L tank placed on a scale to permit measurement of its loss in weight with time, thereby giving a confirmatory measure of the water flow rate to the vessel. Nitrogen is bubbled through the water continuously to remove dissolved oxygen and exits the water supply tank through a water seal. A peristaltic pump removes water from the supply tank and delivers it to two manually controlled heaters in series, which vaporize the water and generate steam. The steam is then sent to the reactor, or it can be diverted to a drain. Nitrogen flows from one of two cylinders connected to a header, through a two-stage pressure regulator, a mass flow sensor, and a rotameter to a preheater. The hot nitrogen exiting the preheater is mixed with the steam. A controller adjusts the power input to the nitrogen preheater to regulate the temperature of the steam/nitrogen mixture. The steam/nitrogen mixture then flows through a final heater before entering the reactor vessel through two 1/ -in. sparger tubes. The temperature of the sparge gas 4 entering the reactor is regulated by a controller that adjusts the power input to the final heater. The sparger tubes are inserted within the stirred melt pool in the center of the reactor vessel so that intimate contact is achieved as the sparge gas bubbles through the melt. Bourdon tube gauges are used at various points (including at the reactor vessel head flange) to measure the pressure of flowing nitrogen or nitrogen/steam mixtures. The gas leaving the reactor enters a water-cooled glass coil condenser. A portion of the off-gas condenses and is collected in a 4-L tank, while the noncondensable portion is vented. The condensate flow rate can be

estimated by measuring the time required to fill a 10mL buret. The composition of the sparge gas can be varied from entirely steam to predominantly nitrogen by changing the water pump speed to alter the steam flow rate and by adjusting the metering valve at the rotameter inlet to alter the nitrogen flow rate. A data acquisition system (National Instruments Fieldpoint with Labview software) is used to record measurements of the drive torque, drive speed, nitrogen mass flow rate, and all temperatures during an experimental run. These data are collected at a sampling rate of 1 data point every 10 s. 4.3. Procedure. Four experimental runs were performed, at melt temperatures of 263, 271, 281, and 289 °C. Approximately 1.8 kg of preweighed polymer pellets was charged to the reactor for each run. The vessel was sealed by bolting on the head flange and thoroughly purged with nitrogen to remove residual air. All heating zones were activated, and approximately 1 h was allowed for all zones to reach set-point temperatures. Preheated nitrogen was circulated through the reactor vessel during heating. After the temperature in the center of the reactor had reached a value near 200 °C, the drive was started slowly, and the speed was gradually increased to the set-point value of 20 rpm as the polymer melted and began to be pumped by the extruder section through the recirculation channel. After the melt temperature had reached a steady value (usually slightly above the heating-zone set points), the sparge-gas composition was switched to pure steam, and 1 or 2 h was allowed to elapse so that the polymer could reach equilibrium under steam before the first sample was

2952


taken. Several polymer samples were then taken to permit verification of equilibrium conditions by subsequent characterization. The concentration of water in the sparge gas (expressed here as Pw) was then reduced by the addition of nitrogen and lowering of the water pump rate, and the polymer was allowed to reequilibrate while more polymer samples were taken. Pure steam conditions were then reestablished, and the polymer was allowed to equilibrate a third time, again as samples were taken. Sampling was more frequent immediately after a change in sparge-gas composition because concentration variables were changing rapidly during these time periods. Each experimental run contained three equilibrium conditions where concentration variables were constant and two kinetic conditions where concentration variables were changing rapidly. Flow rates of nitrogen and steam were set to achieve constant superficial velocity of sparge gas through the reactor within each run. The superficial gas velocity was approximately 0.04 m s-1, which is well below the upper limit of 0.08 m s-1 given by Treybal53 as a guideline to prevent excessive liquid entrainment from sparged vessels. At the conclusion of a run, the remaining polymer was pumped out of the reactor through the sample valve, the drive and temperature controllers were turned off, and the system was allowed to cool overnight. The reactor was then disassembled, and any residual polymer left on the components of the system was removed by high-pressure water blast cleaning. The reactor was then reassembled for the next experimental run. 4.4. Sample Characterization. 4.4.1. End-Group Analyses. Polymer samples for end-group and solutionviscosity analyses of approximately 10 g each were taken into a stainless steel bowl filled with cold domestic water to rapidly quench and solidify the molten polymer. The samples were cut into smaller pieces, cooled by immersion in liquid nitrogen, and ground using an electric grinder. Grinding the samples at a low temperature prevented softening and sticking due to generation of heat. End-group analyses were performed using methods similar to those outlined by Sibila et al.22 For carboxylic acid end-group titrations, 1.50-2.00 g of each ground polymer sample was dissolved in 60 mL of 95/5 o-cresol/o-dichlorobenzene and titrated at 25 °C with 0.04 N potassium hydroxide in benzyl alcohol. For amine end-group titrations, 0.75-1.00 g of each ground polymer sample was dissolved in 75 mL of 90/10 phenol/ methanol and titrated at 25 °C with 0.03 N perchloric acid in methanol/water. An automatic potentiometric titrator was used to perform both types of titration. In both cases, the normality of the titrant was measured by titration with a known standard, and blank corrections were made for the titration of the polymer samples. Two measurements of each type of end group were performed for each sample, and the results were averaged. The standard deviations associated with carboxylic acid and amine end-group measurements, calculated by pooling the variances from each set of measurements, are 2.4 and 0.6 equiv Mg-1, respectively. These values correspond to uncertainties (95% confidence level) of (4.8 and (1.2 equiv Mg-1, respectively, indicating that measurements of acid end-group concentration are inherently less precise than measurements of amine end-group concentration (using these methods). 4.4.2. Inherent Viscosity Measurements. This procedure for inherent viscosity (IV) measurements is

based on the ISO307 standard.54 For these measurements, 0.20 g of each ground polymer sample was dissolved in 40 mL of m-cresol (>99%) to give a polymer concentration of 0.5 g dL-1. Each solution was filtered using a 200-mesh screen, and the flow times of the sample solution and the solvent (tsolution and tsolvent, respectively) were measured at 25 °C using a SchottGerate type II Ubbelohde viscometer with a capillary inside diameter of 1.03 mm. The inherent viscosity was calculated as

( )

IV ) ln

tsolution /0.5 tsolvent

(12)

Three measurements were made for each sample, and the results were averaged. The calculated uncertainty for an IV determinations, obtained by pooling the variances from each set of measurements, is (0.008 dL g-1 (95% confidence level). 4.4.3. Water Content Measurements. Initial attempts to use the Karl Fisher titration method22 to measure the water contents of polymer samples taken from the reactor into mineral oil were unsuccessful. The nylon samples are very hygroscopic, and their water content is very low, so small amounts of moisture absorbed from the air during sample handling or from the mineral oil resulted in large deviations and unacceptable scatter in the experimental water concentration data. To circumvent this problem, a new sampling procedure and analytical method were adopted. Polymer samples were taken from the reactor system into glass septum vials under a stream of gaseous nitrogen, and analyzed as rapidly as possible using a Computrac Vapor Pro moisture analyzer from Arizona Instruments. The principle of operation of this moisture analyzer55 and the details of the water content measurements32 have been described previously. Because the moisture analyzer was available on loan for only one of the four experimental runs (at 263 °C), reliable water content data could be acquired for only this run. Replicate measurements on the same sample were not available, but several samples were taken for each equilibrium condition. These were used to estimate a pooled standard deviation of 9.4 mol Mg-1 (or 0.017 wt %) for water concentration measurements, corresponding to an uncertainty of (21 mol Mg-1 (or (0.038 wt %, at the 95% confidence level). Water concentration measurements are far less precise than concentration measurements of both types of end group. 5. Experimental Results The range of conditions employed in this study is 263-289 °C and 0.01-0.12 wt % water, which are relatively high temperatures and low water concentrations in comparison with those used in previous studies5,9,12-14,19 of nylon polycondensation. The experimental end-group and water concentration and inherent viscosity data are plotted versus reaction time in Figures 3-7, along with the end-group and water concentration predictions of the mathematical models of Steppan et al.27 and Mallon and Ray29 and the new model developed in the present work. The less-precise nature of acid end-group concentration measurements is reflected by the greater degree of scatter in these data than in the amine end-group concentration data. In the initial stages of each experimental run, equilibrium is established under a steam atmosphere, as indicated by


Figure 3. Experimental data and model predictions for run at T ) 263 °C. Sparge-gas humidity was decreased from Pw ) 760 mm Hg to Pw ) 169 mm Hg at 3.09 h and increased to Pw ) 760 mm Hg at 7.00 h. (2) Measured carboxylic acid end-group concentration, (b) measured amine end-group concentration, (0) measured IV. (- - -) Steppan et al. model, (- ‚ - ‚ -) Mallon and Ray model, (s) present model.




the relatively constant end-group concentration and IV values. When Pw is decreased, the water concentration in the melt decreases rapidly, and there is a net polycondensation reaction, so that the end-group concentrations decrease as amide linkages are formed, and the IV increases as a result of the increased polymer molecular weight. Equilibrium is reestablished at these conditions of lower water concentration and then Pw is increased, and the water concentration increases again. There is a net hydrolysis of amide linkages, and the endgroup concentrations increase, and the IV decreases until equilibrium is established under conditions similar to those at the outset of the experimental run. Note that the time scales differ in Figures 3-6 and that the rate of approach to equilibrium increases as the temperature increases, consistent with Arrhenius behavior of the apparent rate constant.

The observed end-group concentration changes within each run indicate significant changes in the numberaverage polymer molecular weight, from values of around 17 000 g mol-1 at high water concentrations to values of around 24 000 g mol-1 at low water concentrations. The concentrations of the two types of end-groups behave similarly, increasing and decreasing in parallel, as they should in a system where thermal degradation of the polymer does not occur to any appreciable extent. This was not the case in several other studies56-58 where nylon 66 was held for extended time periods under similar conditions of temperature and water content; substantial increases in the concentration of amine end groups and decreases in the concentration of carboxylic acid end groups were observed. This indicates that the cyclization reactions suspected to occur as the initial steps in nylon 66 thermal degradation are negligible in

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Figure 7. Water concentration data and model predictions for experimental run at T ) 263 °C. Sparge-gas humidity was decreased from Pw ) 760 mm Hg to Pw ) 169 mm Hg at 3.09 h and increased to Pw ) 760 mm Hg at 7.00 h. (b) Measured water concentration. (s) Present model, Steppan et al. model, and Mallon and Ray model (lines are coincident).

the nylon 612 system employed in the present study. Further evidence of the absence of thermal degradation in the present study is the relatively constant value of the difference between the end-group concentrations ([C] - [A]) within each experimental run and the fact that changes in polymer molecular weight corresponded to changes in IV, indicating that the polymer remained predominantly linear and unbranched. Furthermore, only very small changes in the reactor drive torque, following the same pattern as the IV measurements and likely arising from the changes in polymer molecular weight, were observed throughout each run. If the polymer became appreciably branched or gelled, the drive torque would be expected to increase substantially because of the greatly increased viscosity of the polymer melt. A previous study52 of mixing in the present reactor system under nonsparged conditions using a model fluid at room temperature indicated that the reactor contents are well-mixed after approximately 104 impeller revolutions. This corresponds to approximately 5.2 min after the start of a run at the impeller speed used here. Because the first samples were not taken until at least 60 min after the impellers were started, the assumption that the molten polymer is well-mixed at the beginning of a run is reasonable. On the basis of this short mixing time in comparison with the time scale of the end-group concentration data and the additional agitation provided by the bubbling of a sparge gas through the melt, mixing effects after a change in sparge-gas humidity were also neglected. 6. Literature Model Predictions The predictions of recent mathematical models of Steppan et al.27 and Mallon and Ray29 for nylon polycondensation were compared with the present experimental data. Both models attempt to describe polycondensation across the entire range of temperatures and water concentrations encountered in nylon polymerization processes, whereas the present experimental conditions encompass a much narrower range of conditions, for which few data were previously available. Some

additions to and modifications of the literature models were required to permit their application to the present experimental situation. A value for the volumetric masstransfer coefficient was required; 24.3 h-1, the value obtained for the present model in the parameter estimation section below, was used in all of the models. Also, Ka values are expected to differ for nylons with different ratios of amide groups to methylene groups in the polymer repeat unit.59 Because the literature mathematical models were fit using nylon 6 and nylon 66 data but we wish to apply these models to nylon 612, a correction must be made to account for the effect of nylon type on Ka. Assuming that all of the variation in Ka due to nylon type arises from different activity coefficients for water (the thermodynamic equilibrium constant and the activity coefficients of end groups and amide links are assumed to be the same in all systems), the ratio of eqs 10 and 11 can be used to estimate the ratio of the value of Ka for nylon 612 to that for nylon 66

K612 a K66 a

) exp[-3(1.078 - 451.63/T)]

(13)

This correction factor was applied to the Ka expressions in the literature mathematical models. In the temperature range of the present study, the ratio in eq 13 has values of 0.4-0.5. Equation 13 can also be used to apply the results of the present study to other nylon systems. Equation 10 was used to estimate the equilibrium water concentration in the melt for all simulations. The model of Mallon and Ray makes a distinction between bound water and free water in the melt, but it is not clear whether analytical methods would yield a measure of the free water concentration or the total water concentration. It was assumed that the total water concentration is the variable that would be measured experimentally and estimated by eq 10, but in any event, the total water concentration predicted by the Mallon and Ray model is never very much larger than the free water concentration under the conditions used in the present study; the free water concentration was 84-92% of the total water concentration in all simulations. Matlab was used to perform numerical integration of the differential eqs 8 and 9 using values for Ka and kp from the literature mathematical models. The fourthorder Runge-Kutta method was used with a fixed step size of 0.01 h. The initial conditions used were the same as those for the new model in the parameter estimation section below. The model predictions are shown in Figures 3-7. Both models appear to describe the experimentally observed kinetic behavior quite well; the rates of change of the end-group concentrations predicted by both models seem comparable to the experimentally observed rates. However, the models differ in the predicted equilibrium values of the end-group concentrations. At 263 °C, the Mallon and Ray model underpredicts the experimental end-group concentration data, and the Steppan et al. model overpredicts the endgroup concentrations. As the temperature increases, the agreement between the Mallon and Ray model predictions and the data becomes progressively worse, and the agreement between the Steppan et al. model predictions and the data becomes better. The Mallon and Ray model predictions of the equilibrium values of the end-group concentrations tend to be lower than the experimental data, particularly at higher temperatures. This likely


where b and m are constants. Rearranging eq 4, incorporating the temperature dependence of the thermodynamic equilibrium constant using eq 5, and substituting for the ratio of activity coefficients using eq 14 gives an expression for Ka

Ka )

(

) (

)

b + m[W]eq ∆H ∆S exp + γW RT R

(15)

The equilibrium water concentration, [W]eq, was estimated using eq 10. Equation 16 is an expression for the activity coefficient for water, γw, obtained using a previously proposed Flory-Huggins-based model32

(

γw ) exp 9.624 Figure 8. Apparent polycondensation equilibrium constant calculated from the present experimental data as a function of temperature and water concentration. Values at (O) high and (b) low water concentrations. Error bars are 95% confidence intervals for the true mean values of Ka.

occurs because the phenomenon of Ka decreasing with decreasing water content at low water contents observed by Giori and Hayes9 and shown in Figure 1 was neglected by Mallon and Ray, who considered Ka to vary only with temperature at low water concentrations. The present experimental data also indicate a decrease in Ka as the water content decreases, as shown in Figure 8. The values of Ka predicted by the Mallon and Ray model are too high, so that, at a fixed equilibrium water concentration, the predicted equilibrium values of the end-group concentrations are too low. The model of Steppan et al. incorporates the decreasing Ka behavior and generally agrees better with the present experimental data than does the model of Mallon and Ray. Upon application of the correction of eq 13 and use of our value for km, the model of Steppan et al. agrees quite well with the present data, which were not used to fit their model. This lends credence to the use of this model to describe nylon polycondensation at high temperatures and low water contents. Although the Steppan et al. model is comprehensive in that it describes nylon polycondensation across a wide range of water contents and temperatures, it is also highly empirical and mathematically complex. An effort was therefore made to develop a simpler model capable of describing the new experimental data. 7. New Mathematical Model and Parameter Estimation Initial attempts to describe the experimental data using a model incorporating an expression for Ka as a function of temperature alone produced unsatisfactory results. As Figure 8 indicates, the experimentally observed apparent equilibrium constant is significantly smaller at lower water concentrations than it is at higher water concentrations. To account for this behavior, an expression for the ratio of activity coefficients from eq 4 as a linear function of the equilibrium water concentration was incorporated into the new mathematical model

γ Cγ A ) b + m[W]eq γL

(14)

3613 T

)

(16)

Considering the controversy in the literature regarding the order of the polycondensation reaction, both purely second-order and purely third-order kinetics were used to fit the present model. The overall third-order case will be discussed first. To allow improved estimation of model parameters, eqs 15 and 7 for Ka and kp were rearranged to a form involving a reference temperature and a reference value, as in eqs 17 and 18, respectively

Ka )

(

)

[ (

1 + g[W]eq 1 ∆H 1 Ka0 exp γW/γW0 R T T0

[ (

kc ) kc0 exp -

)]

Ec 1 1 R T T0

)]

(17)

(18)

The reference temperature, T0, was chosen as 549 K, the middle of the temperature range used in the present experiments. The parameter g is a constant that is equal to m/b. The reference state for the apparent equilibrium constant, Ka0, was chosen as T0 and zero water concentration

Ka0 )

( ) (

)

b ∆H ∆S exp + γw0 RT0 R

(19)

kc0 and γw0 are constants that represent the values of the rate constant and the water activity coefficient, respectively, at T0. kc0 is a parameter to be estimated, whereas the valule of γw0 was calculated as 20.97 using eq 16. Estimates of kc0 can be converted to the corresponding values of Bc for comparison with values from the literature in Table 1. The model consists of the differential eqs 8 and 9, with Ka given by eq 17, and kp given by eqs 6 and 18 with ku set equal to zero. The model parameters to be estimated are ∆H, Ka0, g, Ec, kc0, and km. Because it is known that the carboxylic acid end-group and water concentration measurements are less reliable, an effort should be made to ensure that the parameter estimates are less influenced by these measurements than by the more precise amine end-group concentration measurements. This was done by using weighted least squares; the errors between the model predictions and the experimental end-group and water concentration data were weighted by the reciprocal of the estimated standard deviation for the given measurement type, and the sum of the squared weighted errors was minimized using the “lsqnonlin” Matlab routine with the Levenberg-Marquardt algorithm.60 A similar approach was used by Tai

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Table 3. Parameter Summary for the Present Model parameter

units

estimate

95% confidence interval (()

∆H Ka0 g Ec kc0 km

kcal mol-1 Mg mol-1 kcal mol-1 Mg2 equiv-2 h h-1

-1.82 63.1 2.03 × 10-2 22.6 3.19 × 10-4 24.3

1.42 6.2 0.45 × 10-2 7.7 0.71 × 10-4 15.4

et al.31 to estimate rate and equilibrium parameters for nylon 6 polymerization. Reasonable initial guesses for the model parameters were obtained by fitting the equilibrium constant data in Figure 8 and by selection of values from Table 1. The parameters were scaled so that the initial guesses were of the same order of magnitude. Rather than using the first end-group concentration values in each run, initial conditions were estimated as parameters to reduce the dependence on a single (and in the case of carboxylic acid, a relatively uncertain) experimental data point. The model differential equations were numerically integrated using the same methods as for the literature models in the previous section. Table 3 shows the converged parameter estimates; the 95% confidence intervals for the true values of the parameters; and the parameter estimate correlation matrix, calculated using methods outlined by Nash and Sofer.60 The parameter estimates were relatively insensitive to the starting point; the routine converged to the same optimum for a wide range of reasonable initial parameter guesses. The incorporation of γw and g into the model expression for Ka precludes direct comparison of the ∆H estimate and the corresponding expression for ∆S for the present model with literature values. However, the Ec estimate obtained agrees quite well with several of the literature values in Table 1, and the km estimate also appears reasonable in comparison with the literature values for nylon systems in Table 2. The value of Bc (3.15 × 105 Mg2 equiv-2 h-1) corresponding to the estimated value of kc0 is larger than other values listed in Table 1, but the literature values also have secondorder contributions to kp, whereas the present model is purely third order. All of the parameters are statistically significant, as none of the confidence intervals contain 0. The parameters Ka0, g, Ec, and kc0 are well-determined, but ∆H and km are not. The most highly correlated pairs of parameters are Ka0 with g and kc0 with km, meaning that independent estimates of these parameters can not be obtained using the present data. The first correlation likely arises because of the form of the model eq 17, but efforts to use other equation forms did not yield less-correlated parameter estimates. The second correlation likely stems from the fact that the kinetic and mass-transfer parameters are both estimated from the same nonequilibrium conditions in the experimental runs. Despite the uncertainties in the parameter estimates, the predictions of the fitted model follow the experimental data in Figures 3-7 quite well and agree more closely with the amine end-group concentration data than with the carboxylic acid end-group concentration data because of the heavier weighting of the moreprecise amine end-group concentration data in the estimation procedure. In terms of agreement with the new experimental data, the new model performs better than both literature models at lower temperatures, and as well as the Steppan et al. model at higher temper-

approximate correlation matrix 1.000 -0.526 0.548 0.203 0.227 -0.115

1.000 -0.978 0.059 -0.196 -0.004

1.000 -0.020 0.280 -0.064

1.000 0.425 -0.546

1.000 -0.842

1.000

atures. The proposed model is therefore a more easily implemented and more accurate alternative to both of the literature models for nylon polycondensation at conditions of very low water concentration and high temperature. 8. Discussion 8.1. Kinetic Order of Polycondensation. Overall second-order kinetics were also used to fit the model to the experimental data. The value of Bu corresponding to the estimated value of ku0 was 2.64 × 107 Mg equiv-1 h-1. All of the other parameters changed only slightly from their values for the third-order case. The degree of agreement with the experimental data was indistinguishable from the third-order case, and the sum of the squared weighted residuals showed no significant change, indicating that it is not possible to determine whether polycondensation is acid-catalyzed or not on the basis of the present experimental data. Future experiments where the initial end-group concentrations are altered by deliberate addition of an excess of diamine or diacid monomer have been planned and should help to resolve this issue. 8.2. Effect of Water Concentration on the Apparent Equilibrium Constant. The decrease in Ka with decreasing water content was accounted for in the new model using eq 14. One interpretation of this expression is that the relative activity of the end groups decreases with decreasing water concentration. There are at least three potential mechanistic explanations for this behavior. First, ionization of end groups might be involved, as suggested by Giori and Hayes,9 but this seems improbable, as the end groups likely exist predominantly in the un-ionized state at these very low water concentrations. Two other possible explanations stem from the observation that the variation in Ka with water concentration does not necessarily indicate a causal relationship, as several other variables in molten nylon systems are also correlated with the water concentration. As the water concentration decreases, the concentrations of both types of end group also decrease. If polycondensation is catalyzed by acid end groups but hydrolysis is not, then Ka would decrease with decreasing acid end-group concentration, giving a second possible explanation for the observed behavior. Further research into the mechanism and kinetics of amide formation and hydrolysis using low-molecular-weight aliphatic monocarboxylic acids and aliphatic monoamines at high temperatures as a model system might help to clarify this issue. Because the preferred synthetic route to low-molecular-weight amides is through acid chloride intermediates, apparently only one study61 of amide preparation by direct amidation has been published, and these authors did not investigate the mechanism and kinetics of the reaction. As the water concentration decreases, the melt viscosity increases, and a third potential explanation for the observed


decrease in Ka is the onset of diffusion limitation of the polycondensation reaction. End groups must undergo bulk and segmental diffusion before they can react with each other, and a substantial decrease in polymer chain diffusivity due to increasing melt viscosity could decrease the effective value of the polycondensation rate constant.62 The rate constant of the hydrolysis reaction might be less sensitive to melt viscosity because water is a more mobile species in the melt than the much larger polymer molecules, and so Ka decreases with increasing viscosity because kp/kh decreases. 8.3. Volumetric Mass-Transfer Coefficient. A greater quantity of more precise water content data would likely improve the precision of the km estimate and reduce its correlation with other parameters, but the improved water content measurement method was not developed until late in the present experimental program, and more precise methods for the measurement of low water concentrations in nylon polymers are not currently available. The estimation of km using the present experimental apparatus would also likely be improved by the addition of on-line water content measurement of the off-gas from the reactor. This study is nonetheless the first (according to the present authors’ knowledge) in which the time evolution of the water concentration in a nylon melt has been followed, allowing for a direct estimation of a volumetric mass-transfer coefficient from the data. The km estimate obtained is not only consistent with the literature values for other nylon reactor systems in Table 2, but is also near the range of values (4-22 h-1) obtained for the volumetric mass-transfer coefficient of oxygen in highly viscous aqueous solutions of xanthan gum in a sparged vessel mixed with a helical ribbon screw impeller.63 From that study, km is expected to depend on the impeller speed; the superficial gas velocity; and, to a lesser degree, the liquid viscosity. Because all of these quantities were kept relatively constant in the present experiments, the use of a constant km value is justified, but application of this estimate to other reactor systems should be approached with caution. Further research on the effects of changes in operating variables on km would allow the development of improved models for mass transfer in molten nylon polymers.

expressing the ratio of the end-group and amide-link activity coefficients as a linear function of the water concentration. The observed variation of Ka with water content might not indicate a causal relationship; other plausible explanations for this behavior exist. Overall third-order (carboxyl-catalyzed) and overall secondorder kinetic formulations fit the experimentally data equally well, so discernment of the kinetic order of the polycondensation reaction is not possible from the present results. Reasonably precise estimates of several parameters of the new model are in order-of-magnitude agreement with literature values, although some parameters are highly correlated, and others are poorly determined. To our knowledge, this is the first time that polycondensation has been studied using nylon 612, as well as the first time that the volumetric mass-transfer coefficient for a molten nylon/water system has been estimated from experimental melt-phase water concentration data. The results presented here indicate that it is necessary and advisable to include the effect of the apparent equilibrium constant decreasing with decreasing water content, neglected in the past by other researchers, to describe polycondensation at these conditions. The new experimental data and the proposed model should prove useful for simulations of industrial processes for melt-phase nylon polycondensation in various reactor configurations and aid in the design of process improvements for the final stages of nylon production. These results will also be used in ongoing studies using nylon 66, where the rate and equilibrium of the polycondensation reaction must be taken into account simultaneously with the effects of deleterious thermal degradation reactions. On the basis of the present results, further research is recommended involving investigations of the mechanism and kinetic order of the amidation reaction using low-molecular-weight model compounds, the effects of operating and physicochemical variables on the volumetric mass-transfer coefficient, and the effects of the initial end-group concentrations on the kinetics and equilibrium of polycondensation in nylon 612 melt systems.

9. Conclusion

The authors are grateful to Jim Whitmore of DuPont Canada Research and Business Development for performing end-group concentration and inherent viscosity measurements, to Wei Zheng and Karen Splinter for experimental assistance, and to Arizona Instrument for the loan of the moisture analyzer. Financial support provided by DuPont Canada, the Natural Sciences and Engineering Research Council of Canada (NSERC), and the Government of Ontario is greatly appreciated.

In this paper, we investigated the kinetics and equilibrium of polycondensation at high temperatures and low water concentrations using nylon 612 as a more thermally stable model polyamide for nylon 66. A novel reactor system was used to collect multiple polymer samples during each experimental run. The carboxylic acid and amine end-group concentrations and the inherent viscosity were measured for all samples, and the water content was measured for several samples from one experimental run. The model of Steppan et al. agrees well with the experimental data, but the model of Mallon and Ray underpredicts the experimental end-group concentrations, likely because of omission of the phenomenon of Ka decreasing with decreasing water content. A new, simplified mathematical model for polycondensation and water mass transfer under these experimental conditions was developed and found to fit the experimental data as well as or better than the literature models. The effect of the water concentration on the apparent equilibrium constant was described semiempirically by

Acknowledgment

Nomenclature [A] ) concentration of amine end groups, equiv Mg-1 b ) empirical constant to describe the effects of the water content on Ka B ) preexponential factor, Mg equiv-1 h-1 [C] ) concentration of carboxylic acid end groups, equiv Mg-1 E ) activation energy, kcal mol-1 g ) model parameter related to the effect of the water content on Ka, Mg mol-1 ∆H ) apparent enthalpy of polycondensation, kcal mol-1 IV ) inherent viscosity, dL g-1

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kc ) carboxyl-catalyzed apparent polycondensation rate constant, Mg2 equiv-2 h-1 kc0 ) carboxyl-catalyzed polycondensation rate constant at T0, Mg equiv-1 h-1 kh ) apparent hydrolysis rate constant, Mg equiv-1 h-1 km ) volumetric liquid-phase mass-transfer coefficient for nylon/water system, h-1 kp ) apparent polycondensation rate constant, Mg equiv-1 h-1 ku ) uncatalyzed apparent polycondensation rate constant, Mg equiv-1 h-1 ku0 ) uncatalyzed polycondensation rate constant at T0, Mg equiv-1 h-1 Ka ) apparent polycondensation equilibrium constant Ka0 ) apparent polycondensation equilibrium constant at T0 and [W]eq ) 0 K612 ) apparent polycondensation equilibrium constant a for nylon 612 K66 a ) apparent polycondensation equilibrium constant for nylon 66 Kt ) thermodynamic polycondensation equilibrium constant [L] ) concentration of amide links, equiv Mg-1 m ) empirical constant to describe effect of the water content on Ka, Mg mol-1 Pw ) partial pressure of water in the gas phase, mm Hg Psat w ) saturation pressure of water in the gas phase, mm Hg R ) ideal gas law constant, 1.987 × 10-3 kcal mol-1 K-1 ∆S ) apparent entropy of polycondensation, kcal mol-1 K-1 t ) time, h T ) temperature, K T0 ) reference temperature, 549.15 K [W] ) concentration of water, mol Mg-1 [W]eq ) concentration of water at vapor-liquid equilibrium and chemical equilibrium, mol Mg-1 W0 ) initial molar ratio of water to nylon salt, mol of water/ mol of salt Greek Letters γi ) activity coefficient of species i in the nylon melt γw ) activity coefficient of water in the nylon melt γw0 ) activity coefficient of water in the nylon melt at T0 ) dielectric constant of the reaction medium Subscripts a ) apparent A ) amine end group c ) catalyzed C ) carboxylic acid end group eq ) equilibrium h ) hydrolysis L ) amide link p ) polycondensation t ) thermodynamic u ) uncatalyzed W ) water

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Received for review December 13, 2002 Revised manuscript received April 7, 2003 Accepted April 11, 2003 IE021029+

Experimental Study and Modeling of Nylon Polycondensation in the

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