tirrell pearson weiss laurance pes 1975

8/8/2019 Tirrell Pearson Weiss Laurance PES 1975

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An Analysis of Caprolactam PolymerizationM. V. TIRRELL, G. H. PEARSON, R. A. WEISSAND R. L. LAURENCE

DepartmentsPolym er Science and Engineeringan dC,hemical EngineeringUniversity of MassachusettsAmherst, Mass.

of

A versatile model for ecaprolactam polymerization is pre-sented. A deterministic, mathematical basis for obtaining themost probable distribution of molecular weights in batch poly-merization is developed. Continuous polycaproamide productionhas been modeled and shown to give other than most probabledistribution in many cases. The effect of adding monofunc-tional agents has been investigated. Results of some pre-liminary studies toward determining the optimal reactor con-figuration are presented.

INTRODUCTIONR e c e n t p a p e r s by Reimschussel and coworkers( 1 - 4 ) have dealt with various aspects of nylon-6production by hydrolytic polymerization of c-capro-lactam. Focusing on reaction conversion or number-average molecular weight as variables of interest,problems treated have been: condensation equilib-rium in the presence of additives ( l), olymerizationin a CSTR and other series configurations ( 2 ) , theminimum time optimization problem ( 3 ) and the re-equilibration of nylon-6 (4). t has been stated orassumed in all these treatments that a most probabledistribution of polymer chain lengths describes thereaction product. For a product like nylon-6 that istypically processed by extrusion and melt spinning,molecular weight distribution, through its effect onmelt viscosity, is a very important property. T he mostprobable distribution of molecular weights is foundin most commercial nylon-6 products (18) and doesindeed give a desirable product of uniform quality

With these factors in mind, we have developed atreatment of caprolactam polymerization which canpredict not only conversion and number-averagedegree of polymerization, bu t also can describemathematically the molecular weight distribution asa function of reaction time. Our objective has been toformulate a model adaptable enough to b e applied toa wide variety of reactor conditions and configura-tions. We are able to show in which reactor designsa most probable distribution is indeed the expectedproduct and how it may be drastically different in aCSTR or in other reactor configurations. In this samevein, the common practice of adding a monofunc-tional agent to control molecular weight is examinedin some detail with regard to its effect on molecularweight and molecular weight distribution.

(20).

CHEMISTRYOF CAPROLACTAMPOLYMERIZATIONThere are two basic reaction schemes that are of

commercial interest for the polymerization of -cap-rolactam.

The hydrolytic process (5) consists of the reac-tions illustrated in Table 1.There is an abundance ofkinetic information available in the literature on thispolymerization mechanism (6-10). From a chemical

Table 1. Hydrolytic PolymerizationInitiation: ring opening 0

ki IIHN-(CHn)j-C=O + H z O N H ~ ( C H Z ) ~ - C - - O Hki MI (w) (S1)Propagation: polycondensation

kzkz

NH2 + HOOC---- + + HzO-- - CONH- - - -(Sn) (Srn) ( S n + m ) (W)polyaddition

k3----NHz + HN-(CH&-C=O s- 3(Sn) (M I - - - NHCO (CH2)sNHz(Sn + 1)~Reaction with monofunctional species:k4K

---- NHz + H O O C - - . - - - I(Sn) (Am) - - NHCO- - I + Hz0

(An rn) (W)

386~~

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An Analysis ofCaprolactam Polymerizationreaction engineering viewpoint, however, severalfeatures are important. First of all, it has been shownthat this reaction is catalyzed by chain end groups( B S i ) which change in concentration with reactionconversion. This imparts an autocatalytic characterto the reaction. Secondly, this polymerization hasboth step growth and chain growth character (11).There are essential differences in the general typesof molecular weight distributions (MWD ) obtainedin idealized step growth and chain growth polymer-izations. The question of MWD will be dealt with inmore detail later in this paper. Thirdly, the reversi-bility of all the polymerization steps presents a math-ematical challenge in modelling the system ( 12).Caprolactam can also be readily polymerized by avariety of anionic initiators (5, 13-16). The attrac-tiveness of this type process lies in the speed of thereaction. The mechanism is entirely chain growth.This time advantage is largely negated, however, bythe necessity of allowing the narrow distributionproduct to re-equilibrate to the apparently desirablemost probable distribution ( 15, 17) . This factor, plusthe necessity of maintaining scrupulously anhydrousconditions, makes this a little used reaction commer-cially (18). By application of the techniques dem-onstrated in this paper anionic polymerization ofc-caprolactam can be made a tractable mathematicalmodeling problem. However, the remainder of thispaper is devoted to the hydrolytic process, a morecommercially interesting system.

MODELING TECHNIQUEThe hydrolytic process of Table 1 can be repre-sented in the following manner:

k lkl'B ! + W e S , (1)

k2k2'

Sn + Sm i=n+m+W ( 2 )k3

k,'Sn + M*Sn+t ( 3 )

k4k41Sn +Am An+, +W ( 4 )

BatchReactorThe molecular rate equations for the disappear-ance of the various species can be written as follows:

dM- - IM W +kl'S1dt

dW k, - n-l- - 1MW + kl'S1 + 2 2 Sn-msmdt n = l m = lm m n- 1

n = l n = l m = l

m

= klMW - l'SI - 2SI z nS1-t n = lm+ k,'W z n+@ k3MSl-+k;Sp

n = lm m

= ( klMW - ,'S,) 6 dSn-tsj 0- 2'W(Sn- , 6 )+ 2k,'W 2 -

= n + l 1-1+k3M(Sn-1-sn) -k3'(Sn-Sn+l)

m+ k;S1 6 - 4Sn 2 A,,,m= l

---I - k4A1 sn+k,'W 2 A n + P (9)dt n = l n = lAj 0- 4)W(An- l 6 +kW 2 -

= n + l j - 1(10)where the function:

1Th is term is not exactly correct since an Si moleaule does not resultfrom every reaction between water and a polymer chain. The correctterm is . . . kz'W Z Sn/n - 1. Unfortunately, it cannot be easilytransformed to give the correct term in the moment equations to hedeveloped presently. However, it is apparent that the correct termis some fraction of the term which has been used. Our term repre-sents an upper bound. The small magnitude of the rate constant kz'(see Table 2) argues for the acceptance of this approximation.?Solution of this set of equations including this term requires as-suming that S I = S2 which has been used previously ( 5 ) and is ac-ceptable since both concentrations are quite small. Alternatively, itcould be ignored altogether which has also been done in some theo-retical studies of reversible polymerization (12).3Thi s term gives the proper statistical weight to the hydrolysis re a ction of water with the specific amide linkage in a molecule of size iwhich will just give a molecule of size n.

m* k 5 a

POLYMER ENGINEERING AND SCIENCE, MAY, 1975, Vol. 15, No. 5 387


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An Analysis of Caproluctam Polymerization

The treatment of the terms involving G[A] and the corresponding term for Aj, re-i - 1quired a summation approach detailed in AppendixA. Equutions 14-17 and 23-28 comprise a closed setof simultaneous, nonlinear, ordinary differentialequations which were solved numerically using afourth order Runge-Kutta routine.As pointed out earlier, this reaction is catalyzed bychain ends, so we have. .

j=n+l

ki = k,+ kkpp (29). . . for each of the four forward and reverse reac-tions. The rate constants and equilibrium constantsused in this analysis are tabulated in Table 2. It hasbeen shown in experimental studies of caprolactampolymerization (24) that the addition of lactam oc-curs at the amino end group and is catalyzed by car-boxyl groups. This means that only those chains withuncapped amine ends will be able to add lactam andonly those chains with uncapped acid ends will beable to affect catalysis. Therefore, if a monofunc-tional acid reagent is added to the reaction mixture,some chains will react with it at the amine end andno longer be able to add lactam. The carboxyl endgroup will still be available for catalysis, as will allthe carboxyl groups of the uncapped chains. This isthe case represented by E q 29. If a monofunctionalamine reagent is added, only those chains which donot react with it remain available for catalysis andp o p in E q 29 must be replaced by p o, the zeroth mo-ment of the uncapped chain length distribution. Ifone wished to consider the addition of both types ofmonofunctional reagents simultaneously (the stabilityof the polymer formed would be increased by havingboth ends capped) one must include a fifth molecularrate equation for the reaction with the other type ofmonofunctional reagent. The result will be that thereare now three distributions of species in the productdistribution: unterminated, monofunctionally ter-minated, and difunctionally terminated. The com-bined zeroth moment of the chains with free car-

Table 2. Rate and Equilibrium Constants for CaprolactamPolymerization at 22O0Caki o (kg hr-1 ki, (kg2hr-1i mole-1) mole-4 K1

1 8.0 x 10-4 0.17 2.2 x 10-32 0.9 20.0 8.5 x 10 23 1.0 21.0 1.94 0.9 20.0 8.5 x 1021 Taken from (7-9).POLYMER ENGINEERING AND SCIENCE, MAY, 1975, Yo/. 15, No. 5

boxyl ends will then be the correct term to use inE q 29. The results presented in this paper deal onlywith the addition of monofunctional acid, the caserepresented by E q 29 as written.Continuous StirredTank Reactor

For micromixed CSTRs, the mass balance equa-tions may be written directly from the batch reactorEqs 5-10 by incorporation of the inflow-outflowterms, ie, ( Min-Mout)/8,etc., where e is the averageresidence time. For steady state operation, the timederivatives vanish. The equations are transformedand the moment equations developed in a mannerparalleling that for the batch reactor. Non-linear al-gebraic equations result which are solved by a New-ton-Raphson method. The complete set of CSTRequations is given in Appendix B.RESULTS AND DISCUSSION

Batch ReactorFigures 1 and 2 compare the model presented inthis paper to the published data of Hermans, et a1( 7 ) . We find quite a good fit to the experimentaldata, especially in the initial portions of the curves.Along with the conversion curve in Fig. 3, these

curves demonstrate the autocatalytic nature of thisreaction, The overall reaction is relatively slow untilthe ring-opening has proceeded to a sufficient extent.For this reason, some of the ideas of Kilkson (25)with regard to the concept of slow influx in polycon-densation reactions apply to this reaction. The high-est rate of conversion roughly corresponds to themaximum in the I.LO curve.As pointed out by Hermans, et a1 ( 7 ) , he chang-ing nature of the reaction medium from predomi-nantly caprolactam to predominantly polymer, makesdetermination of rate constants which apply overthe entire conversion range very difficult. The rateconstants we have used, given in Table 2, are a com-bination of those of Hermans ( 7 ) and Wiloth (8,s).This model may provide a means to determining con-

I I I

M

I I I0 5 10 15T i me, hrt.Fig. I. Monomer concentration 0s time in a batch reactor atthree initial water concentrations: (6)JM, = 0.05; ( 0 )W,/Mo = 0.067;(0) o/M, = 0.1. M is in mole k g - 1 ;A = 0. Symbols are experimental data of Hemans, e t al(7) . Solid line is predicted curve.

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M . V. Tirrell, G . H . Paarson, R . A. Weiss and R. L. Laurence

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0 5 10 15t i m e , hrr.Fig. 2. First moment of PCLD us time in a batch reactor atthree initial water concentrat'ons: (0)o/Mo= 0.05; ( 0 )W,/M, = 0.067; (0)o/M, = 0.1. po is in mole kg-Ix 102; A = 0. Sym bols are experimental data of H ermans,e t al. (7). Solid line is predicted curve.stants that provide the statistical best fit to a givense t of data over the entire conversion range. We didnot at tempt to optimize the fit to the da ta in th ismanner, however.Two reactions not considered in the model maycontribute to the discrepancy between the predictedcurves an d the data. T he first is a cyclization reactionwhich, although similar in mechanism to the reversereaction 3, produces no t monomer b ut cyclic oligom-ers. Indeed, commercial products do contain thesespecies in minute amounts up to a cyclic nonomer( 18). If kinetic data were available (nam ely, cycli-zation constants ) this reaction, or an approximationto i t , could be treated by our model, similar to thetreatment of Mochizuki and Ito (26). Th e other re-action n ot considered is th e transamidation reaction.It is difficult to assess a p r i o ~ i he effect of thisreaction. Some kinetic data are available ( 5 ) bu tinclusion of this reaction in a kinetic model wouldbe extremely difficult.Figure 3 gives conversion versus time, as well asthe dev elopm ent of deg ree of polymerization an dMW D, fo r a typical initial water concentration withand without monofunctional acid. Addition of mono-func tional acid somewhat decreases the time for at -tainment of the equilibrium conversion. The mo-lecular weight controlling effect is demonstrated byth e Dp, versus time curve. Considering now themolecular weight distribution, we note that a valueof 2.0 is characteristic of a most probable distribu-tion. Except for a plateau at about 1.75 in the earlystages of th e reaction w here polymerization is dom-inated by th e chain grow th mechanism polyaddition,the value of 2.0 is approached as the equilibriumconversion is neared. It is seen also that addition ofsmall amounts of monofunctional acid is predicted to390

Cba

I0 10 20 30 4 0

Fig . 3. Predicted curves for conuersion x , number averagedegree of polymerizationz,,nd polydispersity Z vs timein u butch reactor at various levels of monofunct'onal acid:( a ) Ao/Mo = 0.00; ( b ) A , / M , = 0.0025; ( c ) A J M , = 0.01.

Ti m e , hrr.

broaden th e M W D somewhat, especially in the earlystages of polymerization. As with any theoretical re-sult, the validity of th e prediction is difficult to arg uein the absenc e of some of t he experim ental results itseeks to predict. This suggests that an experimentalinvestigation of M W D versus conversion would b einteresting.

T he CSTRFigures 4 an d 5 describe the polymerization in aCSTR. We see that very broad distr ibution productmay be ob tained in a CSTR, consistent with the par-tial step growth ch aracter of the polymerization (19,

23). N o dat a on continuous caprolactam polymeriza-tion are available for direct comparison. In Fig. 5it is seen that control of product molecular weightand MWD can be obtained by addition of 0.25 to1.0percent monofunctional acid.One final point with respect to the CSTR is thatwe have assumed perfect mixing. If some degree ofsegregation had been introduced, the predictionwould probably be a narrower PCLD in keepingwith the general results for condensation polymeri-zations (19,2 3 ) .

Series ConfigurationsA primary adva ntag e of this deterministic model

is demonstrated in treatment of series reactor con-figurations. Tubles 3-5 deal with various plug flowreactor-CSTR schemes for producing nylon-6 con-tinuously. E qua l reactor volumes are considered withPOLYMER ENGINEERING AND SCIENCE, MAY, 1975, Vol . 15, No . 5


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An Analysis of Caprolactam PolymerizationI. r

1. I

,OOt

20 c 4

I50 100 I50 200Time, h r t .Fig. 5. Predicted curues for x,oPn and 2, us residence timein a CS TR at various leuels of monofunctional acid: (a ) &/M,= 0.00; ( b ) A , / M , = 0.0025; ( c ) A , / M , = 0.01.

Time, hn.Fig. 4. Predicted curoes for x, so ( m / k g x 102)=, and 2,os residence time in a CSTR at uarious initial water concen-trations: (a) W , / M , = 0.01; ( b ) W , / M , = 0.05; ( c ) W,/M,= 0.1. it is seen that either series configuration can be usedto obtain a similar product at comparable residencetimes. The key point is that it is not recommended totry to obtain high conversion in the CSTR section.The largest part of conversion and growth shouldthe space time, 7, equired to give the specified prod-uct after each stage r:hown. With no water removal,using as acceptable product criterion a DP, of 150,__

Table 3. Two Reactor Schemes, PFR-CSTR in SeriesaFirst reactor: PFR Water removal Second reactor: CSTR Tot al spaceeffluent specifications aft er first reactor effluent specifications tim e (hrs.)- -P, X 2 TI (hrs.) DPn X 2, 72 hrs.1

~~ ~ ~~~

1 50 0.52 1.56 8.0 no ne 150 0.88 6.40 55.0 63.02 100 0.84 1.81 14.0 none 150 0.90 2.68 14.0 28.03 50 0.52 1.56 8.0 complete 150 0.82 3.26 25.0 33.04 100 0.84 1.81 14.0 complete 150 0.89 2.06 8.0 22.0* Wo/Mo = 0.05.

Table 4. Two Reactor Schemes, CSTR-PFR in SeriesaSecond reactor: PFR Tot al spaceeffluent specifications after first reactor effluent specifications ti me (hrs.)First reactor: CSTR Water removal- -Pn X 2 TI hrs.) DPn X 2, 72 hrs.1

1 50 0.41 2.67 5.0 none 150 0.90 2.14 15.0 20.02 100 0.70 4.64 20.0 none 150 0.88 3.60 11.0 31.03 50 0.41 2.67 5.0 complete 150 0.82 1.50 10.0 15.04 100 0.70 4.67 20.0 complete 150 0.88 3.21 6.0 26.0' o/Ma = 0.05.POLYMER ENGINEERING AND SCIENCE, MAY, 1975, Vol. IS, No. 5 391


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M . V . TirreU, G . H . Pearson, R . A. Wei ss and R . L . LaurenceTable 5. Two Reactor Schemes, PFR-PFR in Seriesa

~ ~~~

First reactor: PFR Water removal Second reactor: PFR Total spaceeffluent specifications after first reactor effluent specifications tim e (hrs.)-PIl X 2, T I (hrs.1 DPIl X Z, ~ ~ ( h r s . 11 50 0.52 1.56 8.0 complete 150 0.84 1.54 9.0 17.02 100 0.84 1.81 14.0 complete 150 0.89 1.78 5.0 19.0

Wo/Mo = 0.M.occur in the PFR with the CSTR used as a startingor finishing reactor. These same general rules holdfor the cases of complete water removal after thefirst stage. Water removal does give a considerableprocess time advantage in agreement with resultsobtained by other workers (2 , 3) . This is furtherdemonstrated in Table 5 where tw o PFRs in seriesare run with water removal between stages. Thisconfiguration has interest since it is the limiting caseof an infinite series arrangement of CSTRs. These re-sults show that it is desirable to remove water fromthe reaction as early in the process as possible. How-ever, we would not expect it to be desirable to re-move the water at a residence time lower than thepoint at which the maximum in the p,, curve occurs.The proper choice of series configuration can providea considerable improvement over a single CSTR.

In summary, the deterministic model developedin this paper has been applied to various single andseries reactor configurations. From this model pre-dictions about MWD as well as molecular weightand reaction conversion can be made. Distributionsother than most probable result in many cases. Sometuning of the model is indicated to improve theagreement between the model and the availabledata. A more systematic approach to determiningthe optimal reactor configuration through the use ofthis model is likely to prove quite fruitful.

NOMENCLATUREA, = concentration of monofunctional species ofchain length i (mole kg-)DP, = number average degree of polymerizationDP, = weight average degree of polymerizationki = forward rate constant of ith reactionk; = reverse rate constant of ith reactionKi = equilibrium constant of ith reactionM = concentration of caprolactam (mole kg- )Si = concentration of difunctional species ofchain length i (mole kg-)W = concentration of water (mole kg- )Z,, = polydispersity= D P J D P ,pk = kth moment of the distribution of chainlengths of difunctional speciespk = kth moment of the distribution of chainlengths of monofunctional species

REFERENCES1. H. K. Reimschuessel and G. J. Dege, J. Polym. Sci., A-I,2. K. Nagasubramanian and H. K. Reimschuessel, J. Appl .

--- -

9,2343 (1970).

392

Polym. Sci., 16,929 ( 1972).3. H. K. Reimschuessel and K. Nagasubramanian, Chem.Eng. Sci., 27, 1119 (1972).4. H. K. Reimschuessel and K. Nagasubramanian, Polym.Eng. Sci., 12, 179 (1972).5. H. K. Reimschuessel in Ring Opening Polymerizations,K. C. Frisch and S. L. Reegan, eds., Ch. 7, Marcel Dekker,New York, N. Y . (1969).6. Ch. A . Kruissink, G . M. van der Want and A. J . Staver-man, J. Polym. Sci., 30, 67 ( 1958).7. P. H. Hermans, D. Heikens and P. F. Van Velden, J.Polym. Sci., 30, 81 ( 1958).8. F. Wiloth, 2. Physik. Chem., 5, 66 (1955).9. F. Wiloth, 2. hysik. Chem., 11,78 (1957).10. H . K. Reimschuessel, J. Polym. Sci., 41,457 (1959).11. R. W. Lenz, Organic Chemistry of Synthetic High Poly-

12. C.-R. Huang and H.-H. Wang, J. Polym. Sci., A-I, 10,13. J. Sebenda and V. Kouril, Europ. Polym. J., 7, 163714 . P. Biernacki, S. Chrzczonowicz and M . Wlodarayk, Erirop.15. S. Saunders, J. Polym. Sci., 30,479 (1958).16. Modern Plastics, p. 70, August 1969.17. S. Smith, J . Polym. Sci., 30,459 (1958).18. A. D. Bliss, Foster Gra nt Co., private com munication.19. R. L. Laurence, unpublished manuscript,20. S . I. Calouche, Firestone Synthetic Fibers Co., private21. W. H. Abraham, Ind. Eng. Chem. Fund., 2,221 (1963).22. H. Kilkson, h d . Eng. Chem. Fund . , 3,281 (1964).23. Z. Tadmor, Ph.D. dissertation, Stevens. Inst. Tech.,

mers, Wiley-Interscience, New York, New York ( 1967).791 (1972).( 1971 .Polym. J., 7, 739 (1971).

communication.

(1966).J. Polum. Sci., 44. 437 ( 1960).24. D. Heikens, P. H. Hermans and G. M. an der Want,25. H. Kiikson, l nd . hng. C h e m. Fund., 7, 354 (1968).26. S. Mochizuki and N . Ito, Chem. Eng. Sci., 28, 1139(1973).

APPENDIX AIt can be shown that

-S s -dsr}( S ) ( A - 1 )O (s )3

This is not easily converted to a moment equation.However, since moment equations are the objectiveof applying the transformation, they can be obtainedin an equivalent but different form by expanding thedouble summation and recombining. We have

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An Analysis of Cap rohc tam Polymerizationm

pk:= C kS n (A-2 1n = l

therefore, the following expressions can be evolvedand substituted into equations for the appropriateorder momentm n

m m n

01 m c 1L J ;n2 2 - - = 1 ( 2 f i - p 1 - S 1 ) ( A - 5 )

n-1 j = n + t 1-1 6An dentical treatment is used for the correspond-

ingAj erm.APPENDIX B

Equations for CSTR:

+ 3'b - 3'Sl (B-1)S l , - lO

e= k l M W - l'S1- k2Sp4

POLYMER ENGINEERING AND SCIENCE, MAY, 1975, Vol. IS, No . 5 393

tirrell pearson weiss laurance pes 1975

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