The Open acomolecules Jounal, 008,, 1-5 1 Revisited Kinetic Chain Length and Reactivity Ratio Appoaches fo Linea Polymes and Copolymes ohammad. Faes* Dept. of Applied Chemisty, Jodan Univesity of Science & Technology, P.O. Box: 3030 110, Ibid, Jodan Abstact: Two evisited mathematical inetic elationships wee deived, evaluated and applied on linea polymes such as polystyene and copolymes such as (NIPAAm-alt-HEA) and (AAm-alt-HEA) copolymes espectively. The validity of these equations was successfully veified. The fist elationship, equation 1, inteelates onentially inetic chain length, aveage molecula weight and degee of polymeization of linea polymes with diffeent tempeatues. Futhemoe; equation 1 could novelly define the ate of polymeization (R p ) and consequently the oveall activation enegy (E) of the polymeization pocess could be detemined. The second deived elationship inteelates the eactivity atio poduct ( 1 ) of two monomes inteacting with each othe, with diffeent tempeatue. Application of equation 16 could detemine the behavioal sequence of monome 1 towad monome in the copolymeization pocess. The value of (E 1 +E 1 )(E 11 +E ) could esult with the detemination of type of copolymes fomed. The eactivity atio values fo (NIPAAm-alt-HEA) and (AAm-alt-HEA) copolymes wee detemined using Kelen-Tudos technique. Keywods; Kinetic chain length, eactivity atio, Theoetical Kinetic appoach. INTRODUCTION Radical inetic chain polymeization, as one of the most cucial techniques in the contol and optimization of ecent polymeic industies, is always finding enewable geneated ideas and inteest in the theoy and inetic paametes of polymeization pocesses. This majo concen is due to the outstanding applications, pactical use, and elatively easy contol [1] of adical eactions. This concen have futhe oiented us to deive pactical, adequate and easily handled inetic elationships fo pactical puposes. The detemination of polymeization ate in equation 1 at diffeent tempeatues, in Ahenius equation, implies the detemination of p, d, and t espectively. ln p d t ln A p A d A t E p + E d E t whee p, d, and t ae ate constants fo popagation, initiato dissociation and temination espectively. Since ate of polymeization (R p ) is given by R p p f d [I] t Substituting eq n () in (1) yields; ln R p ln A p A d A t + ln( f [I] [ ])E p The exact detemination of polymeization ate (R p ) is the most impotant facto in Ahenius equation, due to consequence detemination of exact oveall activation enegy. In *Addess coespondence to this autho at the Depatment of Applied Chemisty, Jodan Univesity of Science & Technology, P.O. Box: 3030 110, Ibid, Jodan; E-mail: faes@just.edu.jo (1) () (3) the liteatue R p wee detemined using spectoscopic means such as UV-Vis [], FTIR [3], NR [4], XRD [5], mass spectomety [6] and TGA [9], o by Lase beam technology [8-9], o using conventional %Convesion vesus Time plot by pecipitation of polymes [10], whee R p is detemined fom the non-steady state cuve. Consequently the detemination the oveall activation enegy E a E p +(E d /) (E t /) descibes the inetic changes in the polymeization pocess whethe it shows an Ahenius behavio (i.e. E a >0), which implies that the eaction ate incease as a esult of inceasing tempeatue, o non- Ahenius behavio (i.e. E a <0), which subsequently implies that eaction ate deceases as a esult of inceasing tempeatue. The oveall activation enegy is associated with E p, E d, and E t values, which damatically change with many factos such as monome stuctue and geomety, initiato type, tempeatue, polymeization time, and chain tansfe agent. The aim of this wo is to deive, investigate and apply evisited inetic elationships though aising a new definition of ate of polymeization (R p ) fo linea polymeization and copolymeization pocesses, applying that into Ahenius patten and eventually investigating the consistency and genuinity of such elationships. EXPERIENTAL ateials Styene (99%, Acos), ethacylamide (AAm) (99%, Flua), N-isopopylacylamide (NIPAAm) (99%, Acos) and -Hydoxyethylmethacylate (HEA) (99%, Acos) monomes wee ept in efigeato and used as eceived, N,N,N,N -Tetaethylenediamine (TEED) (Sigma-Aldich) used as an acceleato, was used as eceived, Potassium peoxodisulfate (KPS) (BDH chemicals Ltd), and benzoylpeoxide as an initiato, was futhe puified by ecystallization. All solvents and othe chemicals wee of analytical gade. 1874-3439/08 008 Bentham Science Publishes Ltd.
The Open acomolecules Jounal, 008, Volume ohammad. Faes Synthesis of Polystyene (PS) Styene monome wee conventionally polymeized unde N atmosphee, in bul, in the tempeatue ange of 60-80 ºC using 0.1% benzoylpeoxide, whee at each time inteval 15, 30, 45, 60, 75 min., excess methanol nonsolvent wee used to pecipitate polystyene. Continuous washing with methanol wee done to emove monome taces. Polystyene wee then died and weighed. The weight aveage molecula weight was detemined using light scatteing technique [11]. The degee of polymeization wee detemined fom the atio of absobance of aliphatic CC of monome befoe polymeization and afte polyme pecipitation. Synthesis of (NIPAAm-alt-HEA) and (AAm-alt- HEA) Copolymes 0.66, 1.0, 1.3, 1.5, 3.0, and 9.0 mola atios of NIPAAm to HEA (i.e. NIPAAm / HEA ) and AAm to HEA (i.e. AAm / HEA ) as mentioned peviously [1, 13], wee synthesized as follow; each monome concentation wee dissolved in 5 ml of de-ionized wate. The solutions wee spaged with N fo 5 minutes o until the monome is dissolved. To each solution a 5 ml of 10 % (wt/wt) KPS and 5 ml of 10 %( wt/wt) TEED with espect to total monomes weights wee added unde N atmosphee. Then the mixtue was set in 50 ml ound bottom flas and sealed unde N atmosphee fo 3.5 hous in wate-bath fixed at 30 ºC. Afte the copolymeization was complete, the poduct was poued to an excess of chloofom, stied fo 15 min, and washed with hot de-ionized wate to emove homopolymes, then filteed and died in an oven at 80 ºC fo 8-1 hous. The samples wee futhe puified via centifugation. The weight aveage molecula weight was detemined using light scatteing technique [11]. Reactivity atios 1 and values wee detemined using Kelen-Tudos technique [14] at 0-40 C tempeatue ange fo (NIPAAm-alt-HEA) and at 5-0 C tempeatue ange fo (AAm-alt-HEA) copolymes. THEORETICAL APPROACH (1) Kinetic chain length (L i,t ) is defined as the numbe of monomes added into a gowing macoadical of i th length in unit time inteval. The molecula weight of this chain in the same time inteval,, can be descibed as the inetic chain length, L i,t, times the mola mass of the epeating unit, u, as follows; L i,t u (4) At time, if theoetically assumed all monomes can join all diffeent chains, the oveall inetic chain lengths is then called L and consequently the aveage molecula weight can also be called. Thus the faction of eacted monomes joining the i th length macoadical chain, p i, can be pesented by dividing the inetic chain length of i th length macoadical chain, at cetain time (L i,t ), to the oveall inetic chain lengths L. Consequently this faction can be descied by the atio of molecula weight of i th length macoadical chain at cetain time ( ) by the molecula weight. Thus the elation becomes; p i L i,t L (5) The degee of polymeization (DP i ) is defined as atio of initial monome conc., [A] 0, to monome conc. at polymeization time t, [A] t, (i.e. DP i [A] 0 / [A] t ). The ecipocal of DP i pesents the faction of uneacted monomes (i.e. the monomes that did not join the i th length macoadical chain, whee i pesent the numbe of epeating units in the macoadical chain). Hence, the faction of eacted monomes joining the macoadical chain, p i, is equal to 1(1/DP i ). Thus it can be equalized with equation 5 as follows; 1 1 DP i 1 1 DP i Numbe aveage molecula weight ( n ) [15] is defined in equation 7, whee i is the molecula weight of i th length chain, n i is numbe of chains with i th length, and is the total numbe of chains with diffeent chain lengths. Thus the faction n i / epesents the faction of chains with i th length with espect to total diffeent length chains. i i.n i i n i 1 1 + + 3 3 +...+ n n (7) Futhemoe; it is nown that diffeent chain lengths (i.e. diffeent molecula weight chains) in any polyme follows Boltzmann distibution cuve (Scheme 1) and consequently it follows the Boltzmann distibution law [16], whee faction of chains can be pesented in an onential fom as follows; n i e Ei e E i E e (8) Scheme 1. olecula weight distibution cuve of polystyene. (6)
Revisited Kinetic Chain Length and Reactivity Ratio Appoaches The Open acomolecules Jounal, 008, Volume 3 Fo which E i pesents the activation enegy equied fo monome to join an i th length macoadical chain. The diffeent size chains may have diffeent activation enegies (i.e. E i, E j, E, ) depends on the size length and how much entangled, coalescent, o agglomeated the chain is, in othe wods the activation enegy diffes slightly fo extended chain that can coalescent, agglomeate, and lagely entangled, and consequently E is the esultant oveall activation enegy equied fo any monome to join any chain of any chain length no matte what configuation does it have. Substituting equation 8 in equation 7 tuns to be: ( 1 + + 3 +...+ ) e E Again substituting equation 6 in equation 9 gives ise; (1 1 ) + (1 1 ) + (1 1 ) +...+ (1 1 ) DP 1 DP DP 3 DP n e 1 1 1 1 (1 ) + (1 ) + (1 ) +... + (1 ) DP DP DP DP 1 3 n E e (9) E (10) Thus the molecula weight of any linea polyme at any polymeization time can accodingly be detemined though the following elationship; 1 1 DP i e E 1 1 DP i E e (11) This linea elationship elates the momentaily change of molecula weight and degee of polymeization with the change of tempeatue. Hence by taing the natual logaithm fo both sides; ln i,t 1 1 DP i ln E (1) This linea elationship can detemine the momentaily ate of polymeization (R p ) and consequently the esulting activation enegy (E) at diffeent tempeatues can be detemined fo this type of linea polymeization pocesses. Futhemoe the theoetically assumed molecula weight fo all monomes joining diffeent chains at infinite time ( ) can also be investigated and detemined. The DP i at time zeo of polymeization has a value of 1.0 (i.e. [A] 0 [A] t ), wheeas at time it has a value of infinity () (i.e. [A] t zeo). The detemination of DP i can be pefomed though monitoing the disappeaance of aliphatic CC fo poly addition type, o monitoing the end goup stuctual changes fo poly condensation type, at diffeent time inteval though diffeent spectoscopic techniques such as 13 C-NR, 1 H-NR, FTIR, and UV-Vis, wheeas the molecula weight can be detemined though conventional gel pemeation chomatogaphy (GPC), Osmomety, light scatteing, and Ubbelohde viscomety techniques. Fig. (1) shows the ln [ i /[(1(1/DP i )]] vesus ecipocal tempeatue of polystyene polymeized at diffeent time inteval in the tempeatue ange of 6080 C. Fig. (1). ln [ i /[(1(1/DP i )]] vesus 1/T fo bul polymeized polystyene in diffeent time intevals in the tempeatue ange of 6080 C. It can be clealy seen that the application of equation 1 esults with linea detemination of the oveall activation enegies at diffeent time intevals. The oveall activation enegies detemined fom Fig. (1) ange fom 87-95.5 J/mol, which is in vey good ageement with conventional detemination of activation enegy of diffeent confomational polystyenes in the liteatue [17,18]. Futhemoe; the extapolations of the cuves esult with almost one intecept value (i.e. ) egadless to the time of polymeization, which again confims the consistency and igidity of equation 1 used to show and pesent the Ahenius elationship in pactical and enewable fom. THEORETICAL APPROACH () It is nown the 1 11 1, whee 11 and 1 ae the ate. constants of the inteaction of a macoadical ( 1 ) with eithe 1 o monomes espectively, and whee 1 and 1 ae the ate constants of the inteaction of a macoadical ( ) with eithe o 1 monomes espectively.. If Ahenius equation is applied to the eactivity atio 1 and, then the outcome will be equation 13; 1 11 A 11 E 1 E 11 1 A 1 (13) Consequently; 1 becomes;
4 The Open acomolecules Jounal, 008, Volume ohammad. Faes Table 1. Change of 1 Poduct as Tempeatue Changes fo (NIPAAm-alt-HEA) Copolymes Tempeatue (ºC) 1 1 0 0.0034 0.114 0.0003876 30 0.0509 0.47 0.017343 40 0.0356 0.178 0.0063368 Table. Change of 1 Poduct as Tempeatue Changes fo (AAm-alt-HEA) Copolymes Tempeatue (ºC) 1 1 5 0.0334 0.049 0.0008 10 0.053 0.05 0.0006 0 0.0875 0.04 0.0179 A E 1 E 1 A 1 Thus 1 equals; (14) 1 A 11A ( E 1 E 11 )+ ( E 1 E ) (15) A 1 A 1 Reaangement of equation 15 yields; 1 A A 11 ( E 1 + E 1 ) ( E 11 + E ) A 1 A 1 (16) Equation 16 pesents the linea elationship between the natual logaithm of 1 poduct (ln ( 1 )) with the ecipocal of the tempeatue in Kelvin (1/T), whee the activation enegy could be detemined though the slope value of the cuve. The value of the activation enegy in eq n 16 becomes vey impotant because it can show the type of pefeence of a macoadical (. 1 ) towad eithe 1 o. If (. 1 ) macoadical pefes and (. ) macoadical pefes 1 and then the activation enegy (E 1 +E 1 ) will be much smalle than (E 11 +E ) and consequently the altenating behavio of copolyme will dominate. Wheeas if (. 1 ) macoadical pefes 1 and (. ) macoadical pefes and then the activation enegy (E 1 +E 1 ) will be much lage than (E 11 +E ) and consequently a bloc o phase sepaated homopolyme behavio will dominate. Eventually if (E 1 +E 1 ) (E 11 +E ) then the copolyme is said to be andom. Table 1 and illustate change of 1 poduct as tempeatue changes fo both copolymes (NIPAAm-alt-HEA) and (AAm-alt-HEA) [1,13] espectively. The eactivity atios wee detemined using Kelen-Tudos technique [14]. Figs. ( and 3) show the linea elationship of ln ( 1 ) vesus 1/T, which is deived fom equation 16. The activation enegy (i.e. (E 1 +E 1 ) (E 11 +E )) of (NIPAAm-alt- HEA) and (AAm-alt-HEA) copolyme wee found to be 109 J/mol and -118.4 J/mol espectively. Such negative activation enegies confim that (E 1 +E 1 )<<(E 11 +E ) in both copolymes, and hence confims the altenating behavio of the monomes towad each othe. Futhemoe by compaing the activation enegy values deduced fom equation 16 with simila stuctues mentioned in the liteatue, it was found that they ae in accodance with liteatue values (i.e. E 97±5 J/mol [19]). Fig. (). Change of ln ( 1 ) vesus 1/T fo (NIPAAm-alt-HEA) copolyme. Fig. (3). Change of ln ( 1 ) vesus 1/T fo (AAm-alt-HEA) copolyme.
Revisited Kinetic Chain Length and Reactivity Ratio Appoaches The Open acomolecules Jounal, 008, Volume 5 Fom Figs. ( and 3) it can be clealy seen that not only linea detemination of activation enegies can be detemined but also the type of copolymes fomed can be deduced and detemined. CONCLUSIONS The two evisited mathematical inetic elationships wee deived, evaluated and eventually applied to confim the consistency, genuinity, and lineaity of the fomed elationships. The fist elationship, equation 1, ln i,t 1 1 ln E DP i which elates the change of molecula weight, degee of polymeization momentaily of linea polymes with tempeatue, whee this linea elationship can detemine the oveall activation enegy of the polymeization pocess. The validity of this linea elationship was veified using diffeent time intevals bulily polymeized polystyene as Fig. (1) shows. The second elationship inteelates the eactivity atio poduct ( 1 ) with tempeatues, which again showed a linea elationship, equation 16, 1 A 11 A A 1 A 1 ( E 1 + E 1 ) ( E 11 + E ) This linea elationship can detemine the activation enegy value fo the copolymeization pocess (i.e. (E 1 +E 1 )(E 11 +E )), and consequently the type and sequence of monomes in the copolyme can be descibed. The validity of this equation wee successfully veified fo (NI- PAAm-alt-HEA) and (AAm-alt-HEA) copolymes espectively. ACKNOWLEDGENT This wo is acnowledged fo Jodan Univeisty of Science & Technology. REFERENCES [1] atyjaszwesi, K.; Davis, T. Handboo of adical polymeization,wiley- Intescience, 00. [] Dong, X.; Ding, W.; Zhang, X.; Liang, X. Dyes Pigments, 007, 74(), 470-476. [3] Deshmuh, S.S.; Kovalchu, V. I.; Boovov, V. Yu.; d'iti, J. L. J. Phys. Chem. B, 000, 104(6), 177-184. [4] Lapidot, A.; Reuben, J.; Samuel, D. J. Chem. Edu., 1964, 41, 570. [5] Zema,.; Domeneghette, C.; Tazzoli, V. Am. ineal., 1999, 84, 1895-1901. [6] Pa, J.; Lin,. C. J. Phys. Chem., 1997, 101, 14. [7] Faes,..; El-faqeeh, A. S. J. Them. Anal. Caloimet., 005, 8, 161-166. [8] ilden, R.P.; Pipe, J. A. Opt. Lett., 003, 8, 1936-8. [9] Caman, R. J.; ilden R. P.; Withfod. J.; Bown, D. J. W.; Pipe, J. A. IEEE J. Quantum Electon, 000, 36, 438-49. [10] Vollmet, B. Polyme Chemisty, Spinge-Velag, 1973, pp. 73-94. [11] Caahe, C. E.; Seymou, R. B. Polyme Chemisty, 6 th ed. acel Dee, 003, p. 83. [1] Faes,..; Othman, A. A. J. App. Polym. Sci., accepted, 008. [13] Faes,..; Othman, A. A. submitted, 008. [14] Kelen, T.; Tudos, J. acomol. Sci. Chem. Ed., 1975, 9, 1. [15] Caahe, C. E.; Seymou, R. B. Polyme Chemisty, 6 th ed. acel Dee, 003, p. 71. [16] Laidle, K. J.; eise, J. H.; Sanctuay, B. C. Physical Chemisty, 4 th ed., Houghton ifflin, 003, p. 795. [17] Jaell,.S.; Gates, B.C. J. Catal., 1978, 54(1), 81-93. [18] Lupacu, V.; Picen, S. J.; Wübbenhost. acomolecules, 006, 39(15), 515-5158. [19] Neadovich, D.; Van steenbegen,.j.; Van steelant, L.; eije, Y.J.; Van Nostum, C. F; Hennin, W. E. acomolecules, 003, 36, 7491-7498. Received: Januay 19, 008 Revised: Febuay 06, 008 Accepted: Febuay 0, 008