MOLECLUAR DYNAMICS AND THE CORRESPONDING RHEOLGICAL RESPONSE OF POLYMER NANOCOMPOSITES

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1 THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MOLECLUAR DYNAMICS AND THE CORRESPONDING RHEOLGICAL RESPONSE OF POLYMER NANOCOMPOSITES 1 Introduction D. G. Seong 1*, M. K. Um 1, J. H. Byun 1, J. R. Youn 1 Korea Institute o Materias Science, Changwon, Repubic o Korea, Seou Nationa University, Seou, Repubic o Korea * Corresponding author (dgseong@kims.re.kr) Keywords: Nanocomposite, Moecuar mode, Rheoogy, Brownian dynamics simuation Nanocomposites usuay shows the outstanding improvements in tensie strength and moduus, heat resistance, gas and iquid permeabiity, biodegradabiity, ionic conductivity, and so on [1-6]. The improved properties o nanocomposites are reaized ony when the nanopartices are homogeneousy dispersed throughout poymer matrix and cose interactions between nanopartices and poymer moecues exist. Nanocomposites show dierent rheoogica behaviors with respect to the degree o dispersion o nanopartice [7]. The rheoogica properties are improved by achieving strong interacia bonding as we as homogeneous dispersion. Since the characteristic rheoogica behaviors o nanocomposites are caused by nanoscae interaction between nanopartices and poymer moecues, moecuar-eve modeing is suitabe to study the nanocomposite system. In this study, moecuar modeing using Brownian dynamics simuation are used to mode rheoogica behavior o the nanocomposites. Dynamic behavior o moecue in nanocomposite were predicted by a newy proposed moecuar mode and Brownian dynamics simuation with stochastic process was used to simuate the mode eectivey. composed o the mutipe chain segments having the above inormation is considered to investigate dynamics o the reaistic poymer moecuar chain. The proposed mode is used to predict rheoogica characteristics o the inear poymer and its nanocomposite and aso to understand the characteristic rheoogica behaviors on the moecuar eve.. Simuation procedure Mode evauation starts rom construction o the reaistic mutipe chain geometry composed o L beads and (L-1) connectors which is represented in the Fig.1. The geometrica description is represented as oows. x 1 x u ' (1) u ' u () where x is the position o the -th bead, u is the connector vector connecting rom x to x 1, and is the chain stretch ratio o the -th connector vector which is deined as ratio o the present chain ength to the equiibrium one. Theory.1 Moecuar modeing The new mode proposed in this study incorporates the ideas rom both the thermodynamicay admissibe singe segment reptation mode and the u chain geometry. The evoution equation o the thermodynamicay admissibe reptation mode is used to incorporate doube reptation, convective constraint reease, and chain stretching o the individua chain segments [8-9]. Fu chain geometry x 1 u 1 x u x L-1 Fig.1. Moecuar geometry o poymer chain u L-1 The individua chain segment oows the evoution equations o the thermodynamicay admissibe reptation mode [9]. The diusion equation or the x L

2 conigurationa distribution unction,, is given by the conigurationa variabes, u and s, because terms or the anisotropic tube cross-sections are negected in this mode. D Dt uu 1 1 κ u 1 s u u s 1 uu 1 D s u u d u dissip dissip (3) The variabe u is the unit vector representing orientation o the poymer chain segment and s represents the reative position within a chain segment. The scaar variabe s is in the range o [,1] and s, 1 represents both ends o the chain segment. κ is the transpose veocity gradient tensor, d is the reptation time and D is the orientationa diusion constant. Stress tensor o the mode is expressed as the oowing equation. max ( 1) τ 3NnkT 1 ( max ) L i1 u u i i i u (4) where is stretch ratio o chain segment and max is maximum possibe stretch ratio. The anguar bracket represents the ensembe average over the trajectories o the reptation processes. The evoution equations o the u chain reptation mode are evauated by utiizing Brownian dynamics simuation with stochastic processes. The new conigurations are constructed by the oowing equation. κ t t κ t DW DW (5) where W is the three dimensiona Wiener process representing Brownian diusion o poymer chains. 3 Experiments Rheoogica properties o poyamide 6/organocay nanocomposites were measured in this study. Poyamide 6 was suppied by Koon and organicay modiied nanocay (Coisite 93A) was suppied by Southern Cay Products. Nanocomposites were prepared by met compounding using the Brabender counter-rotating intermeshing twin screw extruder at the barre temperature o 4 C and the screw speed o 7 rpm. Degree o dispersion and interna structure o nanocomposites were characterized by the sma ange X-ray scattering (SAXS, Rigaku Max-3 Cg X-ray Diractometer) and transmission eectron microscope (TEM, JEM-EX Ⅱ). SAXS was used to determine the interayer spacing between cays in nanocomposites. TEM specimens were microtomed to an utra-thin section with the thickness o about 8 nm and coated with carbon or 7 minutes to prevent specimens rom degradation by the irradiation o eectrons. Linear viscoeastic response o the poyamide 6/organocay nanocomposite met was investigated through sma ampitude osciatory shear ow measurement by using the Advanced Rheometric Expansion System (ARES). Storage and oss modui G, G, and compex viscosity * were determined with respect to requency variations. Parae pate coniguration with the diameter o 5 mm was used and the temperature was controed at 4 C. Maximum strain was ixed to 5 % which was within the inear viscoeastic region and requency ranging rom.1 to 1 s -1 was appied to the moten state sampe. Eongationa viscosity was measured at a constant extension rate by using Eongationa Mets Rheometer (RME). The moten sampe was eongated to the strain o 7 % at 4 C and the transient eongationa viscosity was obtained by measuring the appied stress. 4 Resuts and discussion 4.1 Experimenta resuts Rheoogica behaviors in shear and eongationa ows o poymer nanocomposites with the dierent dispersion states were investigated by observing the dispersion state and measuring the corresponding rheoogica properties. Dispersion states and interna structure o poyamide 6/organocay nanocomposites were veriied by using SAXS and TEM as shown in Fig. and Fig.3. Characteristic diraction peaks corresponding to the interayer distance o nanocays disappeared in the cases o nanocomposites containing 1, 3, 5, 7 wt% o the nanocay as shown in Fig., which means that the ayered cay structure

3 PAPER TITLE is uy broken. The nano-scae dispersion o siicate ayers in the nanocomposite is shown by the TEM pictures in Fig.3. The poyamide 6/organocay nanocomposite has the exoiated structure with homogeneous dispersion and superior interaction between nanocays and poymer moecues are achieved. On the other hands, the composite with unmodiied cay shows the poor dispersion state and weak interaction between cays and poymer moecues. Intensity 14 MMT 1% 3% 1 5% 7% (a)poyamide 6/MMT (b) Poyamide 6/organocay Fig.3. Dispersion state o nanocomposites with respect to surace treatment o nanocay. Rheoogica behavior o the two kinds o nanocomposites with dierent dispersion state is represented in the Fig.4. In shear ow, the exoiated nanocomposites show soid-ike pateau behavior in storage moduus and strong shear thinning behavior in shear viscosity. In eongationa ow, ony uy exoiated nanocomposites show strain hardening behavior which is caused by the interaction between nanopartices as we as the interaction between poymer moecues and nanopartices. Intensity (a) Organocay 1% 3% 5% 7% Storage moduus, G' [Pa] 1e+7 1e+6 1e+ 1e+1 1e+ /MMT, 5% 1e Frequency [s -1 ] (a) Storage moduus (b) Fig.. Sma ange X-ray scattering peaks o the nanocomposites containing 1, 3, 5, 7 wt% o (a) montmorionite (MMT) and (b) organocay. Viscosity, * [Pa. s] /MMT, 5% 1e Frequency [s -1 ] (b) Shear viscosity 3

4 Extensiona viscosity, Pa. s] 1e+6 /MMT, 5% Time [s] (c) Eongationa viscosity Fig.4. Rheoogica behaviors o nanocomposites with respect to dispersion state. (a) Storage moduus, (b) shear viscosity, and (c) eongationa viscosity 1/λ. It is known that excessive shear thinning is caused by extremey strong orientation o moecuar chains aong the ow direction and such moecuar conormations do not produce signiicant resistance to ow. When the vaue o is much arger than 1, probabiity o constraint reeases rom chain stretch and retraction is increased. It means that more chain segments do not oow the externa ow ied but are randomy oriented. As increasing the portion o randomy oriented chain segments, it is expected that the resistance to ow is increased and resuting stresses become higher. In concusion, excessive decrease in shear viscosity is aeviated by increasing the portion o constraint reease and is neary independent o chain extensibiity. 4. Numerica resuts Numerica resuts are compared with the experimenta data o poyamide 6/cay nanocomposites to study the rheoogica behavior o poymer nanocomposites. Eects o maximum chain stretch and constraint reease on dynamics o macromoecuar chain in poymeric nanocomposites are the main concern o this study. Steady shear and uniaxia eongationa ow behaviors are investigated by varying the maximum chain stretch ( max ) and parameters o constraint reease ( 1, ). Moecuar motion o a poymer chain exposed to the appied ow is traced and chain characteristics are denoted by cacuated tota contour ength L t and moecuar orientation actor M deined by the oowing equation. M 1 1 L Lt 1 u u (6) where u is the unit vector aong the main ow direction. Fig.5 shows shear rate dependence o the steady shear viscosity predicted by the u chain reptation mode with various parameters o constraint reease and experimenta resuts o poyamide 6/cay nanocomposites. The mode predicts non-newtonian power aw behavior o nanocomposites at a ow shear rate region, which shows a good agreement with the experimenta resuts. However, the mode predicts excessive shear thinning at high shear rate regions when vaues o are not as arge as about 1e+ 1e+1 1e+ 1e-1 1e- 1e-3 1e-4 1e-5 /cay(5%) nanocomposite FCR mode ( ) FCR mode ( ) FCR mode ( ) FCR mode ( ) 1e Strain rate [s -1 ] (a) Shear viscosity o nanocomposite t= t=.5 t=1 (b) Dynamic behavior o poymer chain in shear ow Fig.5. Dynamic behavior o poymer chain and the corresponding viscosity in shear ow Strain hardening o the nanocomposite mets is predicted successuy and dynamic motions o poymer chain in the eongationa ow are visuaized in the Fig.6.

5 PAPER TITLE Acknowedgement This work was supported by a grant rom the genera research program supported by Korea Institute o Materias Science (KIMS). (a) Eongationa viscosity o nanocomposite t= t=.5 t=1 (b) Dynamic behavior o poymer chain in eongationa ow Fig.6. Dynamic behavior o poymer chain and the corresponding viscosity in eongationa ow 5 Concusions A new moecuar mode was proposed rom the idea o the thermodynamicay admissibe reptation theory to describe more reaistic chain dynamics and predict rheoogica properties o poymers and poymeric nanocomposites. Brownian dynamics simuation was utiized to cacuate the mode without any signiicant approximations and the proposed stepwise Wiener process was appied to obtain more improved curves o rheoogy, especiay at uniaxia eongationa ow with ow eongation rates. The mode predicted the characteristic rheoogica behavior o poymeric nanocomposites, e.g., strong non-newtonian behavior rom ow shear rates in shear ow and noninear strain hardening in eongationa ow. Eongationa ow properties were strongy aected by chain extensibiity and constraint reease, whie shear ow properties were amost independent o chain extensibiity but aected by constraint reease o chain retraction. Poymer moecuar chains showed dierent deormation in shear and eongationa ows, the ormer was dominated by moecuar orientation and the atter was strongy aected by chain stretch as we as orientation. Reerences [1] M. Aexandre and P. Dubois, Poymer-ayered siicate nanocomposites: preparation, properties and uses o a new cass o materias, Materias Science and Engineering, Vo. 8, pp 1-63,. [] Y. Kojima, A. Usuki, M. Kawasumi, A. Okada, Y. Fukushima, T. Kurauchi, and O. Kamigaito, Mechanica properties o nyon 6-cay hybrid, J. Mater. Res. 8, 1185 (1993). [3] Y. Kojima, A. Usuki, M. Kawasumi, A. Okada, T. Kurauchi, and O. Kamigaito, One-pot synthesis o nyon 6-cay hybrid, J. Poym.. Sci. Part A:Poym. Chem. 31, 1755 (1993). [4] R. Xu, E. Manias, A. J. Snyder, and J. Runt, New biomedica poy(urethane urea)-ayered siicate nanocomposites, Macromoecues 34, 337 (1). [5] S. Shinha Ray, K. Yamada, M. Okamoto, and K. Ueda, Poyactide-ayered siicate nanocompoaite: a nove biodegradabe materia, Nano Lett., 193 (). [6] R. A. Vaia, S. Vasudevan, W. Krawiec, L. G. Scanon, and E. P. Gianneis, New poymer eectroyte nanocomposites: met intercaation o poy(ethyene oxide) in mica-type siicates, Adv. Mater. 7, 154 (1995). [7] D. G. Seong, T. J. Kang, J. R. Youn, Rheoogica characterization o poymer-based nanocomposites with dierent nanoscae dispersions, e-poymers, Vo. 5, pp 1-14, 5. [8] M. Doi and S. F. Edwards, The theory o poymer dynamics, Carendon Press, Oxord (1986). [9] H. C. Öttinger, A thermodynamicay admissibe reptation mode or ast ows o entanged poymers, Journa o Rheoogy, Vo. 43, pp ,