- Email: [email protected]
Molecular observation of contour length fluctuations in polymer melts
ARTICLE IN PRESS
Physica B 350 (2004) 193–195
Molecular observation of contour length fluctuations in polymer melts A. Wischnewskia,*, M. Zamponia, M. Monkenbuscha, L. Willnera, W. PyckhoutHintzena, D. Richtera, A.E. Likhtmanb, T.C.B. McLeishb, B. Faragoc Institut fur Forschungszentrum Julich, D-52425 Julich, Germany . Festkorperforschung, . . . b IRC in Polymer Science and Technology, University of Leeds, Leeds LS2 9JT, UK c Institut Laue-Langevin, B.P. 156X, Avenue des Martyrs, F-38042 Grenoble Cedex 9, France a
Abstract The close comparison of linear rheology data of some long-chain polymer melts with the reptation model indicates the existence of additional degrees of freedom limiting the topological chain confinement. As one candidate contour length fluctuations (CLF) were proposed and indeed account for the observed power law in the dynamic loss modulus G00 ðoÞ: In order to study these mechanisms on a microscopic scale we have performed neutron spin echo investigations of the single-chain dynamic structure factor from polyethylene (PE) melts over a large range of chain lengths. A systematic loosening of the confinement with decreasing chain length is found and can be described quantitatively by the effect of CLF on the confining tube establishing this mechanism on a molecular level in space and time. r 2004 Elsevier B.V. All rights reserved. PACS: 83.80.Sg; 61.12.q; 83.10.Hn Keywords: Neutron spin-echo; Rheology; Polymer melt; Reptation
In the melt, long-chain polymers heavily interpenetrate each other and mutually restrict their motions due to formation of topological constraints. In his famous reptation model de Gennes described the effect of these entanglements by a tube (with diameter d) along the coarse grained chain profile localizing the chain and confining the chain motion [1,2]. The dominant motional mechanisms in this model are (i) a curvilinear version of the Rouse *Corresponding author. Fax: +49-2461-61-2610. E-mail address: [email protected] (A. Wischnewski).
motion at short times (also termed local reptation), (ii) and escape of the whole molecule from the tube at long times—the reptation process. The reptation model treated at this level is able to describe macroscopic melt dynamics qualitatively. However, in order to achieve quantitative agreement with the rheology of polymer melts at time scales less than the Rouse time, i.e. the longest relaxation time of internal chain modes, one needs an additional mechanism of chain motion, namely contour length fluctuations. Fig. 1 shows the dynamic loss modulus G 00 ðoÞ vs. frequency for polyisoprene. While the reptation
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.04.024
ARTICLE IN PRESS A. Wischnewski et al. / Physica B 350 (2004) 193–195
194
-1/2 5
G" (Pa)
10
-1/4 10
4
10
-2
10
0
10
2
10
4
10
6
ω (rad/s) Fig. 1. G00 ðoÞ of polyisoprene ðMw ¼ 1000 kg=molÞ at T ¼ 300 K measured at the rheometer in Julich. .
1. 00
S(Q,t) / S(Q)
0. 75
0. 50
0. 25
M w = 190 kg/mol
0. 00
S(Q,t) / S(Q)
0. 75
0. 50
0. 25
M w = 12.4 kg/mol 0. 00
0
50
100
150
Fourier time t / ns Fig. 2. Neutron spin echo-spectra (IN15, ILL) from polyethylene melts with Mw ¼ 190 and 12:4 kg=mol: The Q-values correspond to: ( 1 ; triangles: Q ¼ 0:077 A ( 1 ; crosses: Q ¼ 0:096 A ( 1 ; diamonds: Q ¼ 0:115 A ( 1 : Lines: ( 1 ; circles: Q ¼ 0:05 A squares: Q ¼ 0:03 A explanation see text.
ARTICLE IN PRESS A. Wischnewski et al. / Physica B 350 (2004) 193–195 65 Reptation model Reptation + tube length fluctuations
60
tube diameter / Å
model predicts a power law po1=2 for the pure reptation process the data show a power law of po1=4 thereby clearly indicating an additional relaxation process at intermediate frequencies. Taking into account the effect of contour length fluctuations, the observed power law can be reproduced. Whereas, rheology is an indirect probe of molecular motion, only recently it became possible to observe the tube confinement and the associated restrictions of segment motion directly in space and time exploiting the capabilities of ultra high-resolution neutron spin-echo (NSE) spectroscopy at the IN15 instrument (ILL, Grenoble) [3]. In this study the dynamic structure factor of the reptation model was corroborated for high molecular weight ðMw Þ PE: Here, we present a systematic study of the single-chain dynamic structure factor SðQ; tÞ of PE-melts for weight averaged molecular weights between 12:4 kg=molpMw p190 kg=mol with a narrow distribution Mw =Mn o1:05: Fig. 2 displays the obtained spectra for the highest and the lowest molecular weight. While for the high molecular weight the data show a plateau at long times, for the lowest molecular weight of our series a slope is visible reflecting a significant loosening of confinement with decreasing chain length. The data were analysed both using the pure reptation model neglecting contour length fluctuations and by an alternative approach, where the contour length fluctuations are considered. The fits were performed fixing the elementary Rouse rate W taken from earlier measurements on PE at short times [4] and varying the tube diameter d as the only parameter. First, the data were analysed in terms of the pure reptation model yielding a good fit. Here, the constraint reduction discussed above is reflected by an apparent tube diameter which increases with decreasing chain length. This is illustrated in Fig. 3. In an alternative approach we took into account the contour length fluctuations [5]. If we compare the experimental spectra with the model prediction (see lines in Fig. 2), we generally find good agreement. The gradually increasing decay of SðQ; tÞ with decreasing Mw is described very well both with respect to the
195
55 50 45 40 35 30
10
100
molecular weight (/ kg/mol) Fig. 3. Resulting d from the model fits with pure reptation (circles) and reptation and contour length fluctuations (squares) as a function of molecular weight. The line is a guide for the eye.
magnitude of the effect as well as to the shape of SðQ; tÞ without introducing any new parameter. The squares in Fig. 3 show the resulting tube diameters. Besides some small fluctuations they now remain constant, independent of Mw : In conclusion, at high Mw only ‘‘local reptation’’ is active and de Gennes model is confirmed, with decreasing Mw we observe end effects with relative weight causing an apparent gradual speed-up of the chain escape mechanism. Formulating the CLF-effect on the level of the chain and calculating the corresponding structure factor we are able to quantitatively describe all experimental results and thus for the first time confirm the concept of contour length fluctuations on a molecular level in space and time.
References [1] P.G. DeGennes, J. Phys. 42 (1981) 735. [2] M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford Science Publications, Clarendon Press, Oxford, 1988. [3] P. Schleger, B. Farago, C. Lartigue, A. Kollmar, D. Richter, Phys. Rev. Lett. 81 (1998) 124. [4] D. Richter, B. Farago, R. Butera, L.J. Fetters, J.S. Huang, B. Ewen, Macromolecules 26 (1993) 795. [5] A. Wischnewski, M. Monkenbusch, L. Willner, D. Richter, A.E. Likhtman, T.C.B. McLeish, B. Farago, Phys. Rev. Lett. 88 (2002) 058301.
Physica B 350 (2004) 193–195
Molecular observation of contour length fluctuations in polymer melts A. Wischnewskia,*, M. Zamponia, M. Monkenbuscha, L. Willnera, W. PyckhoutHintzena, D. Richtera, A.E. Likhtmanb, T.C.B. McLeishb, B. Faragoc Institut fur Forschungszentrum Julich, D-52425 Julich, Germany . Festkorperforschung, . . . b IRC in Polymer Science and Technology, University of Leeds, Leeds LS2 9JT, UK c Institut Laue-Langevin, B.P. 156X, Avenue des Martyrs, F-38042 Grenoble Cedex 9, France a
Abstract The close comparison of linear rheology data of some long-chain polymer melts with the reptation model indicates the existence of additional degrees of freedom limiting the topological chain confinement. As one candidate contour length fluctuations (CLF) were proposed and indeed account for the observed power law in the dynamic loss modulus G00 ðoÞ: In order to study these mechanisms on a microscopic scale we have performed neutron spin echo investigations of the single-chain dynamic structure factor from polyethylene (PE) melts over a large range of chain lengths. A systematic loosening of the confinement with decreasing chain length is found and can be described quantitatively by the effect of CLF on the confining tube establishing this mechanism on a molecular level in space and time. r 2004 Elsevier B.V. All rights reserved. PACS: 83.80.Sg; 61.12.q; 83.10.Hn Keywords: Neutron spin-echo; Rheology; Polymer melt; Reptation
In the melt, long-chain polymers heavily interpenetrate each other and mutually restrict their motions due to formation of topological constraints. In his famous reptation model de Gennes described the effect of these entanglements by a tube (with diameter d) along the coarse grained chain profile localizing the chain and confining the chain motion [1,2]. The dominant motional mechanisms in this model are (i) a curvilinear version of the Rouse *Corresponding author. Fax: +49-2461-61-2610. E-mail address: [email protected] (A. Wischnewski).
motion at short times (also termed local reptation), (ii) and escape of the whole molecule from the tube at long times—the reptation process. The reptation model treated at this level is able to describe macroscopic melt dynamics qualitatively. However, in order to achieve quantitative agreement with the rheology of polymer melts at time scales less than the Rouse time, i.e. the longest relaxation time of internal chain modes, one needs an additional mechanism of chain motion, namely contour length fluctuations. Fig. 1 shows the dynamic loss modulus G 00 ðoÞ vs. frequency for polyisoprene. While the reptation
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.04.024
ARTICLE IN PRESS A. Wischnewski et al. / Physica B 350 (2004) 193–195
194
-1/2 5
G" (Pa)
10
-1/4 10
4
10
-2
10
0
10
2
10
4
10
6
ω (rad/s) Fig. 1. G00 ðoÞ of polyisoprene ðMw ¼ 1000 kg=molÞ at T ¼ 300 K measured at the rheometer in Julich. .
1. 00
S(Q,t) / S(Q)
0. 75
0. 50
0. 25
M w = 190 kg/mol
0. 00
S(Q,t) / S(Q)
0. 75
0. 50
0. 25
M w = 12.4 kg/mol 0. 00
0
50
100
150
Fourier time t / ns Fig. 2. Neutron spin echo-spectra (IN15, ILL) from polyethylene melts with Mw ¼ 190 and 12:4 kg=mol: The Q-values correspond to: ( 1 ; triangles: Q ¼ 0:077 A ( 1 ; crosses: Q ¼ 0:096 A ( 1 ; diamonds: Q ¼ 0:115 A ( 1 : Lines: ( 1 ; circles: Q ¼ 0:05 A squares: Q ¼ 0:03 A explanation see text.
ARTICLE IN PRESS A. Wischnewski et al. / Physica B 350 (2004) 193–195 65 Reptation model Reptation + tube length fluctuations
60
tube diameter / Å
model predicts a power law po1=2 for the pure reptation process the data show a power law of po1=4 thereby clearly indicating an additional relaxation process at intermediate frequencies. Taking into account the effect of contour length fluctuations, the observed power law can be reproduced. Whereas, rheology is an indirect probe of molecular motion, only recently it became possible to observe the tube confinement and the associated restrictions of segment motion directly in space and time exploiting the capabilities of ultra high-resolution neutron spin-echo (NSE) spectroscopy at the IN15 instrument (ILL, Grenoble) [3]. In this study the dynamic structure factor of the reptation model was corroborated for high molecular weight ðMw Þ PE: Here, we present a systematic study of the single-chain dynamic structure factor SðQ; tÞ of PE-melts for weight averaged molecular weights between 12:4 kg=molpMw p190 kg=mol with a narrow distribution Mw =Mn o1:05: Fig. 2 displays the obtained spectra for the highest and the lowest molecular weight. While for the high molecular weight the data show a plateau at long times, for the lowest molecular weight of our series a slope is visible reflecting a significant loosening of confinement with decreasing chain length. The data were analysed both using the pure reptation model neglecting contour length fluctuations and by an alternative approach, where the contour length fluctuations are considered. The fits were performed fixing the elementary Rouse rate W taken from earlier measurements on PE at short times [4] and varying the tube diameter d as the only parameter. First, the data were analysed in terms of the pure reptation model yielding a good fit. Here, the constraint reduction discussed above is reflected by an apparent tube diameter which increases with decreasing chain length. This is illustrated in Fig. 3. In an alternative approach we took into account the contour length fluctuations [5]. If we compare the experimental spectra with the model prediction (see lines in Fig. 2), we generally find good agreement. The gradually increasing decay of SðQ; tÞ with decreasing Mw is described very well both with respect to the
195
55 50 45 40 35 30
10
100
molecular weight (/ kg/mol) Fig. 3. Resulting d from the model fits with pure reptation (circles) and reptation and contour length fluctuations (squares) as a function of molecular weight. The line is a guide for the eye.
magnitude of the effect as well as to the shape of SðQ; tÞ without introducing any new parameter. The squares in Fig. 3 show the resulting tube diameters. Besides some small fluctuations they now remain constant, independent of Mw : In conclusion, at high Mw only ‘‘local reptation’’ is active and de Gennes model is confirmed, with decreasing Mw we observe end effects with relative weight causing an apparent gradual speed-up of the chain escape mechanism. Formulating the CLF-effect on the level of the chain and calculating the corresponding structure factor we are able to quantitatively describe all experimental results and thus for the first time confirm the concept of contour length fluctuations on a molecular level in space and time.
References [1] P.G. DeGennes, J. Phys. 42 (1981) 735. [2] M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford Science Publications, Clarendon Press, Oxford, 1988. [3] P. Schleger, B. Farago, C. Lartigue, A. Kollmar, D. Richter, Phys. Rev. Lett. 81 (1998) 124. [4] D. Richter, B. Farago, R. Butera, L.J. Fetters, J.S. Huang, B. Ewen, Macromolecules 26 (1993) 795. [5] A. Wischnewski, M. Monkenbusch, L. Willner, D. Richter, A.E. Likhtman, T.C.B. McLeish, B. Farago, Phys. Rev. Lett. 88 (2002) 058301.