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Controlling the sub-molecular motions to increase the glass transition temperature of polymers
Chemical Physics Letters 593 (2014) 24–27
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Controlling the sub-molecular motions to increase the glass transition temperature of polymers Sudharsan Pandiyan a,b, Priya V. Parandekar c, Om Prakash c, Thomas K. Tsotsis d, Nisanth N. Nair a,⇑, Sumit Basu b,⇑ a
Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India Boeing Research & Technology, India-Centre, Bangalore 560016, India d Boeing Research & Technology, Huntington Beach, CA 92647, USA b c
a r t i c l e
i n f o
Article history: Received 6 October 2013 In final form 30 December 2013 Available online 6 January 2014
a b s t r a c t Employing atomistic molecular dynamics (MD) simulations, we scrutinize the relationship between submolecular motions in a glassy polymer and its glass-transition temperature (T g ). This molecular understanding allows us to modify the polymer to manipulate atomistic motions, thereby controlling the glass transition temperature. We demonstrate this using a high performance polymer, HFPE-30, which has applications in aerospace industry. Control over sub-molecular motion is achieved by chemical substitution and it leads to increase in the glass transition temperature without affecting its mechanical properties. The approach laid out here could pave a way to achieve highly cross-linked high temperature polymers with better thermo-chemical stability. Ó 2014 Elsevier B.V. All rights reserved.
High performance polymers [1–3] (HPP) are widely deployed in aerospace applications as ultra-high temperature lightweight composites. In general, polyimides possess excellent thermal stability and high modulus [4,5]. The PMR-15 polyimide [6,3], developed in the 1970’s, is used extensively in aerospace applications and has Tg = 288 °C combined with good processibility and mechanical properties. While the glass transition temperature of PMR-15 is significantly higher than other common commercial polymers, the need to have lightweight structures that can withstand even more exacting temperatures has led to attempts focused at raising the T g of polyimides. Achieving even higher T g without sacrificing processibility and mechanical properties is a major technical challenge. Qualitatively, polymers with flexible backbone chains exhibit low glass transition temperatures. Glass transition is known to be influenced by molecular weight, crystallinity, blending and cross-linking [7]. In highly cross-linked polymers, like epoxy resins, crosslinks hinder the motion of the neighboring main chain segments and thus lead to an increase in T g with crosslink density [8]. The influence of the polyimide architecture on T g has been studied quite extensively [9,10]. The glass transition temperature of polyimides have been shown to depend on the flexibility of the links between the diamines. However, as noted by Negi and Basu [11], in general, most of the effects that increase the T g of a particular polymer also reduce its ⇑ Corresponding authors. E-mail addresses: [email protected] (N.N. Nair), [email protected] (S. Basu). 0009-2614/$ - see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.12.076
ductility. For example, common polycarbonates BPA-PC and TMC-PC (which has a bulkier side-group) have glass transition temperatures of 150 and 239 °C, respectively, but the latter breaks at a lower elongation than the former. [12] In general, polymers with high T g suffer from brittle behavior and low processibility [13]. Can molecular simulations help in designing polyimides while balancing the seemingly contradictory aims of attaining a high T g and adequate ductility? In this Letter, we show that, by modifying suitably identified sub-molecular units of an existing polyimide, it is indeed possible to enhance its T g without compromising mechanical properties. To this end, we use HFPE-30, which is employed in building light weight cryogenic engines for aerospace applications [14,15]. The rigid backbone of the HFPE-30 polymer (see Figure 1) makes it mechanically strong while its high packing density and glassy character renders thermal stability [15–19]. With the aim of increasing the T g of HFPE-30, we identify the crucial factors that govern its T g by computing various static and dynamic properties from atomistic molecular dynamics (MD) simulations. We used molecular dynamics (MD) simulations as a tool to construct the fully atomistic model of HFPE-30. The empirical force field parameters were extracted from the OPLS–AA force field [20] and from density functional theory (DFT) calculations. The complete simulation details are presented in the supplementary information. A cubic simulation box containing 300 homo-polymer chains were prepared using GROMACS MD simulation package [21]. Considering the fact that the Flory’s ‘ideality hypothesis’
S. Pandiyan et al. / Chemical Physics Letters 593 (2014) 24–27
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HFPE-30F Figure 1. Chemical structure of HFPE-30 and HFPE-30F. The arrows indicate the diamine benzene torsion around the imide bond.
[22] holds for short oligomers (HFPE-30 has only five repeating monomers) in the melt state, the decorrelation of the initial configuration of polymer chains was achieved by high temperature annealing. The decorrelated chains were subsequently packed and energy minimized and relaxed under NVT conditions for 1 ns. Finally, a NPT simulation for 5 ns was carried out at 298 K and 1 bar pressure, out of which, the final 4 ns was considered as production run and subsequently used for property analyses. Several calculated properties are listed in Table I. A systematic simulated annealing procedure was adopted to calculate the T g of the polymer. The simulation boxes were heated up to 900 K at the rate of 0.1 K/ps and subsequently cooled at the same rate. Every cooling step consisted of a NVT equilibration followed by a NPT equilibration and production run (similar to the protocol described in Ref. [23]). Representative configurations at every 50 K were extracted and allowed to relax for 2 ns under NPT conditions. As shown in Figure 2, the T g of HFPE-30 was estimated to be 660 5 K from the intersection of the linear fits to the high and low regimes of the density versus temperature plot. The experimentally observed T g of uncross-linked HFPE-30 is 513 K [15]. Our estimated T g of 660 ± 5 K is reasonable considering the high heating and cooling rates employed. The computation of the dihedral autocorrelation [24] as a function of temperature revealed that the torsional rotation around the diamine benzene in the HFPE-30 backbone (see Figure 3) plays an important role on the melting dynamics of the polymer. It is noted that the potential energy barriers for the other weak bond rotations in the HFPE-30 backbone are very small (<2 kJ mol1) and hence they are freely rotatable at room temperature and decorrelate much faster. On the other hand, the potential energy barrier for the diamine benzene to rotate around the imide bond is
Figure 2. Percentage change in density of HFPE-30 and HFPE-30F (with respect to their densities at room temperature) with temperature. The values of T g are also indicated.
Figure 3. The time evolution of the dihedral autocorrelation function, CðtÞ ¼ hcos½hðsÞ hðs þ tÞis for diamine benzene rotation around imide bond in HFPE-30 and HFPE-30F at different temperatures. The open and full symbols correspond to HFPE-30 and HFPE-30F respectively.
8 kJ mol1 and its rotational frequency and decorrelation time depend strongly on the temperature. Increase in temperature increases the diamine benzene rotation frequency and eventually affects the structured packing of the rings, leading to increase in average intermolecular distance between the polymer chains; see Figure 2 in the Supplementary Data. This results in the lowering of the packing density of the polymer, driving it to its melt state. Our analyses showed that other sub-molecular motions do not have any major effect with increasing temperature. Evolution of the decorrelation function for the diamine benzene in HFPE-30 is shown in Figure 3. The above discussion implies that a higher potential energy barrier for the rotation of benzene molecule about the imide bond in the diamine residue would slow down the torsional rotation, consequently increase the T g . An effect of rotational potential energy barriers on T g has been studied in some of the earlier Letters. [11] Hence, a substitution in the benzene rings of the diamine residues that could increase the torsional rotational barrier is a potentially viable route to obtain higher T g . On carrying out benchmark in vacuo DFT/B3LYP calculations using the benzene–phthalimide moiety, we observed that replacing the benzene hydrogens by fluorine increases the potential energy barrier of the benzene rotation about the imide bond from 8 kJ mol1 to 75 kJ mol1. This hints that substitution of the diamine benzene by flourine can achieve the purpose of increasing the rotational barriers about the imide bond. It is well known that polyimides show improved physical properties on flourination, in particular by the introduction of triflouromethyl moeties [25]. Synthesis and properties of such flourinated polyimides are also well discussed in the literature [26–28,25]. Recently, it has been reported that flourinated dimamine moiety results in high T g and improved thermal–oxidative
26
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stability.[29] In the current Letter, we propose modification by susbstituting 2,3,5,6 positions of diamine residue by flourine [30]. We will refer to the fluorine substituted HFPE-30 as HFPE30F; see also Figure 1. A fully atomistic model of fluorine HFPE-30F was prepared and its T g was determined using the same procedure as for HFPE-30. The sharp peaks in the diamine torsional angle distribution for HFPE-30F in Figure 4 show that the fluorine substitution restricted the number of diamine rotations dramatically by a factor of about 103 at 600 K (see also Figure 3). Expectedly, the T g of the HFPE-30F increased to 740 ± 5 K as shown in Figure 2. This increase can be accounted by the electrostatic and steric repulsions between fluorine and oxygen atoms in the substituted diamine and dianhydride moieties. As noted earlier, alteration of the backbone structure has the potential of changing other properties of HFPE-30, especially ductility. Hence we analyzed various physical and mechanical properties of HFPE-30F and compared it with HFPE-30. The results obtained are presented in Table 1. The estimated structural factor showed that both the polymer models are highly amorphous (see Figure 1 in the Supplementary Data). The small difference in the peaks at lower values of q for HFPE-30F can be explained by its better structured packing (see Figure 2 in the Supplementary Data). This suggests that the HFPE-30F should have higher density than its unsubstituted counterpart but interestingly we found a slight decrease (<2%) in the density of HFPE-30F. The decrease in density is due to the strong inter-molecular repulsion between fluorine and oxygen atoms in the diamine and dianhydride groups in HFPE-30F. Also, the difference in the fractional free volume calculated using Bondi’s group contribution method [31] can be attributed to the difference in the van der Waals volume between hydrogen and fluorine atoms and the small difference in their packing density. The individual contributions to the (average) potential energy per chain are comparable between the two polymers. The only exception is in the average torsional energy, which is lower in HFPE-30F, due to the elevated free energy barrier of the diamine benzene rotation. The comparison of end-to-end distance and radius of gyration also indicate that both the polymers are expected to have similar bulk characteristics. The stress strain simulations were done by increasing the zdimension of the simulation box at a constant rate of 2 1010 s1 for a period of 5 ns in a N rx ry T ensemble. The mechanical properties are compared by applying a uniaxial tension in the z-direction keeping the other two stress free. Further, the zz component of the virial stress and engineering strain are used to plot the stress strain curves in Figure 5. To the best of our knowledge uniaxial stress strain response of un-crosslinked HFPE-30 has
Figure 4. Torsional angle distributions of diamine benzene in HFPE-30 (red) and HFPE-30F (black) at temperatures of 600 K (squares) and 900 K (circles). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Comparison of various physical properties between HFPE-30 and HFPE-30F. All values (except T g ) are calculated at 298 K and 1 bar. The energy values are given per chain. The fractional free volume (FFV) was estimated using Bondi’s group contribution method [31].
a
Property
HFPE-30
HFPE-30F
Density [kg m3] T g [K] FFV End-to-end distance [nm] Radius of gyration [nm] Bending energy [kJ mol1] Torsional energy [kJ mol1] Non-bonded energy [kJ mol1] Potential energy [kJ mol1]
1310 ± 5 660 ± 5 (513)a 0.254 ± 0.002 1.650 ± 0.003 5.50 ± 0.01 2196 ± 4 1230 ± 3 452 ± 7 2974 ± 17
1285 ± 5 740 ± 5 0.304 ± 0.002 1.570 ± 0.003 5.50 ± 0.01 2169 ± 4 993 ± 3 371 ± 6 2791 ± 16
Experimentaly determined value of T g for the uncrosslinked HFPE-30.
Figure 5. Stress–strain response of HFPE-30 and HFPE-30F for a strain rate of 2 1010 s1 computed at 298 K.
not been reported in the literature. Given the high strain rates used in MD simulations, it is expected that the maximum stress levels borne by the material in the simulation (180 MPa) will be significantly higher than in real life. However the pertinent point is that, for the given strain rates both the polymers exhibited no major difference in terms of their uniaxial response. Both the polymers could withstand close to 10% strain at failure, indicating that the fluorine substitution has not resulted in any change in ductility. Also for all practical purposes, the failure strain of any brittle material is about 10% at the strain rate employed. Beyond this strain, the material rapidly loses its stress carrying capacity. We have simulated the uniaxial stress strain response at lower strain rates of up to 2 108 s1 and both HFPE-30 and HFPE-30F show similar behavior at these rates. Interestingly, fluorine substitution also increases the thermo oxidative stability of the polymer compared to the unsubstituted polymers due to the reduced possibility of oxidation and hydrolysis reactions between the residual solvent molecules and polymer chains. [25] Hence the suggested substitution is useful to increase the oxidative stability and T g of the polymer without altering the backbone structure significantly, evidenced by the almost unaltered physical and mechanical properties. In conclusion, the present letter has shown that sub-molecular motions have a critical role in dictating the T g of a glassy polyimide. By identifying these crucial molecular motions, it is possible to suggest chemical modifications of the polymer backbone that can lead to changes in T g . Molecular simulations have a large role to play in deciding modifications that can suitably increase T g without compromising oxidative and mechanical properties. In the specific example of HFPE-30 studied in this Letter, we have found a simple viable route for achieving these seemingly contradictory goals by the fluorination of the diamine moiety. The
S. Pandiyan et al. / Chemical Physics Letters 593 (2014) 24–27
proposed modification of HFPE-30 has importance in their applications to the aerospace industry. Most importantly, 2,3,5,6tetrafluorobenzene 1,4-diamine is commercially available for the synthesis of HFPE-30F, and its synthesis has been reported earlier. [30] We are not aware of any experimental or theoretical works that has reported any thermo-mechanical property of HFPE-30F. Finally, it should be noted that all simulations have been done on the uncross-linked system whereas commercial HFPE-30 is crosslinked. While we believe that the same effects should apply to cross-linked HFPE-30 and HFPE-30F, we are doing further simulations to investigate this point. Acknowledgments Authors are grateful to The Boeing Company, U.S.A. for funding the project ‘‘Investigation into the Thermo-oxidative and Mechanical Response of Commercial Polyimide Resins and Polyimide Nano-composites for Aerospace Application’’ under which this Letter has been carried out. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2013.12. 076. References [1] [2] [3] [4] [5] [6] [7]
D. McDanels, T. Serafini, J. DiCarlo, J. Mat. Energy Syst. 8 (1986) 80. P.M. Hergenrother, Angew. Chem. Int. Ed. 29 (1990) 1262. M.A. Meador, Annu. Rev. Mater. Sci. 28 (1998) 599. T.T. Serafini, P. Delvigs, G.R. Lightsey, J. App. Poly. Sci. 16 (1972) 905. D.A. Scola, J.H. Vontell, Poly. Composites 9 (1988) 443. D. Wilson, Brit. Poly. J. 20 (1988) 405. J. Mark, K. Ngai, W. Graessley, L. Mandelkern, E. Samulski, J. Koenig, G. Wignall, Physical Properties of Polymers, third ed., Cambridge University Press, Cambridge, 2004.
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[8] J.L. Halary, F. Laupretre, L. Monnerie, Polymer Materials: Macroscopic Properties and Molecular Interpretations, Wiley, New York, 2011. [9] S.-H. Hsiao, Y.-J. Chen, Eur. Polym. J. 38 (4) (2002) 815. [10] I. Ronova, M. Bruma, Struct. Chem. 21 (2010) 1013. [11] A. Negi, S. Basu, Modelling Simul. Mater. Sci. Eng. 14 (4) (2006) 563. [12] W. Brostow, Performance of Plastics, Hanser Publications, Cincinnati, 2000. [13] A. Yee, L. Xiangyang, High Glass Transition Temperature, Ductile, and Processable Thermoplastic Containing Conformable Ring Segments, US Patent:US6203,922, 2001. [14] K.C. Chuang, C.L. Bowman, T.K. Tsotsis, C.P. Arendt, High Perf. Polym. 15 (2003) 459. [15] Y. Li, R.J. Morgan, J. Appl. Polym. Sci. 101 (2006) 4446. [16] Y. Li, L.A. Murphy, J.E. Lincoln, R.J. Morgan, Macromol. Mat. Eng. 292 (2007) 78. [17] J.E. Lincoln, Ph.D. thesis, Michigan State University, East Lansing, MI, 2001. [18] R.J. Morgan, Characterization of the structure-processing-performance relations of phenylethynyl phthalic anhydride crosslinked fluorinated polyimides (AFR-PEPA-N) and their carbon fiber composites, Tech. Rep. AFRL-SR-AR-TR-07-0178, Texas A&M University, Texas Engineering Experiment Station, 2007. [19] J.C. Grunlan, K.R. Rajagopal, J. Reddy, Performance characterization of polyimide-carbon fiber composites for future hypersonic vehicles, Tech. Rep. AFRL-OSR-VA-TR-2012-0052, Texas A&M University, Texas Engineering Experiment Station, 2010. [20] W.L. Jorgensen, D.S. Maxwell, J. Tirado-Rives, J. Am. Chem. Soc. 118 (1996) 11225. [21] B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, J. Chem. Theory Comput. 4 (2008) 435. [22] P.J. Flory, Statistical Mechanics of Chain Molecules, Interscience Publishers, New York, 1969. [23] D.H.M. Minelli, M.G. De Angelis, Fluid Phase Equilib. 333 (2012) 87. [24] D. van der Spoel, H.J.C. Berendsen, Biophys. J. 72 (1997) 2032. [25] M.G. Dhara, S. Banerjee, Prog. Poly. Sci. 35 (2010) 1022. [26] H. Kameshima, N. Nemoto, T. Endo, J. Poly. Sci. A 39 (2001) 3143. [27] D.-J. Liaw, K.-L. Wang, Y.-C. Huang, K.-R. Lee, J.-Y. Lai, C.-S. Ha, Prog. Poly. Sci. 37 (2012) 907. [28] T. Liang, C.N. Neumann, T. Ritter, Angew. Chem. Int. Ed. 52 (2013) 8214. [29] S.K. Sen, S. Banerjee, RSC Adv. 2 (2012) 6274. [30] D.C. Rich, P. Cebe, A.K. St.Clair, High-Temperature Properties and Applications of Polymeric Materials, vol. 603, ACS Symposium Series, Washington DC, 1995, p. 238. ch. 17. [31] D.W. Van Krevelen, K. Te Nijenhuis, Properties of Polymers: Their Correlation with Chemical Structure; their Numerical Estimation and Prediction from Additive Group Contributions, 4th Edition., Elsevier, Amsterdam, 2009.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Controlling the sub-molecular motions to increase the glass transition temperature of polymers Sudharsan Pandiyan a,b, Priya V. Parandekar c, Om Prakash c, Thomas K. Tsotsis d, Nisanth N. Nair a,⇑, Sumit Basu b,⇑ a
Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India Boeing Research & Technology, India-Centre, Bangalore 560016, India d Boeing Research & Technology, Huntington Beach, CA 92647, USA b c
a r t i c l e
i n f o
Article history: Received 6 October 2013 In final form 30 December 2013 Available online 6 January 2014
a b s t r a c t Employing atomistic molecular dynamics (MD) simulations, we scrutinize the relationship between submolecular motions in a glassy polymer and its glass-transition temperature (T g ). This molecular understanding allows us to modify the polymer to manipulate atomistic motions, thereby controlling the glass transition temperature. We demonstrate this using a high performance polymer, HFPE-30, which has applications in aerospace industry. Control over sub-molecular motion is achieved by chemical substitution and it leads to increase in the glass transition temperature without affecting its mechanical properties. The approach laid out here could pave a way to achieve highly cross-linked high temperature polymers with better thermo-chemical stability. Ó 2014 Elsevier B.V. All rights reserved.
High performance polymers [1–3] (HPP) are widely deployed in aerospace applications as ultra-high temperature lightweight composites. In general, polyimides possess excellent thermal stability and high modulus [4,5]. The PMR-15 polyimide [6,3], developed in the 1970’s, is used extensively in aerospace applications and has Tg = 288 °C combined with good processibility and mechanical properties. While the glass transition temperature of PMR-15 is significantly higher than other common commercial polymers, the need to have lightweight structures that can withstand even more exacting temperatures has led to attempts focused at raising the T g of polyimides. Achieving even higher T g without sacrificing processibility and mechanical properties is a major technical challenge. Qualitatively, polymers with flexible backbone chains exhibit low glass transition temperatures. Glass transition is known to be influenced by molecular weight, crystallinity, blending and cross-linking [7]. In highly cross-linked polymers, like epoxy resins, crosslinks hinder the motion of the neighboring main chain segments and thus lead to an increase in T g with crosslink density [8]. The influence of the polyimide architecture on T g has been studied quite extensively [9,10]. The glass transition temperature of polyimides have been shown to depend on the flexibility of the links between the diamines. However, as noted by Negi and Basu [11], in general, most of the effects that increase the T g of a particular polymer also reduce its ⇑ Corresponding authors. E-mail addresses: [email protected] (N.N. Nair), [email protected] (S. Basu). 0009-2614/$ - see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.12.076
ductility. For example, common polycarbonates BPA-PC and TMC-PC (which has a bulkier side-group) have glass transition temperatures of 150 and 239 °C, respectively, but the latter breaks at a lower elongation than the former. [12] In general, polymers with high T g suffer from brittle behavior and low processibility [13]. Can molecular simulations help in designing polyimides while balancing the seemingly contradictory aims of attaining a high T g and adequate ductility? In this Letter, we show that, by modifying suitably identified sub-molecular units of an existing polyimide, it is indeed possible to enhance its T g without compromising mechanical properties. To this end, we use HFPE-30, which is employed in building light weight cryogenic engines for aerospace applications [14,15]. The rigid backbone of the HFPE-30 polymer (see Figure 1) makes it mechanically strong while its high packing density and glassy character renders thermal stability [15–19]. With the aim of increasing the T g of HFPE-30, we identify the crucial factors that govern its T g by computing various static and dynamic properties from atomistic molecular dynamics (MD) simulations. We used molecular dynamics (MD) simulations as a tool to construct the fully atomistic model of HFPE-30. The empirical force field parameters were extracted from the OPLS–AA force field [20] and from density functional theory (DFT) calculations. The complete simulation details are presented in the supplementary information. A cubic simulation box containing 300 homo-polymer chains were prepared using GROMACS MD simulation package [21]. Considering the fact that the Flory’s ‘ideality hypothesis’
S. Pandiyan et al. / Chemical Physics Letters 593 (2014) 24–27
O
O
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HFPE-30F Figure 1. Chemical structure of HFPE-30 and HFPE-30F. The arrows indicate the diamine benzene torsion around the imide bond.
[22] holds for short oligomers (HFPE-30 has only five repeating monomers) in the melt state, the decorrelation of the initial configuration of polymer chains was achieved by high temperature annealing. The decorrelated chains were subsequently packed and energy minimized and relaxed under NVT conditions for 1 ns. Finally, a NPT simulation for 5 ns was carried out at 298 K and 1 bar pressure, out of which, the final 4 ns was considered as production run and subsequently used for property analyses. Several calculated properties are listed in Table I. A systematic simulated annealing procedure was adopted to calculate the T g of the polymer. The simulation boxes were heated up to 900 K at the rate of 0.1 K/ps and subsequently cooled at the same rate. Every cooling step consisted of a NVT equilibration followed by a NPT equilibration and production run (similar to the protocol described in Ref. [23]). Representative configurations at every 50 K were extracted and allowed to relax for 2 ns under NPT conditions. As shown in Figure 2, the T g of HFPE-30 was estimated to be 660 5 K from the intersection of the linear fits to the high and low regimes of the density versus temperature plot. The experimentally observed T g of uncross-linked HFPE-30 is 513 K [15]. Our estimated T g of 660 ± 5 K is reasonable considering the high heating and cooling rates employed. The computation of the dihedral autocorrelation [24] as a function of temperature revealed that the torsional rotation around the diamine benzene in the HFPE-30 backbone (see Figure 3) plays an important role on the melting dynamics of the polymer. It is noted that the potential energy barriers for the other weak bond rotations in the HFPE-30 backbone are very small (<2 kJ mol1) and hence they are freely rotatable at room temperature and decorrelate much faster. On the other hand, the potential energy barrier for the diamine benzene to rotate around the imide bond is
Figure 2. Percentage change in density of HFPE-30 and HFPE-30F (with respect to their densities at room temperature) with temperature. The values of T g are also indicated.
Figure 3. The time evolution of the dihedral autocorrelation function, CðtÞ ¼ hcos½hðsÞ hðs þ tÞis for diamine benzene rotation around imide bond in HFPE-30 and HFPE-30F at different temperatures. The open and full symbols correspond to HFPE-30 and HFPE-30F respectively.
8 kJ mol1 and its rotational frequency and decorrelation time depend strongly on the temperature. Increase in temperature increases the diamine benzene rotation frequency and eventually affects the structured packing of the rings, leading to increase in average intermolecular distance between the polymer chains; see Figure 2 in the Supplementary Data. This results in the lowering of the packing density of the polymer, driving it to its melt state. Our analyses showed that other sub-molecular motions do not have any major effect with increasing temperature. Evolution of the decorrelation function for the diamine benzene in HFPE-30 is shown in Figure 3. The above discussion implies that a higher potential energy barrier for the rotation of benzene molecule about the imide bond in the diamine residue would slow down the torsional rotation, consequently increase the T g . An effect of rotational potential energy barriers on T g has been studied in some of the earlier Letters. [11] Hence, a substitution in the benzene rings of the diamine residues that could increase the torsional rotational barrier is a potentially viable route to obtain higher T g . On carrying out benchmark in vacuo DFT/B3LYP calculations using the benzene–phthalimide moiety, we observed that replacing the benzene hydrogens by fluorine increases the potential energy barrier of the benzene rotation about the imide bond from 8 kJ mol1 to 75 kJ mol1. This hints that substitution of the diamine benzene by flourine can achieve the purpose of increasing the rotational barriers about the imide bond. It is well known that polyimides show improved physical properties on flourination, in particular by the introduction of triflouromethyl moeties [25]. Synthesis and properties of such flourinated polyimides are also well discussed in the literature [26–28,25]. Recently, it has been reported that flourinated dimamine moiety results in high T g and improved thermal–oxidative
26
S. Pandiyan et al. / Chemical Physics Letters 593 (2014) 24–27
stability.[29] In the current Letter, we propose modification by susbstituting 2,3,5,6 positions of diamine residue by flourine [30]. We will refer to the fluorine substituted HFPE-30 as HFPE30F; see also Figure 1. A fully atomistic model of fluorine HFPE-30F was prepared and its T g was determined using the same procedure as for HFPE-30. The sharp peaks in the diamine torsional angle distribution for HFPE-30F in Figure 4 show that the fluorine substitution restricted the number of diamine rotations dramatically by a factor of about 103 at 600 K (see also Figure 3). Expectedly, the T g of the HFPE-30F increased to 740 ± 5 K as shown in Figure 2. This increase can be accounted by the electrostatic and steric repulsions between fluorine and oxygen atoms in the substituted diamine and dianhydride moieties. As noted earlier, alteration of the backbone structure has the potential of changing other properties of HFPE-30, especially ductility. Hence we analyzed various physical and mechanical properties of HFPE-30F and compared it with HFPE-30. The results obtained are presented in Table 1. The estimated structural factor showed that both the polymer models are highly amorphous (see Figure 1 in the Supplementary Data). The small difference in the peaks at lower values of q for HFPE-30F can be explained by its better structured packing (see Figure 2 in the Supplementary Data). This suggests that the HFPE-30F should have higher density than its unsubstituted counterpart but interestingly we found a slight decrease (<2%) in the density of HFPE-30F. The decrease in density is due to the strong inter-molecular repulsion between fluorine and oxygen atoms in the diamine and dianhydride groups in HFPE-30F. Also, the difference in the fractional free volume calculated using Bondi’s group contribution method [31] can be attributed to the difference in the van der Waals volume between hydrogen and fluorine atoms and the small difference in their packing density. The individual contributions to the (average) potential energy per chain are comparable between the two polymers. The only exception is in the average torsional energy, which is lower in HFPE-30F, due to the elevated free energy barrier of the diamine benzene rotation. The comparison of end-to-end distance and radius of gyration also indicate that both the polymers are expected to have similar bulk characteristics. The stress strain simulations were done by increasing the zdimension of the simulation box at a constant rate of 2 1010 s1 for a period of 5 ns in a N rx ry T ensemble. The mechanical properties are compared by applying a uniaxial tension in the z-direction keeping the other two stress free. Further, the zz component of the virial stress and engineering strain are used to plot the stress strain curves in Figure 5. To the best of our knowledge uniaxial stress strain response of un-crosslinked HFPE-30 has
Figure 4. Torsional angle distributions of diamine benzene in HFPE-30 (red) and HFPE-30F (black) at temperatures of 600 K (squares) and 900 K (circles). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Comparison of various physical properties between HFPE-30 and HFPE-30F. All values (except T g ) are calculated at 298 K and 1 bar. The energy values are given per chain. The fractional free volume (FFV) was estimated using Bondi’s group contribution method [31].
a
Property
HFPE-30
HFPE-30F
Density [kg m3] T g [K] FFV End-to-end distance [nm] Radius of gyration [nm] Bending energy [kJ mol1] Torsional energy [kJ mol1] Non-bonded energy [kJ mol1] Potential energy [kJ mol1]
1310 ± 5 660 ± 5 (513)a 0.254 ± 0.002 1.650 ± 0.003 5.50 ± 0.01 2196 ± 4 1230 ± 3 452 ± 7 2974 ± 17
1285 ± 5 740 ± 5 0.304 ± 0.002 1.570 ± 0.003 5.50 ± 0.01 2169 ± 4 993 ± 3 371 ± 6 2791 ± 16
Experimentaly determined value of T g for the uncrosslinked HFPE-30.
Figure 5. Stress–strain response of HFPE-30 and HFPE-30F for a strain rate of 2 1010 s1 computed at 298 K.
not been reported in the literature. Given the high strain rates used in MD simulations, it is expected that the maximum stress levels borne by the material in the simulation (180 MPa) will be significantly higher than in real life. However the pertinent point is that, for the given strain rates both the polymers exhibited no major difference in terms of their uniaxial response. Both the polymers could withstand close to 10% strain at failure, indicating that the fluorine substitution has not resulted in any change in ductility. Also for all practical purposes, the failure strain of any brittle material is about 10% at the strain rate employed. Beyond this strain, the material rapidly loses its stress carrying capacity. We have simulated the uniaxial stress strain response at lower strain rates of up to 2 108 s1 and both HFPE-30 and HFPE-30F show similar behavior at these rates. Interestingly, fluorine substitution also increases the thermo oxidative stability of the polymer compared to the unsubstituted polymers due to the reduced possibility of oxidation and hydrolysis reactions between the residual solvent molecules and polymer chains. [25] Hence the suggested substitution is useful to increase the oxidative stability and T g of the polymer without altering the backbone structure significantly, evidenced by the almost unaltered physical and mechanical properties. In conclusion, the present letter has shown that sub-molecular motions have a critical role in dictating the T g of a glassy polyimide. By identifying these crucial molecular motions, it is possible to suggest chemical modifications of the polymer backbone that can lead to changes in T g . Molecular simulations have a large role to play in deciding modifications that can suitably increase T g without compromising oxidative and mechanical properties. In the specific example of HFPE-30 studied in this Letter, we have found a simple viable route for achieving these seemingly contradictory goals by the fluorination of the diamine moiety. The
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proposed modification of HFPE-30 has importance in their applications to the aerospace industry. Most importantly, 2,3,5,6tetrafluorobenzene 1,4-diamine is commercially available for the synthesis of HFPE-30F, and its synthesis has been reported earlier. [30] We are not aware of any experimental or theoretical works that has reported any thermo-mechanical property of HFPE-30F. Finally, it should be noted that all simulations have been done on the uncross-linked system whereas commercial HFPE-30 is crosslinked. While we believe that the same effects should apply to cross-linked HFPE-30 and HFPE-30F, we are doing further simulations to investigate this point. Acknowledgments Authors are grateful to The Boeing Company, U.S.A. for funding the project ‘‘Investigation into the Thermo-oxidative and Mechanical Response of Commercial Polyimide Resins and Polyimide Nano-composites for Aerospace Application’’ under which this Letter has been carried out. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2013.12. 076. References [1] [2] [3] [4] [5] [6] [7]
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