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Correlations between alkyl side chain length and dynamic mechanical properties of poly(n-alkyl acrylates) and poly(n-alkyl methacrylates)
Polymer 53 (2012) 665e672
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Polymer journal homepage: www.elsevier.com/locate/polymer
Correlations between alkyl side chain length and dynamic mechanical properties of poly(n-alkyl acrylates) and poly(n-alkyl methacrylates) Xiaoan Wang 1, Xiaojun He 1, Guangsu Huang*, Jinrong Wu* College of Polymer Science and Engineering, State Key Laboratory of Polymer Material Engineering, Sichuan University, Chengdu 610065, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 July 2011 Received in revised form 31 October 2011 Accepted 27 November 2011 Available online 3 December 2011
In the present paper, dynamic mechanical properties of poly(n-alkyl acrylates) (PnAA) and poly(n-alkyl methacrylates) (PnAMA) with different alkyl side chain length were studied. The results show that with the increase of alkyl side chain length, the storage modulus changes more steadily, and the loss modulus peak and the tand peak become broader for PnAA and PnAMA. At the same time, the tand peak is more and more apart from the loss modulus peak and the point where the storage modulus begins to drop. For quantitative discussion, three variables, the steepness index (S), the transition wideness (W) of storage modulus and the integration area (A) of tand were defined to investigate the potential correlation between the dynamic mechanical properties and alkyl side chain length. It can be observed that S decreases while W and A increase with increasing alkyl side chain length. Moreover, the relaxation spectra of the two series of polymers are calculated from the corresponding mechanical spectra. The shapes of the relaxation spectra are broader and broader with the increase of the alkyl side chain length. These phenomena are interpreted by the perspective of fragility, molecular packing efficiency and intermolecular coupling. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Poly(n-alkyl acrylates) Poly(n-alkyl methacrylates) Alkyl side chain length
1. Introduction In the past several decades, advanced understanding the mechanisms of glass transition in the supercooled liquids has been a hot topic in condensed matter physics [1e6], [7e9], [10]. Anderson [1] proposed “the deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition. This could be the next breakthrough in the coming decade.” Sixteen years later, a breakthrough has not been achieved yet, but some important advances have been made, such as Coupling Model and the concept of fragility. Coupling Model [11,12] mainly describes the intermolecular coupling in the glass-forming liquids which encompass many-body interaction. According to this model, the intensity of intermolecular cooperativity of the local segmental relaxation is quantitatively described by the coupling parameter (n), which is related to the exponent (b) of KohlrauscheWilliamseWatts (KWW) function by n ¼ 1b. Fragility, another important parameter, was introduced by Angell [13] in 1985. Now it has become a unifying standard to classify the
* Corresponding authors. Tel.: þ86 28 854 634 33; fax: þ86 28 854 054 02. E-mail addresses: [email protected] (G. Huang), wujinrong@scu. edu.cn (J. Wu). 1 Xiaoan Wang and Xiaojun He contributed equally to this work. 0032-3861/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2011.11.059
dynamic behavior and non-linear relaxation of glass-forming liquids along a strong to fragile scale. The variation of mass transport or relaxation properties (e.g., relaxation time s, viscosity h, shift factor log (aT)) in glass-forming liquids is generally represented by a reduced Arrhenius profile (Angell plot). According to the Angell plot, those dynamic properties of strong liquids behave nearly Arrhenius temperature dependence. The fragile liquids, on the contrary, typically display non-Arrhenius behavior which is generally described by VogeleFulchereTammaneHesse (VFTH) equation [14e16] or WilliamseLandeleFerry (WLF) equation [17]. The dynamic fragility index m is quantified as [13]:
m ¼
dlogc d Tg =T
T¼Tg
where c can be viscosity, relaxation time or other dynamic variables. The dynamic fragility is associated with various internal properties of glass-forming liquids such as glass transition temperature [18], apparent activation energy Eg at glass transition [19], Poisson ratio [20] and dynamic mechanical properties [21]. During the last decades, much effort has been made to understand the effect of molecular structure [22e24], nano-filler [25e27], nano-confinement [28] on the molecular dynamics of various polymers. For being of typical amorphous polymer and industrial importance, it is important to study the influence of alkyl
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side group on the relaxation behaviors of poly(n-alkyl acrylates) (PnAA) and poly(n-alkyl methacrylates) (PnAMA). By using neutron studies on labeled side chain poly(methyl methacrylate), Alegria et al. found that the rotational tunneling of methyl groups is independent of the backbone, which suggests the heterogeneous dynamics of the polymer [29,30]. Beiner et al [31,32] found that the poly(alkyl methacrylates) show a systematic shift of the a relaxation to lower frequency values with increasing length of the alkyl side group, while the secondary b relaxation remains nearly unchanged. Thus, the splitting region between the a and b relaxation is also shifted toward lower frequency with the size of the alkyl group. They also found that the deviations from the equilibrium state decrease with increasing length of the linear alkyl side group in the supercooled state. Besides, the incompatibility between the main-chain and the side chain leads to nanophase separation in poly(n-alkyl acrylates), in which the self-assembled alkyl nanodomains with a typical size of 0.5e2 nm shows polyethylene-like glass transition [33,34]. PnAA and PnAMA are widely used as pressure-sensitive adhesives, paints, coatings, seals and damping elements [35,36]. The wide applications endow us the practical reason to study the relationship between the molecular structure and the macroscopic properties of PnAA and PnAMA, which is of significance for direct molecular design during the synthesis for specific applications. Thus, in the current work, the dynamic mechanical properties of PnAA and PnAMA were systematically measured and then correlated with the alkyl side chain length. 2. Experimental Each monomer of the acrylates and methacrylates was distilled under the pressure of 16 KPa and stored at 0 C. All polymers were synthesized by solution polymerization with azobisisobutyronitrile (AIBN) as initiator and 2-butanone as solvent. The polymerization was carried out at 70 2 C under nitrogen for 10 h. The resulting reaction mixture was distilled under a pressure of 20 KPa. Then the polymer was finally dried in an oven (75 C) under vacuum for several days. Please note that acrylates and methacrylates monomers are toxic and irritant and can induce sensitization, so care was taken in their use. The procedure of producing a film: the polymers were put into a rectangular mold whose dimensions were 20 mm long, 12 mm wide and 3 mm thick. Then the mould was hot compressed at 140 C under a pressure of 5.0e10 MPa for 20 min. The molecular weights (Mn and Mw) and the molecular weight distribution (Mw/Mn) of the polymers are determined by means of gel-permeation chromatography (GPC), using polystyrene as a standard. The values of Mn, Mw and Mw/Mn are given in Table 1. The calorimetric glass transition temperatures (Tgs) of PnAA and PnAMA are determined using a differential scanning calorimetry DSC Q20 (TA Instruments, Inc.). The samples were firstly cooled to 90 C at a cooling rate of 10 C/min and stabilized for 5 min, and
then heated at a heating rate of 10 C/min. The heat flow of the heating process was recorded. The glass transition temperature was determined as the midpoint of the glass transition region of the heat flow curve. Table 1 shows the resulting Tg values, which are in accordance with the values found in the literature [18,19,35] (taking into account the influence of the heating rate on the detected Tg). Dynamic mechanical analysis was carried out on Q800 (TA instruments) by using a mode of dual or single cantilever clamp and a testing method of temperature step-frequency sweep with each temperature step of 4e6 K and a frequency range from 0.1 Hz to 100 Hz. The sample dimensions are 20 mm long, 12 mm wide and 3 mm thick. The oscillation strain amplitude was set to be 20 mm. Because each sample was tested for once, just the systematic errors can be determined. The systematic error for temperature is 0.1 K. 3. Results The dynamic mechanical properties of PnAA and PnAMA were measured by DMA at different temperatures. Fig. 1 takes PMMA as an example to show the dynamic mechanical spectra of PnAA and PnAMA. If we compare the dynamic mechanical spectra of PnAA and PnAMA from a short alkyl side chain length to a long one, it is evident that the loss tangent peak is further from the loss modulus peak with an increase of alkyl side chain length. For quantitative discussion, three corresponding temperatures, defined as Tstorage, Tloss and Ttand, are determined from the storage modulus (E0 ), loss modulus (E00 ) and loss tangent (tand), respectively, as shown in Fig. 2. The results are tabulated in Table 1. If we define 6Tlossstorage ¼ TlossTstorage, 6Ttandloss ¼ TtandTloss and 6Ttandstorage ¼ TtandTstorage, it is evident that 6Ttandloss and 6Ttandstorage decrease when PnAA and PnAMA go from a long alkyl side chain length to a short one. That is to say the tand peak is more and more apart from the loss modulus peak and the point where the storage modulus begins to drop as the alkyl side chain length increases. From Fig. 3, it can also be observed that 6Tlossstorage seems to be independent of the alkyl side chain length. Therefore, the variation of 6Ttandstorage with the alkyl side chain length mainly comes from the contribution of 6Ttandloss. It is still under consideration whether the timeetemperature superposition (TTS) principle [37] could be accurately used to construct master curves of PnAA and PnAMA for a wide frequency range. For simplicity, only the master curves of PnBA are shown in Fig. 4, for a reference temperature of 210.5 K. It is obvious that there are some small fluctuations on the high and low frequency sides of the master curves, where the thermo-rheological complexity interferes [38]. This would mean that in fact the viscoelastic spectrum consists of several viscoelastic mechanisms that have different shift factors [38,39]. Therefore, the breakdowns at high frequency and low frequency are due to the b relaxation and terminal regimes respectively, which have shift factors different from the a relaxation.
Table 1 Characterization of the samples and three corresponding temperatures (Tstorage, Tloss and Ttand) determined from DMA data for PnAA and PnAMA. Polymers
Tga (0.1 K)
Mn (g mol1)
Mw (g mol1)
Mw/Mn (g mol1)
mb
Tstorage (0.1 K)
Tloss (0.1 K)
Ttand (0.1 K)
PMA PEA PnBA PnBMA PEMA PMMA
286.4 254.8 219.9 304.1 345.2 380.3
49653 61218 72354 67476 68645 37886
136750 142870 154380 212310 178520 95036
2.7 2.4 2.1 3.2 2.6 2.5
108 83 65 67 79 102
286.7 256.8 223.7 304.5 348.0 384.8
288.2 258.2 224.9 305.1 348.7 386.0
297.3 268.3 236.2 326.0 367.3 402.1
a b
Glass transition temperatures were detected by DSC Q20. Fragility index obtained from our calculation. Please see ref. [7].
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Fig. 2. A schematic representation of determining Tstorage, Tloss and Ttand at 1 Hz. Tstorage is the corresponding temperature of the intersection of the two tangent lines. Tloss and Ttand are the corresponding temperatures of E" peak and tand peak.
Fig. 1. DMA isothermal curves on PMMA at different temperatures as an example to show the mechanical spectra of PnAA and PnAMA. (a) Storage modulus (E0 ) vs. frequency. (b) Loss modulus (E00 ) vs. frequency. (c) Loss tangent (tand) vs. frequency. For clarity, not all measured curves are presented.
Fig. 5 exhibits the scaled isochronal dynamic mechanical spectra of PnAA and PnAMA. Here the storage modulus, loss modulus and tand are normalized by the storage modulus at the glassy state, the maximum loss modulus and the maximum tand, respectively, while
Fig. 3. The 6Tlossstorage, 6Ttandstorage and 6Ttandloss of PnAA (a) and PnAMA (b) with different alkyl carbons per side chain.
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In order to reveal the correlations between alkyl side chain length and dynamic mechanical properties of PnAA and PnAMA more intuitively and effectively, we calculated the relaxation spectra for both systems. Relaxation spectra could be calculated from mechanical spectra by using the relationship between E0 , E00 and angular frequency (u ¼ 2pf) given by the following integrals [41]:
ZN
0
E ðuÞ ¼ E0 þ 0
E00 ðuÞ ¼
ZN 0
Fig. 4. The master curves of E’, E", and tand obtained from TTS analysis of DMA results taking PnBA as an example, for a reference temperature of 210.5 K.
the corresponding abscissas are normalized by Tstorage, Tloss and Ttand. It is evident that the shapes of the dynamic mechanical spectra change systematically with different alkyl side chain length. As can be seen in Fig. 5(a) and (d), PnBA and PnBMA display a slow descending process in their storage modulus going from the glassy state to the liquid state. With the decrease of alkyl side chain length, the storage modulus curve becomes steeper and steeper around the glass transition region. Finally, PMA and PMMA with the shortest alkyl side chain length reveal a dramatic decrease of 0 )/d (Tstorage/T) storage modulus. Taking the derivative d log (E0 /Eglass immediately reveals the differences among these curves, as shown in Fig. 6. It can be observed that polymers like PnBA and PnBMA with longer alkyl side chain length have lower peak values but broader peak regions, while shorter ones like PMA and PMMA show higher peak values but narrower peak regions. Aklonis and Rele [40] used a steepness index, which was defined as the maximum value of d log(G(t)) vs. d log(t) going from the glassy state to the high-elastic state (where G(t) is the shear modulus), to characterize the broadness of glass transition region. Similarly, we can define another steepness index (S) as the maximum value of d log (E0 / 0 )/d (Tstorage/T) for our case, and plot it against the alkyl carbons Eglass per side chain, as shown in Fig. 7. It can be observed that S goes up with the decrease of alkyl side chain length. Fig. 5(b) and (e) illustrate that the loss modulus peak becomes broader and broader with the increase of alkyl side chain length. A similar trend can also be observed in the tand curves of Fig. 5(c) and Fig. 5(f). It is clear from Fig. 5(aef) that the dynamic mechanical properties of polymers with a long alkyl side chain length change slower than short one with temperature, which leads to their broad glass transition regions. It is worthwhile to establish a relationship between the alkyl side chain length and the dynamic mechanical properties of polymers. For quantitative discussion, we need to define two variables. The one is the transition wideness (W) of the storage modulus, which is 1 subtracted by the intersect value of two tangent lines on the lower part of the storage modulus in the scaled plot. The other one is the integration area (A) of the scaled tand, which is defined as area between the tand curve and the baseline. Fig. 8 is a schematic demonstration of determining the values of W and A. The resulting W and A of polymers are plotted against alkyl carbons per side chain, which are show in Figs. 9 and 10. As shown in Fig. 9, W decreases with the decrease of alkyl side chain length. The same trend can also be observed in the Fig. 10. As alkyl side chain length increases, A goes up gradually.
HðsÞ
HðsÞ
u2 s2 ds , 1 þ u2 s 2 s
us ds , 1 þ u2 s 2 s
(1)
(2)
where H(s) is the relaxation spectra (the distribution function of the elements with relaxation time s), while E0 is the equilibrium modulus which is zero for a viscoelastic liquid. Numerical methods for calculating the function H(s) has been accomplished by Kontogiorgos [42]. For clarity, the sample of PMMA was chosen to illustrate how to obtain the relaxation spectra from mechanical spectra. Fig. 11 presents the isothermal curve of loss modulus (E00 ) vs. angular frequency (u) on PMMA at Tg ¼ 380.3 K. After acquiring loss modulus data, it is necessary to calculate the optimum regularization parameter l from Fig. 11. The regularization parameter controls the filtering of the spectrum noise or in other words, the balance between the regularization error and the loss of resolution (smoothness) of the solution. The most appropriate tool to analyze this type of problem is the so-called L-curve method, which is a plot of the solution and residual norms for all valid regularization parameters. The vertical part of the curve corresponds to solutions that are sensitive to perturbation errors whereas the horizontal part to solutions where the regularization (calculation) error dominates. The optimum regularization parameter l is located at the corner of the curve and this value is used to calculate the optimum least square solution of the spectrum. Fig. 12 reproduces the result of the calculation of the optimum regularization parameter using the L-curve method for PMMA as an example. As it is evident, the vertical part of the curve corresponds to data where the solution norm is very sensitive to changes in the regularization parameter because the error in measurements dominates the regularized solution. The horizontal part corresponds to solutions where the residual norm is the most sensitive to the regularization parameter because the regularized solution is now dominated by the regularization error. Selection of a regularization parameter smaller than the optimum point will result in an “arbitrary noise generator” as the solution to the problem, whereas a value of l greater than optimum will yield over-smoothed answers thus missing vital information from the experimental spectrum. Following optimization of the parameters, the relaxation spectrum of PMMA was calculated (Fig. 13b). Two relaxation processes can be identified for PMMA, one at short relaxation time (s < 1 s) and the other at long relaxation time s (s > 1 s), which are assigned to b and a relaxation process respectively. In addition, the relaxation spectra of PnAA and PnAMA were also calculated and shown in Fig. 13a and b, respectively. It can be seen that both b and a relaxation process are obviously identified in all the relaxation spectra. Moreover, the shapes of the relaxation spectra are broader and broader with the increase of the alkyl side chain length. In other words, the two relaxation processes are more and more separated from each other with the increase of the alkyl side chain length.
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0 00 Fig. 5. The scaled dynamic mechanical spectra of PnAA and PnAMA. Eglass , Emax and tandmax represent the storage modulus at the glassy state, the maximum loss modulus and the maximum tand, respectively.
4. Discussion The results above can be explained by the following three aspects. First, from previous investigation [38,43e45], it is found that as the alkyl side chain length decreases, the fragility of PnAA and PnAMA increases. Strong glass-forming liquids usually possess self-reinforcing tetrahedral network, stable structures and local to intermediate range order [46]. As to PnAA and PnAMA, previous reports demonstrate that some local order structure gradually develops as the carbon number in the side chain increases, because some self-assembly takes place to form supramolecular systems like “hairy rods” [47,48]. Moreover, M. Balabin studied the enthalpy difference between conformations of normal alkanes and showed that n-alkyl chain is more and more flexible with chain length increase [49e53]. Thus, the microstructure is much easier to form with longer chain length. Such a microstructure leads to stabilized main-chain conformations; as a result, the chain units need to
reorient cooperatively in a highly anisotropic axial local motion [47,48]. It is this microstructure that prevents the dynamic properties of PnAA and PnAMA with long alkyl side chains from changing rapidly, thus broader glass transition regions have been observed, i.e., their structural relaxation time or viscosity changes smoothly with temperature. Second, the main transition of amorphous polymers from the glassy state to the high-elastic state usually involves different modes of molecular motion, including local segmental motion, subRouse mode and Rouse mode [38,54]. From local segmental motion to the Rouse mode, the mobile unit becomes larger and larger, from local motion of only a few backbone bonds to the motion of Gaussian sub-molecules. The motion of different modes with different chain lengths needs different size of free volume holes. Sub-Rouse mode and Rouse mode need larger free volume holes to move, while local segments need smaller free volume holes to move. The gap between two molecular chains becomes larger and
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Fig. 8. A schematic representation of determining transition wideness of storage modulus and integration area of tand.
0 Fig. 6. Derivative of storage modulus curves, i.e., d log (E0 /Eglass )/d (Tstorage/T), obtained from Fig. 5(a) were plotted against Tstorage/T.
larger with increasing alkyl side chain length, leading to more free volume holes in PnAA and PnAMA with longer alkyl side chain length. So the motion of different modes including local segmental motion, sub-Rouse mode and Rouse mode becomes more and more active, this will also broadens the relaxation spectra. According to the point of view put forward by Donth [54] and Ngai [38], the loss modulus peak and the point where the storage modulus begins to drop mainly reflect the motion of local segments, while the tand peak mainly reflects the sub-Rouse mode and Rouse mode. As a result of the decreasing values of n with increasing alkyl side chain length, the sub-Rouse mode and Rouse mode are more separated from the local segmental motion in the time or temperature scale. This is the reason why the tand peak is more and more apart from the loss modulus peak and the point where the storage modulus begins to drop. Third, the shape of the relaxation spectra changing with different alkyl side chain length illustrates that the intermolecular coupling varies in PnAA and PnAMA according to coupling model proposed by Ngai et al. [11,12]. The basis of the coupling model is the KohlrauscheWilliamseWatts (KWW) equation [55,56], which expressed as:
h
fðtÞ ¼ f0 exp ðt=sÞ1n
0 Fig. 7. Maximum values of d log (E0 /Eglass )/d (Tstorage/T) of PnAA and PnAMA with different alkyl carbons per side chain.
i
(3)
Fig. 9. The transition wideness of the storage modulus of PnAA and PnAMA with different alkyl carbons per side chain.
X. Wang et al. / Polymer 53 (2012) 665e672
Fig. 10. The integration area of tand of PnAA and PnAMA with different alkyl carbons per side chain.
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Fig. 12. Representative L-curve plot for PMMA calculated from Fig. 11. The optimum regularization parameter lopt is located at the corner of the curve (0.55681). Lower values than lopt result in noisy spectra whereas higher estimates yield over-smoothed spectra and the loss of molecular information.
where fðtÞ is the correlation function, s is the KWW relaxation time and n (0 < n < 1) is the coupling parameter which reflects the degree of correlation or cooperativeness in the relaxation process coming from the interactions of molecular chains (smaller n indicates smaller capacity of intermolecular coupling). K.L. Ngai has calculated the coupling parameters n for PMMA (0.51), PEMA (0.41) and PnBMA (0.27), showing that n decreases with increasing alkyl side chain length [45]. As a result, the motions of chain segments with different lengths are separated from each other in the time or temperature scale, which lead to a broader relaxation spectra. In other words, the two relaxation processes are more and more separated from each other with the increase of the alkyl side chain length. Therefore, with the coaction of the three effects mentioned above, it is expected that E0 will decay more smoothly (Fig. 5 (a) and (d)), and the width of the maxima for E00 (Fig. 5(b) and (e)) and of the tand (Fig. 5 (c) and (f)) will be broader for PnAA and PnAMA with long alkyl side chain length. The same is true for the derivative analysis (Fig. 6(a) and (b)), steepness (Fig. 7), width (Fig. 9) and area (Fig. 10).
Fig. 11. The isothermal curve of loss modulus (E00 ) vs. angular frequency (u) on PMMA at Tg ¼ 380.3 K.
Fig. 13. Relaxation spectra of PnAA (a) and PnAMA (b) obtained from corresponding mechanical spectra.
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5. Conclusion Dynamic mechanical analysis was used to research the correlation between dynamic mechanical properties of PnAA and PnAMA and different alkyl side chain length. With increasing alkyl side chain length, the loss modulus peak and the tand peak become broader. For quantitative illustration, three variables defined as the steepness index (S), the transition wideness (W) of storage modulus and the integration area (A) of tand were correlated with alkyl side chain length. It is found that S decreases while W and A increase with increasing alkyl side chain length. Moreover, relaxation spectra of PnAA and PnAMA were calculated and indicated that the shapes of the relaxation spectra are broader and broader with the increase of the alkyl side chain length. These phenomena are interpreted by the perspective of the fragility, free volume holes and the intermolecular coupling. Acknowledgments This work was financially supported by the National Natural Science Foundation of China (Grant No. 50873070). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
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Polymer journal homepage: www.elsevier.com/locate/polymer
Correlations between alkyl side chain length and dynamic mechanical properties of poly(n-alkyl acrylates) and poly(n-alkyl methacrylates) Xiaoan Wang 1, Xiaojun He 1, Guangsu Huang*, Jinrong Wu* College of Polymer Science and Engineering, State Key Laboratory of Polymer Material Engineering, Sichuan University, Chengdu 610065, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 July 2011 Received in revised form 31 October 2011 Accepted 27 November 2011 Available online 3 December 2011
In the present paper, dynamic mechanical properties of poly(n-alkyl acrylates) (PnAA) and poly(n-alkyl methacrylates) (PnAMA) with different alkyl side chain length were studied. The results show that with the increase of alkyl side chain length, the storage modulus changes more steadily, and the loss modulus peak and the tand peak become broader for PnAA and PnAMA. At the same time, the tand peak is more and more apart from the loss modulus peak and the point where the storage modulus begins to drop. For quantitative discussion, three variables, the steepness index (S), the transition wideness (W) of storage modulus and the integration area (A) of tand were defined to investigate the potential correlation between the dynamic mechanical properties and alkyl side chain length. It can be observed that S decreases while W and A increase with increasing alkyl side chain length. Moreover, the relaxation spectra of the two series of polymers are calculated from the corresponding mechanical spectra. The shapes of the relaxation spectra are broader and broader with the increase of the alkyl side chain length. These phenomena are interpreted by the perspective of fragility, molecular packing efficiency and intermolecular coupling. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Poly(n-alkyl acrylates) Poly(n-alkyl methacrylates) Alkyl side chain length
1. Introduction In the past several decades, advanced understanding the mechanisms of glass transition in the supercooled liquids has been a hot topic in condensed matter physics [1e6], [7e9], [10]. Anderson [1] proposed “the deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition. This could be the next breakthrough in the coming decade.” Sixteen years later, a breakthrough has not been achieved yet, but some important advances have been made, such as Coupling Model and the concept of fragility. Coupling Model [11,12] mainly describes the intermolecular coupling in the glass-forming liquids which encompass many-body interaction. According to this model, the intensity of intermolecular cooperativity of the local segmental relaxation is quantitatively described by the coupling parameter (n), which is related to the exponent (b) of KohlrauscheWilliamseWatts (KWW) function by n ¼ 1b. Fragility, another important parameter, was introduced by Angell [13] in 1985. Now it has become a unifying standard to classify the
* Corresponding authors. Tel.: þ86 28 854 634 33; fax: þ86 28 854 054 02. E-mail addresses: [email protected] (G. Huang), wujinrong@scu. edu.cn (J. Wu). 1 Xiaoan Wang and Xiaojun He contributed equally to this work. 0032-3861/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2011.11.059
dynamic behavior and non-linear relaxation of glass-forming liquids along a strong to fragile scale. The variation of mass transport or relaxation properties (e.g., relaxation time s, viscosity h, shift factor log (aT)) in glass-forming liquids is generally represented by a reduced Arrhenius profile (Angell plot). According to the Angell plot, those dynamic properties of strong liquids behave nearly Arrhenius temperature dependence. The fragile liquids, on the contrary, typically display non-Arrhenius behavior which is generally described by VogeleFulchereTammaneHesse (VFTH) equation [14e16] or WilliamseLandeleFerry (WLF) equation [17]. The dynamic fragility index m is quantified as [13]:
m ¼
dlogc d Tg =T
T¼Tg
where c can be viscosity, relaxation time or other dynamic variables. The dynamic fragility is associated with various internal properties of glass-forming liquids such as glass transition temperature [18], apparent activation energy Eg at glass transition [19], Poisson ratio [20] and dynamic mechanical properties [21]. During the last decades, much effort has been made to understand the effect of molecular structure [22e24], nano-filler [25e27], nano-confinement [28] on the molecular dynamics of various polymers. For being of typical amorphous polymer and industrial importance, it is important to study the influence of alkyl
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side group on the relaxation behaviors of poly(n-alkyl acrylates) (PnAA) and poly(n-alkyl methacrylates) (PnAMA). By using neutron studies on labeled side chain poly(methyl methacrylate), Alegria et al. found that the rotational tunneling of methyl groups is independent of the backbone, which suggests the heterogeneous dynamics of the polymer [29,30]. Beiner et al [31,32] found that the poly(alkyl methacrylates) show a systematic shift of the a relaxation to lower frequency values with increasing length of the alkyl side group, while the secondary b relaxation remains nearly unchanged. Thus, the splitting region between the a and b relaxation is also shifted toward lower frequency with the size of the alkyl group. They also found that the deviations from the equilibrium state decrease with increasing length of the linear alkyl side group in the supercooled state. Besides, the incompatibility between the main-chain and the side chain leads to nanophase separation in poly(n-alkyl acrylates), in which the self-assembled alkyl nanodomains with a typical size of 0.5e2 nm shows polyethylene-like glass transition [33,34]. PnAA and PnAMA are widely used as pressure-sensitive adhesives, paints, coatings, seals and damping elements [35,36]. The wide applications endow us the practical reason to study the relationship between the molecular structure and the macroscopic properties of PnAA and PnAMA, which is of significance for direct molecular design during the synthesis for specific applications. Thus, in the current work, the dynamic mechanical properties of PnAA and PnAMA were systematically measured and then correlated with the alkyl side chain length. 2. Experimental Each monomer of the acrylates and methacrylates was distilled under the pressure of 16 KPa and stored at 0 C. All polymers were synthesized by solution polymerization with azobisisobutyronitrile (AIBN) as initiator and 2-butanone as solvent. The polymerization was carried out at 70 2 C under nitrogen for 10 h. The resulting reaction mixture was distilled under a pressure of 20 KPa. Then the polymer was finally dried in an oven (75 C) under vacuum for several days. Please note that acrylates and methacrylates monomers are toxic and irritant and can induce sensitization, so care was taken in their use. The procedure of producing a film: the polymers were put into a rectangular mold whose dimensions were 20 mm long, 12 mm wide and 3 mm thick. Then the mould was hot compressed at 140 C under a pressure of 5.0e10 MPa for 20 min. The molecular weights (Mn and Mw) and the molecular weight distribution (Mw/Mn) of the polymers are determined by means of gel-permeation chromatography (GPC), using polystyrene as a standard. The values of Mn, Mw and Mw/Mn are given in Table 1. The calorimetric glass transition temperatures (Tgs) of PnAA and PnAMA are determined using a differential scanning calorimetry DSC Q20 (TA Instruments, Inc.). The samples were firstly cooled to 90 C at a cooling rate of 10 C/min and stabilized for 5 min, and
then heated at a heating rate of 10 C/min. The heat flow of the heating process was recorded. The glass transition temperature was determined as the midpoint of the glass transition region of the heat flow curve. Table 1 shows the resulting Tg values, which are in accordance with the values found in the literature [18,19,35] (taking into account the influence of the heating rate on the detected Tg). Dynamic mechanical analysis was carried out on Q800 (TA instruments) by using a mode of dual or single cantilever clamp and a testing method of temperature step-frequency sweep with each temperature step of 4e6 K and a frequency range from 0.1 Hz to 100 Hz. The sample dimensions are 20 mm long, 12 mm wide and 3 mm thick. The oscillation strain amplitude was set to be 20 mm. Because each sample was tested for once, just the systematic errors can be determined. The systematic error for temperature is 0.1 K. 3. Results The dynamic mechanical properties of PnAA and PnAMA were measured by DMA at different temperatures. Fig. 1 takes PMMA as an example to show the dynamic mechanical spectra of PnAA and PnAMA. If we compare the dynamic mechanical spectra of PnAA and PnAMA from a short alkyl side chain length to a long one, it is evident that the loss tangent peak is further from the loss modulus peak with an increase of alkyl side chain length. For quantitative discussion, three corresponding temperatures, defined as Tstorage, Tloss and Ttand, are determined from the storage modulus (E0 ), loss modulus (E00 ) and loss tangent (tand), respectively, as shown in Fig. 2. The results are tabulated in Table 1. If we define 6Tlossstorage ¼ TlossTstorage, 6Ttandloss ¼ TtandTloss and 6Ttandstorage ¼ TtandTstorage, it is evident that 6Ttandloss and 6Ttandstorage decrease when PnAA and PnAMA go from a long alkyl side chain length to a short one. That is to say the tand peak is more and more apart from the loss modulus peak and the point where the storage modulus begins to drop as the alkyl side chain length increases. From Fig. 3, it can also be observed that 6Tlossstorage seems to be independent of the alkyl side chain length. Therefore, the variation of 6Ttandstorage with the alkyl side chain length mainly comes from the contribution of 6Ttandloss. It is still under consideration whether the timeetemperature superposition (TTS) principle [37] could be accurately used to construct master curves of PnAA and PnAMA for a wide frequency range. For simplicity, only the master curves of PnBA are shown in Fig. 4, for a reference temperature of 210.5 K. It is obvious that there are some small fluctuations on the high and low frequency sides of the master curves, where the thermo-rheological complexity interferes [38]. This would mean that in fact the viscoelastic spectrum consists of several viscoelastic mechanisms that have different shift factors [38,39]. Therefore, the breakdowns at high frequency and low frequency are due to the b relaxation and terminal regimes respectively, which have shift factors different from the a relaxation.
Table 1 Characterization of the samples and three corresponding temperatures (Tstorage, Tloss and Ttand) determined from DMA data for PnAA and PnAMA. Polymers
Tga (0.1 K)
Mn (g mol1)
Mw (g mol1)
Mw/Mn (g mol1)
mb
Tstorage (0.1 K)
Tloss (0.1 K)
Ttand (0.1 K)
PMA PEA PnBA PnBMA PEMA PMMA
286.4 254.8 219.9 304.1 345.2 380.3
49653 61218 72354 67476 68645 37886
136750 142870 154380 212310 178520 95036
2.7 2.4 2.1 3.2 2.6 2.5
108 83 65 67 79 102
286.7 256.8 223.7 304.5 348.0 384.8
288.2 258.2 224.9 305.1 348.7 386.0
297.3 268.3 236.2 326.0 367.3 402.1
a b
Glass transition temperatures were detected by DSC Q20. Fragility index obtained from our calculation. Please see ref. [7].
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Fig. 2. A schematic representation of determining Tstorage, Tloss and Ttand at 1 Hz. Tstorage is the corresponding temperature of the intersection of the two tangent lines. Tloss and Ttand are the corresponding temperatures of E" peak and tand peak.
Fig. 1. DMA isothermal curves on PMMA at different temperatures as an example to show the mechanical spectra of PnAA and PnAMA. (a) Storage modulus (E0 ) vs. frequency. (b) Loss modulus (E00 ) vs. frequency. (c) Loss tangent (tand) vs. frequency. For clarity, not all measured curves are presented.
Fig. 5 exhibits the scaled isochronal dynamic mechanical spectra of PnAA and PnAMA. Here the storage modulus, loss modulus and tand are normalized by the storage modulus at the glassy state, the maximum loss modulus and the maximum tand, respectively, while
Fig. 3. The 6Tlossstorage, 6Ttandstorage and 6Ttandloss of PnAA (a) and PnAMA (b) with different alkyl carbons per side chain.
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In order to reveal the correlations between alkyl side chain length and dynamic mechanical properties of PnAA and PnAMA more intuitively and effectively, we calculated the relaxation spectra for both systems. Relaxation spectra could be calculated from mechanical spectra by using the relationship between E0 , E00 and angular frequency (u ¼ 2pf) given by the following integrals [41]:
ZN
0
E ðuÞ ¼ E0 þ 0
E00 ðuÞ ¼
ZN 0
Fig. 4. The master curves of E’, E", and tand obtained from TTS analysis of DMA results taking PnBA as an example, for a reference temperature of 210.5 K.
the corresponding abscissas are normalized by Tstorage, Tloss and Ttand. It is evident that the shapes of the dynamic mechanical spectra change systematically with different alkyl side chain length. As can be seen in Fig. 5(a) and (d), PnBA and PnBMA display a slow descending process in their storage modulus going from the glassy state to the liquid state. With the decrease of alkyl side chain length, the storage modulus curve becomes steeper and steeper around the glass transition region. Finally, PMA and PMMA with the shortest alkyl side chain length reveal a dramatic decrease of 0 )/d (Tstorage/T) storage modulus. Taking the derivative d log (E0 /Eglass immediately reveals the differences among these curves, as shown in Fig. 6. It can be observed that polymers like PnBA and PnBMA with longer alkyl side chain length have lower peak values but broader peak regions, while shorter ones like PMA and PMMA show higher peak values but narrower peak regions. Aklonis and Rele [40] used a steepness index, which was defined as the maximum value of d log(G(t)) vs. d log(t) going from the glassy state to the high-elastic state (where G(t) is the shear modulus), to characterize the broadness of glass transition region. Similarly, we can define another steepness index (S) as the maximum value of d log (E0 / 0 )/d (Tstorage/T) for our case, and plot it against the alkyl carbons Eglass per side chain, as shown in Fig. 7. It can be observed that S goes up with the decrease of alkyl side chain length. Fig. 5(b) and (e) illustrate that the loss modulus peak becomes broader and broader with the increase of alkyl side chain length. A similar trend can also be observed in the tand curves of Fig. 5(c) and Fig. 5(f). It is clear from Fig. 5(aef) that the dynamic mechanical properties of polymers with a long alkyl side chain length change slower than short one with temperature, which leads to their broad glass transition regions. It is worthwhile to establish a relationship between the alkyl side chain length and the dynamic mechanical properties of polymers. For quantitative discussion, we need to define two variables. The one is the transition wideness (W) of the storage modulus, which is 1 subtracted by the intersect value of two tangent lines on the lower part of the storage modulus in the scaled plot. The other one is the integration area (A) of the scaled tand, which is defined as area between the tand curve and the baseline. Fig. 8 is a schematic demonstration of determining the values of W and A. The resulting W and A of polymers are plotted against alkyl carbons per side chain, which are show in Figs. 9 and 10. As shown in Fig. 9, W decreases with the decrease of alkyl side chain length. The same trend can also be observed in the Fig. 10. As alkyl side chain length increases, A goes up gradually.
HðsÞ
HðsÞ
u2 s2 ds , 1 þ u2 s 2 s
us ds , 1 þ u2 s 2 s
(1)
(2)
where H(s) is the relaxation spectra (the distribution function of the elements with relaxation time s), while E0 is the equilibrium modulus which is zero for a viscoelastic liquid. Numerical methods for calculating the function H(s) has been accomplished by Kontogiorgos [42]. For clarity, the sample of PMMA was chosen to illustrate how to obtain the relaxation spectra from mechanical spectra. Fig. 11 presents the isothermal curve of loss modulus (E00 ) vs. angular frequency (u) on PMMA at Tg ¼ 380.3 K. After acquiring loss modulus data, it is necessary to calculate the optimum regularization parameter l from Fig. 11. The regularization parameter controls the filtering of the spectrum noise or in other words, the balance between the regularization error and the loss of resolution (smoothness) of the solution. The most appropriate tool to analyze this type of problem is the so-called L-curve method, which is a plot of the solution and residual norms for all valid regularization parameters. The vertical part of the curve corresponds to solutions that are sensitive to perturbation errors whereas the horizontal part to solutions where the regularization (calculation) error dominates. The optimum regularization parameter l is located at the corner of the curve and this value is used to calculate the optimum least square solution of the spectrum. Fig. 12 reproduces the result of the calculation of the optimum regularization parameter using the L-curve method for PMMA as an example. As it is evident, the vertical part of the curve corresponds to data where the solution norm is very sensitive to changes in the regularization parameter because the error in measurements dominates the regularized solution. The horizontal part corresponds to solutions where the residual norm is the most sensitive to the regularization parameter because the regularized solution is now dominated by the regularization error. Selection of a regularization parameter smaller than the optimum point will result in an “arbitrary noise generator” as the solution to the problem, whereas a value of l greater than optimum will yield over-smoothed answers thus missing vital information from the experimental spectrum. Following optimization of the parameters, the relaxation spectrum of PMMA was calculated (Fig. 13b). Two relaxation processes can be identified for PMMA, one at short relaxation time (s < 1 s) and the other at long relaxation time s (s > 1 s), which are assigned to b and a relaxation process respectively. In addition, the relaxation spectra of PnAA and PnAMA were also calculated and shown in Fig. 13a and b, respectively. It can be seen that both b and a relaxation process are obviously identified in all the relaxation spectra. Moreover, the shapes of the relaxation spectra are broader and broader with the increase of the alkyl side chain length. In other words, the two relaxation processes are more and more separated from each other with the increase of the alkyl side chain length.
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0 00 Fig. 5. The scaled dynamic mechanical spectra of PnAA and PnAMA. Eglass , Emax and tandmax represent the storage modulus at the glassy state, the maximum loss modulus and the maximum tand, respectively.
4. Discussion The results above can be explained by the following three aspects. First, from previous investigation [38,43e45], it is found that as the alkyl side chain length decreases, the fragility of PnAA and PnAMA increases. Strong glass-forming liquids usually possess self-reinforcing tetrahedral network, stable structures and local to intermediate range order [46]. As to PnAA and PnAMA, previous reports demonstrate that some local order structure gradually develops as the carbon number in the side chain increases, because some self-assembly takes place to form supramolecular systems like “hairy rods” [47,48]. Moreover, M. Balabin studied the enthalpy difference between conformations of normal alkanes and showed that n-alkyl chain is more and more flexible with chain length increase [49e53]. Thus, the microstructure is much easier to form with longer chain length. Such a microstructure leads to stabilized main-chain conformations; as a result, the chain units need to
reorient cooperatively in a highly anisotropic axial local motion [47,48]. It is this microstructure that prevents the dynamic properties of PnAA and PnAMA with long alkyl side chains from changing rapidly, thus broader glass transition regions have been observed, i.e., their structural relaxation time or viscosity changes smoothly with temperature. Second, the main transition of amorphous polymers from the glassy state to the high-elastic state usually involves different modes of molecular motion, including local segmental motion, subRouse mode and Rouse mode [38,54]. From local segmental motion to the Rouse mode, the mobile unit becomes larger and larger, from local motion of only a few backbone bonds to the motion of Gaussian sub-molecules. The motion of different modes with different chain lengths needs different size of free volume holes. Sub-Rouse mode and Rouse mode need larger free volume holes to move, while local segments need smaller free volume holes to move. The gap between two molecular chains becomes larger and
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Fig. 8. A schematic representation of determining transition wideness of storage modulus and integration area of tand.
0 Fig. 6. Derivative of storage modulus curves, i.e., d log (E0 /Eglass )/d (Tstorage/T), obtained from Fig. 5(a) were plotted against Tstorage/T.
larger with increasing alkyl side chain length, leading to more free volume holes in PnAA and PnAMA with longer alkyl side chain length. So the motion of different modes including local segmental motion, sub-Rouse mode and Rouse mode becomes more and more active, this will also broadens the relaxation spectra. According to the point of view put forward by Donth [54] and Ngai [38], the loss modulus peak and the point where the storage modulus begins to drop mainly reflect the motion of local segments, while the tand peak mainly reflects the sub-Rouse mode and Rouse mode. As a result of the decreasing values of n with increasing alkyl side chain length, the sub-Rouse mode and Rouse mode are more separated from the local segmental motion in the time or temperature scale. This is the reason why the tand peak is more and more apart from the loss modulus peak and the point where the storage modulus begins to drop. Third, the shape of the relaxation spectra changing with different alkyl side chain length illustrates that the intermolecular coupling varies in PnAA and PnAMA according to coupling model proposed by Ngai et al. [11,12]. The basis of the coupling model is the KohlrauscheWilliamseWatts (KWW) equation [55,56], which expressed as:
h
fðtÞ ¼ f0 exp ðt=sÞ1n
0 Fig. 7. Maximum values of d log (E0 /Eglass )/d (Tstorage/T) of PnAA and PnAMA with different alkyl carbons per side chain.
i
(3)
Fig. 9. The transition wideness of the storage modulus of PnAA and PnAMA with different alkyl carbons per side chain.
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Fig. 10. The integration area of tand of PnAA and PnAMA with different alkyl carbons per side chain.
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Fig. 12. Representative L-curve plot for PMMA calculated from Fig. 11. The optimum regularization parameter lopt is located at the corner of the curve (0.55681). Lower values than lopt result in noisy spectra whereas higher estimates yield over-smoothed spectra and the loss of molecular information.
where fðtÞ is the correlation function, s is the KWW relaxation time and n (0 < n < 1) is the coupling parameter which reflects the degree of correlation or cooperativeness in the relaxation process coming from the interactions of molecular chains (smaller n indicates smaller capacity of intermolecular coupling). K.L. Ngai has calculated the coupling parameters n for PMMA (0.51), PEMA (0.41) and PnBMA (0.27), showing that n decreases with increasing alkyl side chain length [45]. As a result, the motions of chain segments with different lengths are separated from each other in the time or temperature scale, which lead to a broader relaxation spectra. In other words, the two relaxation processes are more and more separated from each other with the increase of the alkyl side chain length. Therefore, with the coaction of the three effects mentioned above, it is expected that E0 will decay more smoothly (Fig. 5 (a) and (d)), and the width of the maxima for E00 (Fig. 5(b) and (e)) and of the tand (Fig. 5 (c) and (f)) will be broader for PnAA and PnAMA with long alkyl side chain length. The same is true for the derivative analysis (Fig. 6(a) and (b)), steepness (Fig. 7), width (Fig. 9) and area (Fig. 10).
Fig. 11. The isothermal curve of loss modulus (E00 ) vs. angular frequency (u) on PMMA at Tg ¼ 380.3 K.
Fig. 13. Relaxation spectra of PnAA (a) and PnAMA (b) obtained from corresponding mechanical spectra.
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5. Conclusion Dynamic mechanical analysis was used to research the correlation between dynamic mechanical properties of PnAA and PnAMA and different alkyl side chain length. With increasing alkyl side chain length, the loss modulus peak and the tand peak become broader. For quantitative illustration, three variables defined as the steepness index (S), the transition wideness (W) of storage modulus and the integration area (A) of tand were correlated with alkyl side chain length. It is found that S decreases while W and A increase with increasing alkyl side chain length. Moreover, relaxation spectra of PnAA and PnAMA were calculated and indicated that the shapes of the relaxation spectra are broader and broader with the increase of the alkyl side chain length. These phenomena are interpreted by the perspective of the fragility, free volume holes and the intermolecular coupling. Acknowledgments This work was financially supported by the National Natural Science Foundation of China (Grant No. 50873070). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
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