- Email: [email protected]
Size exclusion chromatography of photo-oxidated LDPE by triple detection and its relation to rheological behavior
Polymer Degradation and Stability 111 (2015) 46e54
Contents lists available at ScienceDirect
Polymer Degradation and Stability journal homepage: www.elsevier.com/locate/polydegstab
Size exclusion chromatography of photo-oxidated LDPE by triple detection and its relation to rheological behavior n-Garrido*, Matthias Kruse, Manfred H. Wagner Víctor H. Rolo Chair of Polymer Engineering/Polymer Physics, Berlin Institute of Technology (TU Berlin), Fasanenstrasse 90, D-10623 Berlin, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2014 Received in revised form 20 October 2014 Accepted 27 October 2014 Available online 1 November 2014
Sheets of low-density polyethylene (LDPE) were subjected to photo-oxidation in the presence of air using a xenon lamp to irradiate the samples for times between 1 day and 6 weeks. The formation of long-chain branching (LCB) up to one week of degradation and the competition between chain scission and crosslinking at longer periods of radiation were investigated by rheological characterization, Fourier n-Garrido and Wagner. Polym transform infrared spectroscopy, and the solvent extraction method (Rolo n-Garrido and Wagner. J Rheol 2014, 58:199). In the present contribution Degrad Stabil 2014, 99:136, Rolo the same samples are studied by size exclusion chromatographic characterization using triple detection (concentration, light scattering and viscosity). The gel content is determined by filtration followed by the analysis of the soluble polymer fraction. The influence of photo-oxidation time on the molecular weight distribution (molar masses and polydispersity), the mean square radius of gyration and the intrinsic viscosity contraction factors is discussed. The results are correlated with the model parameters (b and 2 ) of the molecular stress function (MSF) theory, used to describe quantitatively the rheological data in fmax uniaxial elongation. It is verified that LCB occurs as an aside process, which up to one week of degradation dominates over chain scission, before gelation plays a critical role. It is confirmed that the model parameter b correlates with the gel content, which reflects the competition between chain scission and 2 is found to correlate with the experimentally determined contraction factors. By crosslinking, while fmax comparing the data of this study with those obtained earlier for polystyrene comb melts with well defined structure, the influence of the branching frequency (i.e. the number of branch points per 1000 2 becomes evident. carbon atoms) on fmax © 2014 Elsevier Ltd. All rights reserved.
Keywords: Contraction factor Triple detection Chromatography Rheology MSF model Photo-oxidative degradation
1. Introduction The photo-oxidation of polymers is relevant not only from the scientific [1,2], but also from the industrial point of view. The induced structural modifications through irradiation have been shown to be advantageous for exploring the application of recycled materials [3], and for increasing the performance of polymer materials prior [4] or during processing like in thermoforming [5] or film blowing [6]. The influence of photo-oxidation on low density polyethylene (LDPE) has been studied recently at irradiation times varying from one day, up to six weeks [7,8]. The experimental techniques applied were the solvent extraction method, rheology and Fourier transform infrared (FTIR) spectroscopy. In contrast to thermo- [9] and thermo-oxidative degradation [9,10], the linear viscoelastic
* Corresponding author. n-Garrido). E-mail address: [email protected] (V.H. Rolo http://dx.doi.org/10.1016/j.polymdegradstab.2014.10.022 0141-3910/© 2014 Elsevier Ltd. All rights reserved.
response of the samples, measured in small amplitude oscillatory shear flow, was found to be strongly affected by the photooxidative degradation [7]. The rheological data obtained in the nonlinear regime, i.e. measured in uniaxial deformation, were described quantitatively by the molecular stress function (MSF) model for polydisperse randomly branched samples [11,12]. Photo-oxidative degradation causes chain scission and crosslinking, although secondary reactions like chain branching can also occur as a consequence of the free radical polymerization, similar to thermal oxidation [1]. It is known that chain scission and recombination compete and one of them predominates, characterizing the overall behavior under weathering [13]. Since crosslinking and chain scission take place at the same time [14,15], this competition influences the gel content of the samples [16]. The rheological characterization allowed understanding that for samples degraded for up to one week, i.e. when the gel content was low, the induced increase in strain hardening was mainly due to the formation of long-chain branching (LCB), overcoming possible chain scission, as indicated by the non-linear parameters of the MSF
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
model [7]. The MSF model applied to quantify the data contains 2 . b is only two parameters for uniaxial deformation, b and fmax directly related to the molecular structure of the polymer and can be predicted if the structure of the polymer is known [17e19], otherwise it is determined from the slope of the elongational vis2 cosity after inception of strain-hardening [17] (Fig. 1). fmax is determined by fitting to the suprema of the elongational viscosities achieved experimentally (Fig. 1). For more details about the MSF n-Garrido [20]. model and its applications, see Rolo The gel content increased drastically between one and two weeks of degradation, although it decreased at the third week. The changes observed in the linear viscoelastic properties of the samples irradiated for three and five weeks were found to be a consequence of the competition between the chain scission and crosslinking. This was corroborated through the carbonyl index and concentration of acid and aldehyde groups measured by the FTIR technique [8], as well as the uniaxial elongational measurements by the experimentally determined strain hardening index and the 2 non-linear parameters of the MSF model, where fmax increases up to infinity for the samples containing mainly a gel structure, and b correlates with the gel content measured by the solvent extraction method [7]. Size exclusion chromatography (SEC), also known in the literature as gel permeation chromatography (GPC), has been applied to study photo-oxidative degradation of different types of polyethylene [21e23], which also leads to an oscillating gel content with increasing degradation time [24]. It should be noted that the mass average molecular weights reported by SEC solely correspond
47
to the soluble fraction of the samples [13]. This technique has been combined with rheology to study the molecular weight changes during photo-oxidation of polyethylene nanocomposites [25] or the influence of morphology on photo-degradation of LDPE films [26]. Although it was concluded that the SEC data strongly support the results obtained from rheological measurements [26], both studies were limited to characterization in the linear viscoelastic regime. Studies applying SEC coupled with a multi-angle light scattering (MALS) detector and the non-linear rheology of irradiated samples have scarcely been performed, with the exception of polypropylene treated through electron beam and gama-irradiation [4,27e30]. Coupling a SEC device to a viscosity and a MALS detector permits to deepen the analysis of the LCB architecture of the samples through the contraction factors [31,32]
g≡
〈R2g 〉br
g≡
〈R2g 〉l ½hbr ½hl
(1)
(2)
where 〈R2g 〉 and [h] represent the mean square radius of gyration and the intrinsic viscosity, respectively, of branched (br) and linear (l) chains having the same molar mass. It is the objective of this contribution to analyze the photooxidatively degraded LDPE studied before [7,8], using tripledetector SEC characterization, and to correlate the additional information obtained with the non-linear parameters of the MSF model. 2. Experimental data 2.1. Materials The characterized samples were taken from the same sheets studied before [7,8]. For completeness, only a short description of the degradation process is given. The reference sample was lowdensity polyethylene (LDPE) 3020D produced by BASF. The supplied granules were extruded and pressed to produce plates denoted as reference sample LDPE T0. The photo-oxidized samples were produced using previously prepared LDPE T0 plates. They were radiated using a xenon lamp for times between 1, 3 and 5 days, and 1e6 weeks. The notation of the samples is based on the treatment time, stating “D” for day, and “W” for week. Thus, LDPE 3D and LDPE 4 W mean that the samples were photo-oxidatively treated three days and four weeks, respectively. The conditions used to avoid thermo-mechanical degradation during the preparation of the LDPE T0 plates and further details about the photo degradation process are given elsewhere [7]. 2.2. Size exclusion chromatographic characterization
Fig. 1. Examples of uniaxial experiments (symbols) on photo-oxidative degraded LDPE after a) one day and b) three weeks of treatment, compared to the predictions (lines) of the MSF model obtained through the parameters b (determined by the slope at the 2 beginning of the strain hardening) and fmax (determined by the suprema of the n-Garrido and elongational viscosities achieved experimentally). Reprinted from Rolo Wagner. Polym. Degrad. Stabil. 99: 136e145. Copyright © 2014, with the kind permission from Elsevier.
Size exclusion chromatographic (SEC) measurements were carried out by use of a high temperature device (GPC-PL 220, Agilent) with a refractive index (RI) and a viscosity (PL-BV 400HT) detector. Three PLgel Mixed-B columns with a particle size of 10 mm were used. The SEC is coupled with a multi-angle light scattering (MALS) detector (DAWN HELEOS 8þ, Wyatt Technology Corporation). The temperature of the measurements was 140 C, using 1,2,4-trichlorobenzene (TCB) as solvent. The samples were prepared with a concentration of 2 mg/mL, and dissolved in TCB at 160 C for 3 h prior to the experiment [33]. At least four experiments were performed for the reference sample and for each photo-oxidized sample.
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
48
The samples were not filtered prior to their injection in the SEC device. Therefore, crosslinked particles remained on the integrated filter with a pore size of 2 mm located in front of the columns. Consequently, the chromatograms measured correspond to the soluble part of the samples. The area Adeg under the concentration signal curve is therefore proportional to the total mass of the soluble fraction of the degraded sample, while for the reference sample, Aref represents the entire mass of the dissolved specimen. Hence the gel fraction can be calculated as.
Gel wt:% ¼
Aref Adeg Aref
! 100:
(3)
Eq. (3) can be also applied if the samples would be filtered prior to their injection in the SEC device. The additional filtration especially at high temperatures can result in a loss of material, leading to incorrect conclusion of the concentration. 3. Results and discussion 3.1. Gel content The gel content was determined by SEC from Eq. (3) since the samples were not filtered previously to the injection in the device (Fig. 2). The amount of insoluble material remains low up to the first week of degradation. The gel content increases drastically from the first to the second week, but is lower after the third week than expected by comparison to the higher value obtained for LDPE 4W. A similar reduction, although not as dramatic as for LDPE 3W, was also observed for LDPE 5W, before the gel content increases again for LDPE 6W. This cyclic behavior, attributed to the competition between chain scission and crosslinking [7], agrees with previous observations of the carbonyl index and the concentration of acid and aldehyde groups measured by the FTIR technique [8], or with results of rheological experiments in the linear as well as in the nonlinear viscoelastic regime [7]. The unexpected decrease in physical properties of an irradiated sample has also been observed in gel content and tensile strength of ethylene-octene copolymers [16], in carbonyl index and shearing modulus of an LLDPE/LDPE film [14], the yield stress, stress at break and strain at break of linear low density polyethylene [34], density in LDPE films [26], and the degree of crystallinity on LDPE films [35].
Fig. 2. Gel content determined by SEC according to Eq. (3) (squares with error bars), and the nonlinear parameter b of the MSF model (circles) as function of degradation time.
Comparing the magnitude of the gel content measured by SEC and by the solvent extraction method [7], it is noticed that the values obtained by SEC are lower than those measured by the solvent extraction method. This may be a consequence of weak gel particles being susceptible to shear degradation at the integrated filter. It may also be that the gel particles on the filter are flushed by the pressure driven solvent stream, thereby releasing branched molecules located in the matrix of the network, but which are not chemically bonded to the matrix. These molecules would have not been able to diffuse out during the dissolution time of the solvent extraction method due to their entanglements with the polymer matrix. 3.2. Molecular weight distribution The following results are discussed considering that the data presented correspond to the soluble part of the samples, which originate either from samples with low (Fig. 3a) or high (Fig. 3b) gel content. In other words, the SEC technique is taken as a tool to separate the gel content from the entanglement structure, and hence this method allows obtaining a direct and specific insight into the effect of the degradation time on the LCB content of the soluble fraction. It can be observed that up to one week of degradation (Fig. 3a), the general molecular weight distribution (MWD) curve is shifted
Fig. 3. Change in MWD of photo-oxidatively degraded samples with a) low gel content and b) high gel content.
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
to lower molecular weights for every sample compared to the reference. The high molecular weight tail tends to increase apparently only for LDPE 5D and LDPE 1W, in comparison to LDPE T0. In the case of samples degraded between two and six weeks (Fig. 3b), LDPE 2W, LDPE 3W and LDPE 5W present a similar tendency as observed in Fig. 3a. On the other hand, the MWD of LDPE 4W and LDPE 6W is shifted to lower values of molecular weight compared to LDPE T0 in the whole experimental window. For a detailed analysis, the number average molecular weight, Mn, the polydispersity (Mw/Mn) and the z-average molecular weight Mz, will be used as a measure of the induced changes due to the photooxidation in the low molecular weight tail, the broadness of the MWD and the high molecular weight tail, respectively. The number average molecular weight decreases continuously from the reference sample up to LDPE 1W (Fig. 4a). This can be
49
interpreted as the result of chain scission of the molecules. The same trend has been reported for photo-oxidative degradation of high density polyethylene (HDPE) [36]. The Mn value seems to oscillate between LDPE 1W and LDPE 3W, before a drastic decrease occurs from LDPE 3W to LDPE 4W, remaining at a similar low value up to LDPE 6W. Fig. 4a shows the effect of degradation time on chain scission, and the drastic reduction of Mn is related to the observation that the samples LDPE 4W, LDPE 5W and LDPE 6W became increasingly brittle at room temperature [8]. This is in accordance with mechanical tests, which demonstrated that significant brittle behavior seems to occur after 20 days of irradiation [35]. An increase in the polydispersity as a function of the degradation time has been observed in thermo-oxidative degradation of HDPE, based on MWD curves obtained from rheology measurements [37]. This was interpreted as an indication that some crosslinking occurs at the same time as chain scission. In the present contribution, considering that the gel content is low up to LDPE 1W, and that the soluble fraction contains only entangled and not crosslinked molecules, the increase measured in Mz is rather a consequence of an increase in LCB content (Fig. 4c) that occurs at the same time as chain scission (Fig. 4a) and gel formation (Fig. 2), as also identified through non-linear rheological measurements in uniaxial deformation [7]. The change in polydispersity with increasing degradation time due to the both countering reactions, i.e. chain scission and LCB formation, is shown in Fig. 4b. Additionally, the oscillating character can be noticed starting from the second week. The cyclic competition between chain scission and crosslinking has been found to be responsible for the different inherent structure of the gel content in LDPE 3W and LDPE 5W as supported by different techniques [7,8] and also shown in Fig. 2. The present analysis reveals that also in the soluble part of the sample, more molecules with higher LCB content are present in LDPE 5W and in LDPE 3W (Fig. 4c). This is not observed in LDPE 4W and LDPE 6W where a higher amount of chain scission can be inferred from the Mn and the Mz values. The amount of LCB in the molecule influences the possible gel formation in the case of further degradation [38]. If the LCB content is low, further degradation would lead to a stiffer gel than if molecules with a high quantity of LCB are crosslinked. This would explain why the gel stiffness of LDPE 6W was found to be lower than of LDPE 5W, as determined by linear-viscoelastic characterization [7]. In the case of the high molecular weight tail (Fig. 4c), a continuous increase up to LDPE 3W is detectable. This tendency and the increase of LCB content explain the increase of strain hardening in the uniaxial measurements [7], since it has been reported [39,40] that high molar mass components determined by SEC can influence the elongational viscosity even stronger than polydispersity [41]. The low values for LDPE 4W and LDPE 6W is the result of the shifting of MWD towards lower molecular weights due to the predominant crosslinking process in these samples. It is also noticed that the higher LCB content produced in LDPE 5W congruently reflects a high molecular weight tail in its MWD, which does not necessarily mean a higher Mn. 3.3. Contraction factors
Fig. 4. Changes in a) the number average molecular weight Mn, b) the polydispersity (Mw/Mn), and c) the average molecular weight Mz (squares) and gel content (circles) of photo-oxidatively degraded samples.
To obtain the contraction factors (Eq. (1) and Eq. (2)) based on the experimentally determined radius of gyration and intrinsic viscosity of the branched samples as obtained by the MALS and viscosity detectors, respectively, it is necessary to have also the respective values for the linear counterparts. The mean square radius of gyration is related with the molar mass for linear polyethylene by Ref. [42]
50
〈R2g;z 〉l ¼ 0:028Mz0:568 :
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
(4)
The Mark-Houwink equation (also known as Mark-HouwinkKuhn or Mark-Houwink-Kuhn-Sakurada) relates the intrinsic viscosity and molar mass as [31]
½hl ¼ KMa
(5)
The intrinsic viscosity contraction factor g' is given as function of the degradation time in Fig. 5b. Its value decreases continuously up to LDPE 3W, before a clear oscillation in the mean value of g' is observed, with clearly higher values for LDPE 4W and LDPE 6W. The great advantage of the intrinsic viscosity is its high sensitivity to relatively small branched molecules [31]. This explains the different tendency observed in comparison to Fig. 5a. The values LDPE 4W and LDPE 6W are an effect of the competition between chain scission, crosslinking, and as stressed in this contribution, the formation of LCB. Due to their low amount of LCB content (Fig. 4c), they present a high value of g'. Both contraction factors are related by.
where the constants K and a depend on the polymer, solvent and temperature. K ¼ 4.82 104(dL/g) and a ¼ 0.707 have been reported for linear polyethylene in TCB at 140 C [43]. For a polydisperse sample, the intrinsic viscosity is related to the weightaverage molar mass [31], and therefore M in Eq. (5) is taken as Mw. The mean square radius of gyration contraction factor g is presented as function of the degradation time in Fig. 5a. Its value decreases continuously up to LDPE 2W, corresponding to an increase in the degree of branching [31]. At degradation times longer than two weeks, it seems that a constant value is achieved, although still a slight oscillation in the mean value of g is observed, with slightly higher values for LDPE 4W and LDPE 6W. A clear tendency is noticed in the increment of the error bars from the third up to the sixth week of treatment. Considering that g reflects predominantly the high molecular tail of the MWD, i.e. the most branched fraction [42], this would mean a higher amount of molecules with a wider variety in their LCB content with increasing degradation time.
where 3 is a parameter related to drainability of a polymer chain, which value is assumed to vary from 0.5 to 1.5, and depends on solvent, molar mass, temperature and branching [31]. Taking the parameter 3 as indication of the type of structure remaining in the soluble part of the irradiated samples, it can be compared directly with the respective gel content (Fig. 6a). The reference sample is produced by a tubular reactor [10], from which it has been reported that 3 takes values between 0.9 and 1, in agreement with Fig. 6a [44], although higher values have been also reported [45,46]. In terms of the type of structure, 3 has been reported close to 1 for polymer combs [47,48] and 0.6 for a star structure [47]. An analysis
Fig. 5. a) Mean square radius of gyration and b) intrinsic viscosity contraction factors as function of the degradation time.
Fig. 6. a) Relation between the gel content and draining factor and b) close-up in the region of samples with predominantly comb structure.
g ¼ g 3 ;
(6)
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
of the transition between both types of structure has been also presented [49]. Note that in Fig. 6a, and in Fig. 6b (a close-up for the sake of clarity), samples with low gel content (up to 5 wt.%) contain soluble counterparts with an 3 higher than 0.85, meaning that they could have a predominantly comb structure. This means that when LCB formation dominates chain scission, the type of structure formed remains the same. On the other hand, samples with high gel content (higher than 10 wt.%) have soluble counterparts with low 3, meaning that they could have predominantly a star or globular structure. In other words, a transition in the global branched structure of the soluble molecules has occurred as the degradation time increases, with the exception of LDPE 3W, where chain scission dominates over gel formation and again a predominant comb structure is expected, in contrast to LDPE 5W, where rather a more globular one is anticipated. This allows understanding that not only gel structure of LDPE 3W and 5W is different [7], but also their soluble parts. This concurrent alternating character of both soluble and gel fraction and their dependence is also noticed in Fig. 4c. The increase in high molecular tail and in LCB molecules occurs already during the first week, where no gel is detectable. At 2 weeks even higher molecules weights were formed and the formation of a network started, since longer chains are more probable to get incorporated into the network [38]. The following scission process decreases the gel content and thus former gel molecules exist again as LCB (LDPE 3W). Hence the oscillation demonstrates that at least a part of the high molar mass specimens used to be a part of the gel and a certain amount of LCB initiates the reformation of the gel. Additionally an intermediate character at 5 weeks is demonstrated and correlates with the data in Fig. 6. Therefore the formation of a globular structure indicates the transition to a gel network. 3.4. Relation with results of the rheological characterization Samples irradiated up to one week have predominantly entangled structure, as proved with linear and non-linear viscoelastic experiments [7], where LCB dominates over chain scission and samples have a low gel content. In those samples, where the rupture in uniaxial elongation is mainly ductile [8], it is possible to obtain the zero shear viscosity h0. The combination of the SECMALS and rheology techniques allows representing the results in a h0Mw diagram, which has been used to characterize the type of branching [50], considering that h0 is a very sensitive quantity for probing the presence of small amounts of LCB in polyethylenes [51]. The h0Mw representation has been used not only for polyolefins [53], but also for irradiated polypropylene [28,30]. In the present study (Fig. 7), the zero shear-viscosity data have been shifted to 190 C according to previously measured shift factors [9] and the reference line corresponding to linear polyethylene is taken to be 3:41 at 190 C [52]. It is noticed that the reference h0 ¼ 5:8 1014 Mw sample is located above the reference line for linear polyethylene, in agreement with a previous result [53]. The longer the degradation time, the stronger the deviation from the reference line is, reflecting the increase in LCB content, in agreement with the reduction of the coil contraction factors (Fig. 5). The constitutive modeling of the data presented here has been published before [7]. From the present analysis, it can be seen from Fig. 2 that the parameter b correlates with the gel content determined by SEC, as already noticed in the case of the gel content obtained through the solvent extraction method [7]. Recalling that the parameter b signifies the ratio of the number of all entangled chain segments to the number of chain segments stretched [17], the observation that the parameter b remains constant and equal to 2.0 for LDPE T0, LDPE 1D, LDPE 3D, can be interpreted as an indication of the unchanged type of the random branched structure [12], i.e. independently of the LCB formation due to the photo-oxidative
51
Fig. 7. Logelog plot of molar mass dependence of the zero shear-rate viscosity of reference and degraded LDPE samples with mainly entangled structure. Continuous line represents linear polyethylene, according to Janzen and Colby.[52].
treatment, the mass of the entangled branches remains on average equal to the mass of the effective backbone. This is in agreement with previous results analyzing the thermal [9] and thermo-oxidative degradation of LDPE [9,10]. Taking the value of b as an average quantity to describe the entangled or stretchable structure, the fact that both LDPE 5D and LDPE 1W are described by values of b being 2.2, or by a value of 3.0 in the case of LDPE 4W and LDPE 6W, reflects that their structure is similar as proved through the SEC-MALS characterization in this contribution, or previous criteria like their strain hardening index [7] or rupture behavior [8] . 2 , it has been obtained experiIn the case of the parameter fmax mentally as the ratio of the steady-state compliance of the polydisperse to the monodisperse components [40], although its connection with the molecular structure has been less studied. First observations based on polystyrene (PS) melts, having different well defined comb structures, pointed toward the relevance of the 2 number and length of the sidechains [17]. Since large values of fmax indicates a large strain hardening effect [54] and respectively a 2 higher LCB content [55,9], fmax was shown to be related to the experimentally determined contraction factor based on the intrinsic viscosity and a theoretically determined contraction factor related to the mean square radius of gyration [18]. In contrast to this work, based on nearly monodisperse samples, the present study is based on a polymer containing polydisperse randomly branched structure. Furthermore, both contraction factors have been experimentally determined. Up to LDPE 1W, the gel content is low (Fig. 2) and therefore, the 2 correlation of fmax with both contraction factors can be established due to their predominantly entangled structure in the whole sample (Fig. 8), leading to. 2 fmax ¼ 1:22 101 g8:04
(7)
and 2 fmax ¼ 1:22 102 g011:63 :
(8)
Samples treated from two to six weeks cannot be considered in Eqs. (7) and (8) because their rheological response is dominated not by the soluble branched molecules, but by the gel structure [7,8], reflected in the quantification of the uniaxial experiments with 2 infinite values of fmax [7]. It can be observed that with the experimentally determined 2 contraction factors decreasing, fmax is increasing strongly,
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
52
number average molar mass of the nearly monodisperse side chains (in kg/mol). The sample PS-r-95 is the linear reference sample with molar mass of 157 kg/mol. Since the structure of the combs is well defined, Eq. (10) can be applied directly. The results are presented in Fig. 9 for the photo-oxidatively degraded LDPE with predominantly entangled structure, and the PS combs, and can be described by. 2 fmax;LDPE ¼ 2:75l4:16
(11)
and 2 0:67 fmax;PS : combs ¼ 38:15l
(12)
2 Thus it is demonstrated for the first time that fmax is extremely influenced by the branching frequency not only in model systems, but also in an industrially relevant polymer such as LDPE with different degree of LCB induced by photo-oxidative degradation. There is a critical difference to be stressed. The exponent of the 2 power law dependency of fmax is less than one for PS combs, while for LDPE based samples it is larger than one. This could be due to the type of branching. While the side branches of the PS combs are linear and nearly monodisperse, the photo-degraded LDPE samples are rather randomly branched and polydisperse. Another reason for the drastic difference could be the type of monomer. To achieve a definite conclusion, more research is needed.
4. Conclusions
2 Fig. 8. Correlation between the model parameter fmax and the a) mean square radius of gyration, g, and b) intrinsic viscosity, g, contraction ratios.
supporting the fact that the strain hardening is growing with the increasing LCB content the samples. Eqs. (7) and (8) have the same functionality as in the case of PS combs [18], although the exponent is higher in the present case, as a result of the randomly branched structure generated by the irradiation. The contraction factor g can be used further to characterize the branching degree through the number of branch units per molecule m [56]
g¼
0:5 m0:5 4m 1þ þ ; 7 9p
Previously characterized photo-oxidative degraded LDPE [7,8] has been analyzed in this study by size exclusion chromatographic (SEC) using triple detection. The technique used allowed separating the gel content from the soluble fraction. Therefore the gel content was determined quantitatively, and the respective soluble fraction, i.e. the entangled and long-chain branched fraction, can be studied in detail. The effect of photo-oxidation was observed by the change of the molecular weight distribution, including the low and high molecular weight components, by the change of Mn and Mz, respectively, and by the change of polydispersity. The contractions factors based on the mean square radius of gyration and the intrinsic viscosity were also taken into account. Up to one week of radiation, long chain branching (LCB) dominates over crosslinking, in agreement with previous
(9)
where it is assumed that the functionality of the branch unit is three. This assumption is valid in branched polymers formed by radiation, since formation of branch points with higher functionality is statistically improbable [27,28,31]. The branching frequency l, i.e. the number of long-chain branches per 1000 monomer units is given by Ref. [30]
l ¼ 1000
m Mm ; M
(10)
where Mm is the molar mass of the monomer unit and M is the 2 molar mass of the branched polymer. We compare relation of fmax and branching frequency of oxidated LDPE samples to model PS comb polymer melts [18]. The nomenclature PS-x-mG-y indicates that x is the number average molar mass of the polydisperse backbone, m the average number of grafted side chains per molecule, which are randomly attached to the backbone, and y the
2 Fig. 9. Correlation between the model parameter fmax and the branching frequency l for photo-oxidative degraded LDPE (solid symbols) and PS melt combs (empty symbols). The continuous line represents Eq. (11) and the discontinuous one Eq. (12).
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
rheological characterization. The present analysis allows corroborating that in the case of two weeks of degradation and longer, where the gel content starts to be significant in the bulk sample, LCB formation still plays a role, together with the chain scission and gel formation. Furthermore, the type of branching structure in the soluble part changes as well. In connection with the previous rheological characterization and the respective quantitative description of the uniaxial viscosity data by use of the molecular stress function (MSF) model, it was confirmed that the parameter b correlates with the gel content, which reflects the competition between chain scission and cross2 , which quantifies the linking. The exponential dependency of fmax degree of strain hardening in elongational flow, on the experimentally measured contraction factors reveals that the smaller the 2 . contraction factor, i.e. the higher the LCB content, the higher isfmax 2 fmax was also found to be exponentially dependent on the branching frequency not only in the case of the photo-oxidatively degraded LDPE considered here, but also in previously reported model PS comb polymers with well defined structures. The type of 2 - branching branching seems to have a strong influence on the fmax frequency relation. More research is needed towards the promising goal of relating the non-linear rheological macroscopic response to the molecular characteristics of polymers.
Acknowledgments Financial support by the German Science Foundation (DFG) is gratefully acknowledged.
References [1] Rabek JF. Photodegradation of polymers. Physical characteristics and applications. Berlin: Springer; 1996. [2] Al-Malaika S. Oxidative degradation and stabilisation of polymers. Int Mater Rev 2003;48:165. [3] Dintcheva NTz, La Mantia FP, Cascone M, Balloni A. The role of the disposition of the recycled polymer on the properties of films for greenhouses coverage. J Appl Polym Sci 2011;119:1986. [4] Cheng S, Dehaye F, Bailly C, Biebuyck JJ, Legras R, Parks L. Studies on polyethylene pellets modified by low dose radiation prior to part formation. Nucl Instrum Methods Phys Res B, Beam Interact Mater A. T 2005;236:130. [5] Seefried A, Fuchs M, Drummer D. Radiation crosslinking of semicrystalline thermoplastics: a novel approach to modifying a material's thermoformability. Plast Eng 2012;68:14. [6] Cheng S, Phillips E, Parks L. Improving processability of polyethylenes by radiation-induced long chain branching. Rad Phys Chem 2009;78:563. n-Garrido VH, Wagner MH. Linear and non-linear rheological character[7] Rolo ization of photo-oxidative degraded LDPE. Polym Degrad Stabil 2014;99:136. n-Garrido VH, Wagner MH. Elongational rheology and cohesive fracture [8] Rolo of photo-oxidated LDPE. J Rheol 2014;58:199. n-Garrido VH, Luo J, Wagner MH. Enhancement of strain-hardening by [9] Rolo thermo-oxidative degradation of low-density polyethylene. Rheol Acta 2011;50:519. n-Garrido VH, Zatloukal M, Wagner MH. Increase of long-chain branching [10] Rolo by thermo-oxidative treatment of LDPE: chromatographic, spectroscopic, and rheological evidence. J Rheol 2013;57:105. [11] Wagner MH, Rubio P, Bastian H. The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release. J Rheol 2001;45:1387. [12] Wagner MH, Yamaguchi M, Takahashi M. Quantitative assessment of strain hardening of low-density polyethylene melts by the molecular stress function model. J Rheol 2003;47:779. [13] Commereuc S, Askanian H, Verney V, Celli A, Marchese P, Berti C. About the end life of novel aliphatic and aliphatic-aromatic (co)polyesters after UVweathering: structure/degradability relationships. Polym Deg Stab 2013;98: 1321. [14] Zhao BY, Yi XW, Li RY, Zhu PF, Hu KA. Characterization to the weathering extent of LLDPE/LDPE thin film. J Appl Polym Sci 2003;88:12. [15] Hussein IA. Rheological investigation of the influence of molecular structure on natural and accelerated UV degradation of linear low density polyethylene. Polym Deg Stab 2007;92:2026. [16] Liu Z, Chen S, Zhang J. Photodegradation of ethylene-octene copolymers with different octane contents. Polym Deg Stab 2011;96:1961.
53
[17] Wagner MH, Hepperle J, Münstedt H. Relating rheology and molecular structure of model branched polystyrene melts by molecular stress function theory. J Rheol 2004;48:489. n-Garrido VH, Wagner MH. The MSF model: relation of nonlinear pa[18] Rolo rameters to molecular structure of long-chain branched polymer melts. Rheol Acta 2007;46:583. [19] Abbasi M, Ebrahimi NG, Nadali M, Esfahani MK. Elongational viscosity of LDPE with various structures: employing a new evolution equation in MSF theory. Rheol Acta 2012;51:163. n-Garrido VH. The molecular stress function (MSF) model in rheology. [20] Rolo Rheol Acta 2014;53:663. [21] Severini F, Gallo R, Ipsale S. Environmental degradation of stabilized LDPE. Initial step. Polym Degrad Stabil 1986;14:341. [22] Severini F, Gallo R, Ipsale S, Del Fanti N. Environmental degradation of stabilized LDPE. later stages. Polym Degrad Stabil 1987;17:57. [23] Miyagawa E, Tokumitsu K, Tanaka A, Nitta K. Mechanical property and molecular weight distribution changes with photo- and chemical-degradation on LDPE films. Polym Deg Stab 2007;92:1948. [24] Hsu YC, Weir MP, Truss RW, Garvez CJ, Nicholson TM, Halley PJ. A fundamental study on photo-oxidative degradation of linear low density polyethylene films at embrittlement. Polymer 2012;53:2385. [25] Kumnayaka TO, Parthasarathay R, Jollands M, Ivanov I. Molecular weight changes during photo-oxidation of polyethylene nanocomposites. KoreaAustralia Rheol J 2010;22(3):173. [26] Tanaka A, Miyagawa E, Uno H, Kitamura M, Nitta K. Influence of morphology on photo-degradation of low density polyethylene films. Polym Eng Sci 2000;40(9):2007. [27] Sugimoto M, Tanaka T, Masubuchi Y, Takimoto J, Koyama K. Effect of chain structure on the melt rheology of modified polypropylene. J Appl Polym Sci 1999;73:1493. [28] Auhl D, Stange J, Münstedt H, Krause B, Voigt D, Lederer A, et al. Long-chain branched polypropylenes by electron beam irradiation and their rheological properties. Macromolecules 2004;37:9465. [29] Krause B, Sephan M, Volkland S, Voigt D, H€ außler K, Dorschner H. Long-chain branching of polypropylene by electron-beam irradiation in the molten state. J Appl Polym Sci 2006;99:260. [30] Auhl D, Stadler FJ, Münstedt H. Comparison of molecular structrure and rheological properties of electron-beam- and gamma-irradiated polypropylene. Macromolecules 2012;45:2057. [31] Podzimek S. Light scattering, size exclusion chromatography and asymmetric flow field fractionation. Powerful tools for the characterization of polymers, proteins and nanoparticles. Singapure: Wiley and Sons; 2011. [32] Wang WJ, Kharchenko S, Migler K, Zhu S. Triple-detector GPC characterization and processing behavior of long-chain-branched polyethylene prepared by solution polymerization with constrained geometry catalyst. Polymer 2004;45:6495. [33] Piel C, Stadler FJ, Kaschta J, Rulhoff S, Münstedt H, Kaminsky W. Structureproperty relationships of linear and long-chain branched metallocene highdensity polyethylenes characterized by shear rheology and SEC-MALLS. Macromol Chem Phys 2006;207:26. [34] Naddeo C, Guadagno L, De Lica S, Vittoria V, Camino G. Mechanical and transport properties of irradiated linear low density polyethylene (LLDPE). Polym Deg Stabil 2001;72:239. [35] Miyagawa E, Nitta K, Tanaka A. Effects of photo-oxidation on tensile deformation behavior in lod-density polyethylene. e-Polymers 2005:022. [36] Jabarin SA, Lofgren EA. Photooxidative effects on properties and structure of high-density polyethylene. J Appl Polym Sci 1994;53:411. [37] Fayolle B, Colin X, Audouin L, Verdu J. Mechanism of degradation induced embrittlement in polyethylene. Polym Deg Stab 2007;92:231. [38] Andersson LHU, Hjertberg T. The effect of different structure parameters on the crosslinking behaviour and network performance of LDPE. Polymer 2006;47:200. [39] Münstedt H. Dependence of the elongational behaviour of polystyrene melts on molecular weight and molecular weight distribution. J Rheol 1980;24:847. [40] Wagner MH, Kheirandish S, Koyama K, Nishioka A, Minegishi A, Takahashi T. Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory. Rheol Acta 2005;44:235. [41] Münstedt H, Laun HM. Elongational properties and molecular structure of polyethylene melts. Rheol Acta 1981;20:211. [42] Podzimek S. Importance of multi-angle light scattering in polyolefin characterization. Macromol Symp 2013;330:81. [43] Beer F, Capaccio G, Rose LJ. High molecular weight tail and long-chain branching in low-density polyethylenes. J Appl Poly Sci 2001;80:2815. [44] Hert M, Strazielle C. Study of branching structure of low-density polyethylene by viscosity and light-scattering measurements on fractions from exclusion chromatography GPC. Makromol Chem 1983;184:135. [45] Kuhn R, Kromer H, Rossmanith G. Structure and properties of various highpressure polyethylenes. Angew Makromol Chem 1974;40:361e89. [46] Tackx P, Tacx JCJF. Chain architecture of LDPE as a function of molar mass using size exclusion chromatography and multi-angle laser light scattering (SEC-MALS). Polymer 1998;39:3109. [47] Berry GJ. Thermodynamic and conformational properties of polystyrene. III. Dilute solutions studies on branched polymers. J Polym Sci A-2 1971;9:687.
54
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
[48] Radke W, Müller AHE. Synthesis and characterization of comb-shaped polymers by SEC with on-line light scattering and viscometry detection. Macromolecules 2005;38:3949. [49] Berry GJ. Remarks on a relation among the intrinsic viscosity, the radius of gyration, and the translational friction coefficient. J Polym Sci Part B: Polym Phys 1988;26:1137. [50] Gabriel C, Münstedt H. Strain hardening of various polyolefins in uniaxial elongational flow. J Rheol 2003;47:619. €fgren B, Seppa €l€ [51] Gabriel C, Kokko E, Lo a J, Münstedt H. Analytical and rheological characterization of long-chain branched metallocene-catalyzed ethylene homopolymers. Polymer 2002;43:6383.
[52] Janzen J, Colby RH. Diagnosing long-chain branching in polyethylenes. J Mol Struct 1999;485-486:569. [53] Gabriel C, Lilge D. Molecular mass dependence of the zero shear-rate viscosity of LDPE melts: evidence of an exponential behavior. Rheol Acta 2006;45:995. [54] Wagner MH, Ehrecke P, Hachmann P, Meissner J. A constitutive analysis of uniaxial, equibiaxial and planar extension of a commercial linear high-density polyethylene melt. J Rheol 1998;42:621. n-Garrido VH, Pivokonsky R, Filip P, Zatloukal M, Wagner MH. Modelling [55] Rolo elongational and shear rheology of two LDPE melts. Rheol Acta 2009;48:691. [56] Zimm BH, Stockmayer WH. The dimensions of chain molecules containing branches and rings. J Chem Phys 1949;17:1301.
Contents lists available at ScienceDirect
Polymer Degradation and Stability journal homepage: www.elsevier.com/locate/polydegstab
Size exclusion chromatography of photo-oxidated LDPE by triple detection and its relation to rheological behavior n-Garrido*, Matthias Kruse, Manfred H. Wagner Víctor H. Rolo Chair of Polymer Engineering/Polymer Physics, Berlin Institute of Technology (TU Berlin), Fasanenstrasse 90, D-10623 Berlin, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2014 Received in revised form 20 October 2014 Accepted 27 October 2014 Available online 1 November 2014
Sheets of low-density polyethylene (LDPE) were subjected to photo-oxidation in the presence of air using a xenon lamp to irradiate the samples for times between 1 day and 6 weeks. The formation of long-chain branching (LCB) up to one week of degradation and the competition between chain scission and crosslinking at longer periods of radiation were investigated by rheological characterization, Fourier n-Garrido and Wagner. Polym transform infrared spectroscopy, and the solvent extraction method (Rolo n-Garrido and Wagner. J Rheol 2014, 58:199). In the present contribution Degrad Stabil 2014, 99:136, Rolo the same samples are studied by size exclusion chromatographic characterization using triple detection (concentration, light scattering and viscosity). The gel content is determined by filtration followed by the analysis of the soluble polymer fraction. The influence of photo-oxidation time on the molecular weight distribution (molar masses and polydispersity), the mean square radius of gyration and the intrinsic viscosity contraction factors is discussed. The results are correlated with the model parameters (b and 2 ) of the molecular stress function (MSF) theory, used to describe quantitatively the rheological data in fmax uniaxial elongation. It is verified that LCB occurs as an aside process, which up to one week of degradation dominates over chain scission, before gelation plays a critical role. It is confirmed that the model parameter b correlates with the gel content, which reflects the competition between chain scission and 2 is found to correlate with the experimentally determined contraction factors. By crosslinking, while fmax comparing the data of this study with those obtained earlier for polystyrene comb melts with well defined structure, the influence of the branching frequency (i.e. the number of branch points per 1000 2 becomes evident. carbon atoms) on fmax © 2014 Elsevier Ltd. All rights reserved.
Keywords: Contraction factor Triple detection Chromatography Rheology MSF model Photo-oxidative degradation
1. Introduction The photo-oxidation of polymers is relevant not only from the scientific [1,2], but also from the industrial point of view. The induced structural modifications through irradiation have been shown to be advantageous for exploring the application of recycled materials [3], and for increasing the performance of polymer materials prior [4] or during processing like in thermoforming [5] or film blowing [6]. The influence of photo-oxidation on low density polyethylene (LDPE) has been studied recently at irradiation times varying from one day, up to six weeks [7,8]. The experimental techniques applied were the solvent extraction method, rheology and Fourier transform infrared (FTIR) spectroscopy. In contrast to thermo- [9] and thermo-oxidative degradation [9,10], the linear viscoelastic
* Corresponding author. n-Garrido). E-mail address: [email protected] (V.H. Rolo http://dx.doi.org/10.1016/j.polymdegradstab.2014.10.022 0141-3910/© 2014 Elsevier Ltd. All rights reserved.
response of the samples, measured in small amplitude oscillatory shear flow, was found to be strongly affected by the photooxidative degradation [7]. The rheological data obtained in the nonlinear regime, i.e. measured in uniaxial deformation, were described quantitatively by the molecular stress function (MSF) model for polydisperse randomly branched samples [11,12]. Photo-oxidative degradation causes chain scission and crosslinking, although secondary reactions like chain branching can also occur as a consequence of the free radical polymerization, similar to thermal oxidation [1]. It is known that chain scission and recombination compete and one of them predominates, characterizing the overall behavior under weathering [13]. Since crosslinking and chain scission take place at the same time [14,15], this competition influences the gel content of the samples [16]. The rheological characterization allowed understanding that for samples degraded for up to one week, i.e. when the gel content was low, the induced increase in strain hardening was mainly due to the formation of long-chain branching (LCB), overcoming possible chain scission, as indicated by the non-linear parameters of the MSF
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
model [7]. The MSF model applied to quantify the data contains 2 . b is only two parameters for uniaxial deformation, b and fmax directly related to the molecular structure of the polymer and can be predicted if the structure of the polymer is known [17e19], otherwise it is determined from the slope of the elongational vis2 cosity after inception of strain-hardening [17] (Fig. 1). fmax is determined by fitting to the suprema of the elongational viscosities achieved experimentally (Fig. 1). For more details about the MSF n-Garrido [20]. model and its applications, see Rolo The gel content increased drastically between one and two weeks of degradation, although it decreased at the third week. The changes observed in the linear viscoelastic properties of the samples irradiated for three and five weeks were found to be a consequence of the competition between the chain scission and crosslinking. This was corroborated through the carbonyl index and concentration of acid and aldehyde groups measured by the FTIR technique [8], as well as the uniaxial elongational measurements by the experimentally determined strain hardening index and the 2 non-linear parameters of the MSF model, where fmax increases up to infinity for the samples containing mainly a gel structure, and b correlates with the gel content measured by the solvent extraction method [7]. Size exclusion chromatography (SEC), also known in the literature as gel permeation chromatography (GPC), has been applied to study photo-oxidative degradation of different types of polyethylene [21e23], which also leads to an oscillating gel content with increasing degradation time [24]. It should be noted that the mass average molecular weights reported by SEC solely correspond
47
to the soluble fraction of the samples [13]. This technique has been combined with rheology to study the molecular weight changes during photo-oxidation of polyethylene nanocomposites [25] or the influence of morphology on photo-degradation of LDPE films [26]. Although it was concluded that the SEC data strongly support the results obtained from rheological measurements [26], both studies were limited to characterization in the linear viscoelastic regime. Studies applying SEC coupled with a multi-angle light scattering (MALS) detector and the non-linear rheology of irradiated samples have scarcely been performed, with the exception of polypropylene treated through electron beam and gama-irradiation [4,27e30]. Coupling a SEC device to a viscosity and a MALS detector permits to deepen the analysis of the LCB architecture of the samples through the contraction factors [31,32]
g≡
〈R2g 〉br
g≡
〈R2g 〉l ½hbr ½hl
(1)
(2)
where 〈R2g 〉 and [h] represent the mean square radius of gyration and the intrinsic viscosity, respectively, of branched (br) and linear (l) chains having the same molar mass. It is the objective of this contribution to analyze the photooxidatively degraded LDPE studied before [7,8], using tripledetector SEC characterization, and to correlate the additional information obtained with the non-linear parameters of the MSF model. 2. Experimental data 2.1. Materials The characterized samples were taken from the same sheets studied before [7,8]. For completeness, only a short description of the degradation process is given. The reference sample was lowdensity polyethylene (LDPE) 3020D produced by BASF. The supplied granules were extruded and pressed to produce plates denoted as reference sample LDPE T0. The photo-oxidized samples were produced using previously prepared LDPE T0 plates. They were radiated using a xenon lamp for times between 1, 3 and 5 days, and 1e6 weeks. The notation of the samples is based on the treatment time, stating “D” for day, and “W” for week. Thus, LDPE 3D and LDPE 4 W mean that the samples were photo-oxidatively treated three days and four weeks, respectively. The conditions used to avoid thermo-mechanical degradation during the preparation of the LDPE T0 plates and further details about the photo degradation process are given elsewhere [7]. 2.2. Size exclusion chromatographic characterization
Fig. 1. Examples of uniaxial experiments (symbols) on photo-oxidative degraded LDPE after a) one day and b) three weeks of treatment, compared to the predictions (lines) of the MSF model obtained through the parameters b (determined by the slope at the 2 beginning of the strain hardening) and fmax (determined by the suprema of the n-Garrido and elongational viscosities achieved experimentally). Reprinted from Rolo Wagner. Polym. Degrad. Stabil. 99: 136e145. Copyright © 2014, with the kind permission from Elsevier.
Size exclusion chromatographic (SEC) measurements were carried out by use of a high temperature device (GPC-PL 220, Agilent) with a refractive index (RI) and a viscosity (PL-BV 400HT) detector. Three PLgel Mixed-B columns with a particle size of 10 mm were used. The SEC is coupled with a multi-angle light scattering (MALS) detector (DAWN HELEOS 8þ, Wyatt Technology Corporation). The temperature of the measurements was 140 C, using 1,2,4-trichlorobenzene (TCB) as solvent. The samples were prepared with a concentration of 2 mg/mL, and dissolved in TCB at 160 C for 3 h prior to the experiment [33]. At least four experiments were performed for the reference sample and for each photo-oxidized sample.
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
48
The samples were not filtered prior to their injection in the SEC device. Therefore, crosslinked particles remained on the integrated filter with a pore size of 2 mm located in front of the columns. Consequently, the chromatograms measured correspond to the soluble part of the samples. The area Adeg under the concentration signal curve is therefore proportional to the total mass of the soluble fraction of the degraded sample, while for the reference sample, Aref represents the entire mass of the dissolved specimen. Hence the gel fraction can be calculated as.
Gel wt:% ¼
Aref Adeg Aref
! 100:
(3)
Eq. (3) can be also applied if the samples would be filtered prior to their injection in the SEC device. The additional filtration especially at high temperatures can result in a loss of material, leading to incorrect conclusion of the concentration. 3. Results and discussion 3.1. Gel content The gel content was determined by SEC from Eq. (3) since the samples were not filtered previously to the injection in the device (Fig. 2). The amount of insoluble material remains low up to the first week of degradation. The gel content increases drastically from the first to the second week, but is lower after the third week than expected by comparison to the higher value obtained for LDPE 4W. A similar reduction, although not as dramatic as for LDPE 3W, was also observed for LDPE 5W, before the gel content increases again for LDPE 6W. This cyclic behavior, attributed to the competition between chain scission and crosslinking [7], agrees with previous observations of the carbonyl index and the concentration of acid and aldehyde groups measured by the FTIR technique [8], or with results of rheological experiments in the linear as well as in the nonlinear viscoelastic regime [7]. The unexpected decrease in physical properties of an irradiated sample has also been observed in gel content and tensile strength of ethylene-octene copolymers [16], in carbonyl index and shearing modulus of an LLDPE/LDPE film [14], the yield stress, stress at break and strain at break of linear low density polyethylene [34], density in LDPE films [26], and the degree of crystallinity on LDPE films [35].
Fig. 2. Gel content determined by SEC according to Eq. (3) (squares with error bars), and the nonlinear parameter b of the MSF model (circles) as function of degradation time.
Comparing the magnitude of the gel content measured by SEC and by the solvent extraction method [7], it is noticed that the values obtained by SEC are lower than those measured by the solvent extraction method. This may be a consequence of weak gel particles being susceptible to shear degradation at the integrated filter. It may also be that the gel particles on the filter are flushed by the pressure driven solvent stream, thereby releasing branched molecules located in the matrix of the network, but which are not chemically bonded to the matrix. These molecules would have not been able to diffuse out during the dissolution time of the solvent extraction method due to their entanglements with the polymer matrix. 3.2. Molecular weight distribution The following results are discussed considering that the data presented correspond to the soluble part of the samples, which originate either from samples with low (Fig. 3a) or high (Fig. 3b) gel content. In other words, the SEC technique is taken as a tool to separate the gel content from the entanglement structure, and hence this method allows obtaining a direct and specific insight into the effect of the degradation time on the LCB content of the soluble fraction. It can be observed that up to one week of degradation (Fig. 3a), the general molecular weight distribution (MWD) curve is shifted
Fig. 3. Change in MWD of photo-oxidatively degraded samples with a) low gel content and b) high gel content.
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
to lower molecular weights for every sample compared to the reference. The high molecular weight tail tends to increase apparently only for LDPE 5D and LDPE 1W, in comparison to LDPE T0. In the case of samples degraded between two and six weeks (Fig. 3b), LDPE 2W, LDPE 3W and LDPE 5W present a similar tendency as observed in Fig. 3a. On the other hand, the MWD of LDPE 4W and LDPE 6W is shifted to lower values of molecular weight compared to LDPE T0 in the whole experimental window. For a detailed analysis, the number average molecular weight, Mn, the polydispersity (Mw/Mn) and the z-average molecular weight Mz, will be used as a measure of the induced changes due to the photooxidation in the low molecular weight tail, the broadness of the MWD and the high molecular weight tail, respectively. The number average molecular weight decreases continuously from the reference sample up to LDPE 1W (Fig. 4a). This can be
49
interpreted as the result of chain scission of the molecules. The same trend has been reported for photo-oxidative degradation of high density polyethylene (HDPE) [36]. The Mn value seems to oscillate between LDPE 1W and LDPE 3W, before a drastic decrease occurs from LDPE 3W to LDPE 4W, remaining at a similar low value up to LDPE 6W. Fig. 4a shows the effect of degradation time on chain scission, and the drastic reduction of Mn is related to the observation that the samples LDPE 4W, LDPE 5W and LDPE 6W became increasingly brittle at room temperature [8]. This is in accordance with mechanical tests, which demonstrated that significant brittle behavior seems to occur after 20 days of irradiation [35]. An increase in the polydispersity as a function of the degradation time has been observed in thermo-oxidative degradation of HDPE, based on MWD curves obtained from rheology measurements [37]. This was interpreted as an indication that some crosslinking occurs at the same time as chain scission. In the present contribution, considering that the gel content is low up to LDPE 1W, and that the soluble fraction contains only entangled and not crosslinked molecules, the increase measured in Mz is rather a consequence of an increase in LCB content (Fig. 4c) that occurs at the same time as chain scission (Fig. 4a) and gel formation (Fig. 2), as also identified through non-linear rheological measurements in uniaxial deformation [7]. The change in polydispersity with increasing degradation time due to the both countering reactions, i.e. chain scission and LCB formation, is shown in Fig. 4b. Additionally, the oscillating character can be noticed starting from the second week. The cyclic competition between chain scission and crosslinking has been found to be responsible for the different inherent structure of the gel content in LDPE 3W and LDPE 5W as supported by different techniques [7,8] and also shown in Fig. 2. The present analysis reveals that also in the soluble part of the sample, more molecules with higher LCB content are present in LDPE 5W and in LDPE 3W (Fig. 4c). This is not observed in LDPE 4W and LDPE 6W where a higher amount of chain scission can be inferred from the Mn and the Mz values. The amount of LCB in the molecule influences the possible gel formation in the case of further degradation [38]. If the LCB content is low, further degradation would lead to a stiffer gel than if molecules with a high quantity of LCB are crosslinked. This would explain why the gel stiffness of LDPE 6W was found to be lower than of LDPE 5W, as determined by linear-viscoelastic characterization [7]. In the case of the high molecular weight tail (Fig. 4c), a continuous increase up to LDPE 3W is detectable. This tendency and the increase of LCB content explain the increase of strain hardening in the uniaxial measurements [7], since it has been reported [39,40] that high molar mass components determined by SEC can influence the elongational viscosity even stronger than polydispersity [41]. The low values for LDPE 4W and LDPE 6W is the result of the shifting of MWD towards lower molecular weights due to the predominant crosslinking process in these samples. It is also noticed that the higher LCB content produced in LDPE 5W congruently reflects a high molecular weight tail in its MWD, which does not necessarily mean a higher Mn. 3.3. Contraction factors
Fig. 4. Changes in a) the number average molecular weight Mn, b) the polydispersity (Mw/Mn), and c) the average molecular weight Mz (squares) and gel content (circles) of photo-oxidatively degraded samples.
To obtain the contraction factors (Eq. (1) and Eq. (2)) based on the experimentally determined radius of gyration and intrinsic viscosity of the branched samples as obtained by the MALS and viscosity detectors, respectively, it is necessary to have also the respective values for the linear counterparts. The mean square radius of gyration is related with the molar mass for linear polyethylene by Ref. [42]
50
〈R2g;z 〉l ¼ 0:028Mz0:568 :
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
(4)
The Mark-Houwink equation (also known as Mark-HouwinkKuhn or Mark-Houwink-Kuhn-Sakurada) relates the intrinsic viscosity and molar mass as [31]
½hl ¼ KMa
(5)
The intrinsic viscosity contraction factor g' is given as function of the degradation time in Fig. 5b. Its value decreases continuously up to LDPE 3W, before a clear oscillation in the mean value of g' is observed, with clearly higher values for LDPE 4W and LDPE 6W. The great advantage of the intrinsic viscosity is its high sensitivity to relatively small branched molecules [31]. This explains the different tendency observed in comparison to Fig. 5a. The values LDPE 4W and LDPE 6W are an effect of the competition between chain scission, crosslinking, and as stressed in this contribution, the formation of LCB. Due to their low amount of LCB content (Fig. 4c), they present a high value of g'. Both contraction factors are related by.
where the constants K and a depend on the polymer, solvent and temperature. K ¼ 4.82 104(dL/g) and a ¼ 0.707 have been reported for linear polyethylene in TCB at 140 C [43]. For a polydisperse sample, the intrinsic viscosity is related to the weightaverage molar mass [31], and therefore M in Eq. (5) is taken as Mw. The mean square radius of gyration contraction factor g is presented as function of the degradation time in Fig. 5a. Its value decreases continuously up to LDPE 2W, corresponding to an increase in the degree of branching [31]. At degradation times longer than two weeks, it seems that a constant value is achieved, although still a slight oscillation in the mean value of g is observed, with slightly higher values for LDPE 4W and LDPE 6W. A clear tendency is noticed in the increment of the error bars from the third up to the sixth week of treatment. Considering that g reflects predominantly the high molecular tail of the MWD, i.e. the most branched fraction [42], this would mean a higher amount of molecules with a wider variety in their LCB content with increasing degradation time.
where 3 is a parameter related to drainability of a polymer chain, which value is assumed to vary from 0.5 to 1.5, and depends on solvent, molar mass, temperature and branching [31]. Taking the parameter 3 as indication of the type of structure remaining in the soluble part of the irradiated samples, it can be compared directly with the respective gel content (Fig. 6a). The reference sample is produced by a tubular reactor [10], from which it has been reported that 3 takes values between 0.9 and 1, in agreement with Fig. 6a [44], although higher values have been also reported [45,46]. In terms of the type of structure, 3 has been reported close to 1 for polymer combs [47,48] and 0.6 for a star structure [47]. An analysis
Fig. 5. a) Mean square radius of gyration and b) intrinsic viscosity contraction factors as function of the degradation time.
Fig. 6. a) Relation between the gel content and draining factor and b) close-up in the region of samples with predominantly comb structure.
g ¼ g 3 ;
(6)
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
of the transition between both types of structure has been also presented [49]. Note that in Fig. 6a, and in Fig. 6b (a close-up for the sake of clarity), samples with low gel content (up to 5 wt.%) contain soluble counterparts with an 3 higher than 0.85, meaning that they could have a predominantly comb structure. This means that when LCB formation dominates chain scission, the type of structure formed remains the same. On the other hand, samples with high gel content (higher than 10 wt.%) have soluble counterparts with low 3, meaning that they could have predominantly a star or globular structure. In other words, a transition in the global branched structure of the soluble molecules has occurred as the degradation time increases, with the exception of LDPE 3W, where chain scission dominates over gel formation and again a predominant comb structure is expected, in contrast to LDPE 5W, where rather a more globular one is anticipated. This allows understanding that not only gel structure of LDPE 3W and 5W is different [7], but also their soluble parts. This concurrent alternating character of both soluble and gel fraction and their dependence is also noticed in Fig. 4c. The increase in high molecular tail and in LCB molecules occurs already during the first week, where no gel is detectable. At 2 weeks even higher molecules weights were formed and the formation of a network started, since longer chains are more probable to get incorporated into the network [38]. The following scission process decreases the gel content and thus former gel molecules exist again as LCB (LDPE 3W). Hence the oscillation demonstrates that at least a part of the high molar mass specimens used to be a part of the gel and a certain amount of LCB initiates the reformation of the gel. Additionally an intermediate character at 5 weeks is demonstrated and correlates with the data in Fig. 6. Therefore the formation of a globular structure indicates the transition to a gel network. 3.4. Relation with results of the rheological characterization Samples irradiated up to one week have predominantly entangled structure, as proved with linear and non-linear viscoelastic experiments [7], where LCB dominates over chain scission and samples have a low gel content. In those samples, where the rupture in uniaxial elongation is mainly ductile [8], it is possible to obtain the zero shear viscosity h0. The combination of the SECMALS and rheology techniques allows representing the results in a h0Mw diagram, which has been used to characterize the type of branching [50], considering that h0 is a very sensitive quantity for probing the presence of small amounts of LCB in polyethylenes [51]. The h0Mw representation has been used not only for polyolefins [53], but also for irradiated polypropylene [28,30]. In the present study (Fig. 7), the zero shear-viscosity data have been shifted to 190 C according to previously measured shift factors [9] and the reference line corresponding to linear polyethylene is taken to be 3:41 at 190 C [52]. It is noticed that the reference h0 ¼ 5:8 1014 Mw sample is located above the reference line for linear polyethylene, in agreement with a previous result [53]. The longer the degradation time, the stronger the deviation from the reference line is, reflecting the increase in LCB content, in agreement with the reduction of the coil contraction factors (Fig. 5). The constitutive modeling of the data presented here has been published before [7]. From the present analysis, it can be seen from Fig. 2 that the parameter b correlates with the gel content determined by SEC, as already noticed in the case of the gel content obtained through the solvent extraction method [7]. Recalling that the parameter b signifies the ratio of the number of all entangled chain segments to the number of chain segments stretched [17], the observation that the parameter b remains constant and equal to 2.0 for LDPE T0, LDPE 1D, LDPE 3D, can be interpreted as an indication of the unchanged type of the random branched structure [12], i.e. independently of the LCB formation due to the photo-oxidative
51
Fig. 7. Logelog plot of molar mass dependence of the zero shear-rate viscosity of reference and degraded LDPE samples with mainly entangled structure. Continuous line represents linear polyethylene, according to Janzen and Colby.[52].
treatment, the mass of the entangled branches remains on average equal to the mass of the effective backbone. This is in agreement with previous results analyzing the thermal [9] and thermo-oxidative degradation of LDPE [9,10]. Taking the value of b as an average quantity to describe the entangled or stretchable structure, the fact that both LDPE 5D and LDPE 1W are described by values of b being 2.2, or by a value of 3.0 in the case of LDPE 4W and LDPE 6W, reflects that their structure is similar as proved through the SEC-MALS characterization in this contribution, or previous criteria like their strain hardening index [7] or rupture behavior [8] . 2 , it has been obtained experiIn the case of the parameter fmax mentally as the ratio of the steady-state compliance of the polydisperse to the monodisperse components [40], although its connection with the molecular structure has been less studied. First observations based on polystyrene (PS) melts, having different well defined comb structures, pointed toward the relevance of the 2 number and length of the sidechains [17]. Since large values of fmax indicates a large strain hardening effect [54] and respectively a 2 higher LCB content [55,9], fmax was shown to be related to the experimentally determined contraction factor based on the intrinsic viscosity and a theoretically determined contraction factor related to the mean square radius of gyration [18]. In contrast to this work, based on nearly monodisperse samples, the present study is based on a polymer containing polydisperse randomly branched structure. Furthermore, both contraction factors have been experimentally determined. Up to LDPE 1W, the gel content is low (Fig. 2) and therefore, the 2 correlation of fmax with both contraction factors can be established due to their predominantly entangled structure in the whole sample (Fig. 8), leading to. 2 fmax ¼ 1:22 101 g8:04
(7)
and 2 fmax ¼ 1:22 102 g011:63 :
(8)
Samples treated from two to six weeks cannot be considered in Eqs. (7) and (8) because their rheological response is dominated not by the soluble branched molecules, but by the gel structure [7,8], reflected in the quantification of the uniaxial experiments with 2 infinite values of fmax [7]. It can be observed that with the experimentally determined 2 contraction factors decreasing, fmax is increasing strongly,
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
52
number average molar mass of the nearly monodisperse side chains (in kg/mol). The sample PS-r-95 is the linear reference sample with molar mass of 157 kg/mol. Since the structure of the combs is well defined, Eq. (10) can be applied directly. The results are presented in Fig. 9 for the photo-oxidatively degraded LDPE with predominantly entangled structure, and the PS combs, and can be described by. 2 fmax;LDPE ¼ 2:75l4:16
(11)
and 2 0:67 fmax;PS : combs ¼ 38:15l
(12)
2 Thus it is demonstrated for the first time that fmax is extremely influenced by the branching frequency not only in model systems, but also in an industrially relevant polymer such as LDPE with different degree of LCB induced by photo-oxidative degradation. There is a critical difference to be stressed. The exponent of the 2 power law dependency of fmax is less than one for PS combs, while for LDPE based samples it is larger than one. This could be due to the type of branching. While the side branches of the PS combs are linear and nearly monodisperse, the photo-degraded LDPE samples are rather randomly branched and polydisperse. Another reason for the drastic difference could be the type of monomer. To achieve a definite conclusion, more research is needed.
4. Conclusions
2 Fig. 8. Correlation between the model parameter fmax and the a) mean square radius of gyration, g, and b) intrinsic viscosity, g, contraction ratios.
supporting the fact that the strain hardening is growing with the increasing LCB content the samples. Eqs. (7) and (8) have the same functionality as in the case of PS combs [18], although the exponent is higher in the present case, as a result of the randomly branched structure generated by the irradiation. The contraction factor g can be used further to characterize the branching degree through the number of branch units per molecule m [56]
g¼
0:5 m0:5 4m 1þ þ ; 7 9p
Previously characterized photo-oxidative degraded LDPE [7,8] has been analyzed in this study by size exclusion chromatographic (SEC) using triple detection. The technique used allowed separating the gel content from the soluble fraction. Therefore the gel content was determined quantitatively, and the respective soluble fraction, i.e. the entangled and long-chain branched fraction, can be studied in detail. The effect of photo-oxidation was observed by the change of the molecular weight distribution, including the low and high molecular weight components, by the change of Mn and Mz, respectively, and by the change of polydispersity. The contractions factors based on the mean square radius of gyration and the intrinsic viscosity were also taken into account. Up to one week of radiation, long chain branching (LCB) dominates over crosslinking, in agreement with previous
(9)
where it is assumed that the functionality of the branch unit is three. This assumption is valid in branched polymers formed by radiation, since formation of branch points with higher functionality is statistically improbable [27,28,31]. The branching frequency l, i.e. the number of long-chain branches per 1000 monomer units is given by Ref. [30]
l ¼ 1000
m Mm ; M
(10)
where Mm is the molar mass of the monomer unit and M is the 2 molar mass of the branched polymer. We compare relation of fmax and branching frequency of oxidated LDPE samples to model PS comb polymer melts [18]. The nomenclature PS-x-mG-y indicates that x is the number average molar mass of the polydisperse backbone, m the average number of grafted side chains per molecule, which are randomly attached to the backbone, and y the
2 Fig. 9. Correlation between the model parameter fmax and the branching frequency l for photo-oxidative degraded LDPE (solid symbols) and PS melt combs (empty symbols). The continuous line represents Eq. (11) and the discontinuous one Eq. (12).
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
rheological characterization. The present analysis allows corroborating that in the case of two weeks of degradation and longer, where the gel content starts to be significant in the bulk sample, LCB formation still plays a role, together with the chain scission and gel formation. Furthermore, the type of branching structure in the soluble part changes as well. In connection with the previous rheological characterization and the respective quantitative description of the uniaxial viscosity data by use of the molecular stress function (MSF) model, it was confirmed that the parameter b correlates with the gel content, which reflects the competition between chain scission and cross2 , which quantifies the linking. The exponential dependency of fmax degree of strain hardening in elongational flow, on the experimentally measured contraction factors reveals that the smaller the 2 . contraction factor, i.e. the higher the LCB content, the higher isfmax 2 fmax was also found to be exponentially dependent on the branching frequency not only in the case of the photo-oxidatively degraded LDPE considered here, but also in previously reported model PS comb polymers with well defined structures. The type of 2 - branching branching seems to have a strong influence on the fmax frequency relation. More research is needed towards the promising goal of relating the non-linear rheological macroscopic response to the molecular characteristics of polymers.
Acknowledgments Financial support by the German Science Foundation (DFG) is gratefully acknowledged.
References [1] Rabek JF. Photodegradation of polymers. Physical characteristics and applications. Berlin: Springer; 1996. [2] Al-Malaika S. Oxidative degradation and stabilisation of polymers. Int Mater Rev 2003;48:165. [3] Dintcheva NTz, La Mantia FP, Cascone M, Balloni A. The role of the disposition of the recycled polymer on the properties of films for greenhouses coverage. J Appl Polym Sci 2011;119:1986. [4] Cheng S, Dehaye F, Bailly C, Biebuyck JJ, Legras R, Parks L. Studies on polyethylene pellets modified by low dose radiation prior to part formation. Nucl Instrum Methods Phys Res B, Beam Interact Mater A. T 2005;236:130. [5] Seefried A, Fuchs M, Drummer D. Radiation crosslinking of semicrystalline thermoplastics: a novel approach to modifying a material's thermoformability. Plast Eng 2012;68:14. [6] Cheng S, Phillips E, Parks L. Improving processability of polyethylenes by radiation-induced long chain branching. Rad Phys Chem 2009;78:563. n-Garrido VH, Wagner MH. Linear and non-linear rheological character[7] Rolo ization of photo-oxidative degraded LDPE. Polym Degrad Stabil 2014;99:136. n-Garrido VH, Wagner MH. Elongational rheology and cohesive fracture [8] Rolo of photo-oxidated LDPE. J Rheol 2014;58:199. n-Garrido VH, Luo J, Wagner MH. Enhancement of strain-hardening by [9] Rolo thermo-oxidative degradation of low-density polyethylene. Rheol Acta 2011;50:519. n-Garrido VH, Zatloukal M, Wagner MH. Increase of long-chain branching [10] Rolo by thermo-oxidative treatment of LDPE: chromatographic, spectroscopic, and rheological evidence. J Rheol 2013;57:105. [11] Wagner MH, Rubio P, Bastian H. The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release. J Rheol 2001;45:1387. [12] Wagner MH, Yamaguchi M, Takahashi M. Quantitative assessment of strain hardening of low-density polyethylene melts by the molecular stress function model. J Rheol 2003;47:779. [13] Commereuc S, Askanian H, Verney V, Celli A, Marchese P, Berti C. About the end life of novel aliphatic and aliphatic-aromatic (co)polyesters after UVweathering: structure/degradability relationships. Polym Deg Stab 2013;98: 1321. [14] Zhao BY, Yi XW, Li RY, Zhu PF, Hu KA. Characterization to the weathering extent of LLDPE/LDPE thin film. J Appl Polym Sci 2003;88:12. [15] Hussein IA. Rheological investigation of the influence of molecular structure on natural and accelerated UV degradation of linear low density polyethylene. Polym Deg Stab 2007;92:2026. [16] Liu Z, Chen S, Zhang J. Photodegradation of ethylene-octene copolymers with different octane contents. Polym Deg Stab 2011;96:1961.
53
[17] Wagner MH, Hepperle J, Münstedt H. Relating rheology and molecular structure of model branched polystyrene melts by molecular stress function theory. J Rheol 2004;48:489. n-Garrido VH, Wagner MH. The MSF model: relation of nonlinear pa[18] Rolo rameters to molecular structure of long-chain branched polymer melts. Rheol Acta 2007;46:583. [19] Abbasi M, Ebrahimi NG, Nadali M, Esfahani MK. Elongational viscosity of LDPE with various structures: employing a new evolution equation in MSF theory. Rheol Acta 2012;51:163. n-Garrido VH. The molecular stress function (MSF) model in rheology. [20] Rolo Rheol Acta 2014;53:663. [21] Severini F, Gallo R, Ipsale S. Environmental degradation of stabilized LDPE. Initial step. Polym Degrad Stabil 1986;14:341. [22] Severini F, Gallo R, Ipsale S, Del Fanti N. Environmental degradation of stabilized LDPE. later stages. Polym Degrad Stabil 1987;17:57. [23] Miyagawa E, Tokumitsu K, Tanaka A, Nitta K. Mechanical property and molecular weight distribution changes with photo- and chemical-degradation on LDPE films. Polym Deg Stab 2007;92:1948. [24] Hsu YC, Weir MP, Truss RW, Garvez CJ, Nicholson TM, Halley PJ. A fundamental study on photo-oxidative degradation of linear low density polyethylene films at embrittlement. Polymer 2012;53:2385. [25] Kumnayaka TO, Parthasarathay R, Jollands M, Ivanov I. Molecular weight changes during photo-oxidation of polyethylene nanocomposites. KoreaAustralia Rheol J 2010;22(3):173. [26] Tanaka A, Miyagawa E, Uno H, Kitamura M, Nitta K. Influence of morphology on photo-degradation of low density polyethylene films. Polym Eng Sci 2000;40(9):2007. [27] Sugimoto M, Tanaka T, Masubuchi Y, Takimoto J, Koyama K. Effect of chain structure on the melt rheology of modified polypropylene. J Appl Polym Sci 1999;73:1493. [28] Auhl D, Stange J, Münstedt H, Krause B, Voigt D, Lederer A, et al. Long-chain branched polypropylenes by electron beam irradiation and their rheological properties. Macromolecules 2004;37:9465. [29] Krause B, Sephan M, Volkland S, Voigt D, H€ außler K, Dorschner H. Long-chain branching of polypropylene by electron-beam irradiation in the molten state. J Appl Polym Sci 2006;99:260. [30] Auhl D, Stadler FJ, Münstedt H. Comparison of molecular structrure and rheological properties of electron-beam- and gamma-irradiated polypropylene. Macromolecules 2012;45:2057. [31] Podzimek S. Light scattering, size exclusion chromatography and asymmetric flow field fractionation. Powerful tools for the characterization of polymers, proteins and nanoparticles. Singapure: Wiley and Sons; 2011. [32] Wang WJ, Kharchenko S, Migler K, Zhu S. Triple-detector GPC characterization and processing behavior of long-chain-branched polyethylene prepared by solution polymerization with constrained geometry catalyst. Polymer 2004;45:6495. [33] Piel C, Stadler FJ, Kaschta J, Rulhoff S, Münstedt H, Kaminsky W. Structureproperty relationships of linear and long-chain branched metallocene highdensity polyethylenes characterized by shear rheology and SEC-MALLS. Macromol Chem Phys 2006;207:26. [34] Naddeo C, Guadagno L, De Lica S, Vittoria V, Camino G. Mechanical and transport properties of irradiated linear low density polyethylene (LLDPE). Polym Deg Stabil 2001;72:239. [35] Miyagawa E, Nitta K, Tanaka A. Effects of photo-oxidation on tensile deformation behavior in lod-density polyethylene. e-Polymers 2005:022. [36] Jabarin SA, Lofgren EA. Photooxidative effects on properties and structure of high-density polyethylene. J Appl Polym Sci 1994;53:411. [37] Fayolle B, Colin X, Audouin L, Verdu J. Mechanism of degradation induced embrittlement in polyethylene. Polym Deg Stab 2007;92:231. [38] Andersson LHU, Hjertberg T. The effect of different structure parameters on the crosslinking behaviour and network performance of LDPE. Polymer 2006;47:200. [39] Münstedt H. Dependence of the elongational behaviour of polystyrene melts on molecular weight and molecular weight distribution. J Rheol 1980;24:847. [40] Wagner MH, Kheirandish S, Koyama K, Nishioka A, Minegishi A, Takahashi T. Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory. Rheol Acta 2005;44:235. [41] Münstedt H, Laun HM. Elongational properties and molecular structure of polyethylene melts. Rheol Acta 1981;20:211. [42] Podzimek S. Importance of multi-angle light scattering in polyolefin characterization. Macromol Symp 2013;330:81. [43] Beer F, Capaccio G, Rose LJ. High molecular weight tail and long-chain branching in low-density polyethylenes. J Appl Poly Sci 2001;80:2815. [44] Hert M, Strazielle C. Study of branching structure of low-density polyethylene by viscosity and light-scattering measurements on fractions from exclusion chromatography GPC. Makromol Chem 1983;184:135. [45] Kuhn R, Kromer H, Rossmanith G. Structure and properties of various highpressure polyethylenes. Angew Makromol Chem 1974;40:361e89. [46] Tackx P, Tacx JCJF. Chain architecture of LDPE as a function of molar mass using size exclusion chromatography and multi-angle laser light scattering (SEC-MALS). Polymer 1998;39:3109. [47] Berry GJ. Thermodynamic and conformational properties of polystyrene. III. Dilute solutions studies on branched polymers. J Polym Sci A-2 1971;9:687.
54
n-Garrido et al. / Polymer Degradation and Stability 111 (2015) 46e54 V.H. Rolo
[48] Radke W, Müller AHE. Synthesis and characterization of comb-shaped polymers by SEC with on-line light scattering and viscometry detection. Macromolecules 2005;38:3949. [49] Berry GJ. Remarks on a relation among the intrinsic viscosity, the radius of gyration, and the translational friction coefficient. J Polym Sci Part B: Polym Phys 1988;26:1137. [50] Gabriel C, Münstedt H. Strain hardening of various polyolefins in uniaxial elongational flow. J Rheol 2003;47:619. €fgren B, Seppa €l€ [51] Gabriel C, Kokko E, Lo a J, Münstedt H. Analytical and rheological characterization of long-chain branched metallocene-catalyzed ethylene homopolymers. Polymer 2002;43:6383.
[52] Janzen J, Colby RH. Diagnosing long-chain branching in polyethylenes. J Mol Struct 1999;485-486:569. [53] Gabriel C, Lilge D. Molecular mass dependence of the zero shear-rate viscosity of LDPE melts: evidence of an exponential behavior. Rheol Acta 2006;45:995. [54] Wagner MH, Ehrecke P, Hachmann P, Meissner J. A constitutive analysis of uniaxial, equibiaxial and planar extension of a commercial linear high-density polyethylene melt. J Rheol 1998;42:621. n-Garrido VH, Pivokonsky R, Filip P, Zatloukal M, Wagner MH. Modelling [55] Rolo elongational and shear rheology of two LDPE melts. Rheol Acta 2009;48:691. [56] Zimm BH, Stockmayer WH. The dimensions of chain molecules containing branches and rings. J Chem Phys 1949;17:1301.