Accelerated testing of thermo-oxidative degradation of polyvinyl butyral

Accelerated testing of thermo-oxidative degradation of polyvinyl butyral

Thermochimica Acta 589 (2014) 70–75 Contents lists available at ScienceDirect Thermochimica Acta journal homepage: www.elsevier.com/locate/tca Acce...

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Thermochimica Acta 589 (2014) 70–75

Contents lists available at ScienceDirect

Thermochimica Acta journal homepage: www.elsevier.com/locate/tca

Accelerated testing of thermo-oxidative degradation of polyvinyl butyral V.B. Ivanov a , A.A. Zavodchikova a,∗ , E.I. Popova b , O.L. Lazareva b , O.A. Belova b , I.A. Kryuchkov b , E.V. Bykov c a

NN Semenov Institute of Chemical Physics, Russian Academy of Sciences, Str. Kosygina 4, 119991 Moscow, Russia Federal State Unitary Enterprise “All-Russian Research Institute of Automatics”, Str. Suchshevskaya 22, 127055 Moscow, Russia c Closed Join Stock Company “ELEKTRONEFTEMASH”, Str. Krasnokazarmennay 12, 111024 Moscow, Russia b

a r t i c l e

i n f o

Article history: Received 25 March 2014 Received in revised form 12 May 2014 Accepted 13 May 2014 Available online 23 May 2014 Keywords: Activation energy Polyvinyl butyral Thermogravimetric analysis Thermo-oxidative degradation

a b s t r a c t Using thermogravimetric analysis (TGA), gas chromatography, Fourier-IR spectroscopy, and UV–vis spectrophotometry, the thermo-oxidative degradation of polyvinyl butyral (PVB) has been studied at temperatures of 60–300 ◦ C. The kinetic regularities were analysed, and the activation energies of mass loss and the formation of gaseous products and functional groups were determined. The correlations of the activation energy of the first macroscopic stage determined by dynamic TGA and the activation energies of the chemical processes proceeding at 60–120 ◦ C are discussed. © 2014 Published by Elsevier B.V.

1. Introduction Polyvinyl butyral (PVB) is widely applied as an adhesive and binder in different fields of technology. In many cases, PVB-based materials are used in important applications with strict imposed requirements, including long-term storage and operational stability. Despite the publication of multiple studies [1–6] accomplished at a high methodological and technical level, the quantitative characteristics evaluated for the thermal degradation and thermal oxidation of PVB, especially data on their temperature dependence, does not allow reliable forecasting of PVB ageing at low, near-environmental temperatures. This is largely because most of the investigations have been conducted using high-temperature (≥550 K) TGA, with the majority of these analysing the effect of fillers [7–12]. The latter choice seems natural due to the practical importance of producing PVB based ceramics. It is known however that TGA can provide a quick and reliable determination of the kinetics and the activation energies of the processes of polymer degradation and oxidation [13–16]. The goal of this investigation is to analyse the basic processes that occur during PVB thermal oxidation at low temperatures

∗ Corresponding author. Tel.: +7 4959397314. E-mail address: [email protected] (A.A. Zavodchikova). http://dx.doi.org/10.1016/j.tca.2014.05.016 0040-6031/© 2014 Published by Elsevier B.V.

(60–120 ◦ C) using a set of physicochemical methods. Hence, the following basic tasks were performed: - determination of the activation energy for the low-temperature stage of thermo-oxidative PVB degradation using various TGA methods; - establishment of the kinetic regularities for low-molecularweight compound evaluation and the accumulation of carbonyl groups and polyconjugated structures in the low-temperature (60–120 ◦ C) thermal oxidation of PVB; - determination of the activation energies for product formation during thermo-oxidative PVB degradation; - comparison of the results obtained by different methods; - selection of methodologies for PVB thermal stability evaluation during accelerated tests for storage and operational stability forecasting.

2. Materials and methods The industrial PVB specimen (brand PP) studied in this work contained 3.0 and 47 wt% of acetate and butyral groups, respectively. 240-␮m-Thick polymer films were formed by spreading one layer at a time of PVB solution on a glass plate and then drying the plates at room temperature for 7 days. In a number of tests, 30␮m-thick free films were exfoliated from a glass substrate using

V.B. Ivanov et al. / Thermochimica Acta 589 (2014) 70–75 120

1,0

100

220 200

0,8

1

180

0,4

0,2

40

Ea (kJ/mol)

m (%)

2

dm/dT (%/°C)

0,6

80

60

71

160 140 120 100

3

20

80

0,0

60 0 0

100

200

300

400

500

-0,2 600

0

5

10

15

20 25 α (%)

T (°C) Fig. 1. Mass loss curve of the thermal decomposition of the PVB specimen at a heating rate of 2 ◦ C/min in air and its first derivative. The main macroscopic stages of the process are numbered 1, 2 and 3.

distilled water. As a solvent for PVB, ethanol or isopropyl alcohol analytical grade were used. Thermogravimetric measurements were performed using Mettler TGA/SDTA 851e (Mettler Toledo) and Q50 V20.8 (TA Instruments, New Castle, DE) TGA instruments in the air at heating rates of 2, 5, 10 and 20 ◦ C/min. The gases produced during thermal oxidation were analysed using a gas chromatograph (FOCUS, Thermo Electron Corp.). The formation and consumption of functional groups were studied by IR spectroscopy using an Avatar 370 spectrophotometer with a Smart iTR attachment (Thermo Nicolet) and UV–vis absorption spectroscopy using Lambda 1050 WB (Perkin Elmer) and MultiSpec-1501 (Shimadzu) spectrophotometers. The spectral data were processed using the software packages UV WinLab, OMNIC and HYPER UV 1.51. Water vapour sorption was assessed by a gravimetric method. The thermomechanical parameters were determined on a Du Pont Instruments 943 analyser at a heating rate of 10 ◦ C/min. The glass transition point of the PVB powder and films was controlled by DSC using a TA Instruments Q20 calorimeter at a heating rate of 10 ◦ C/min.

ln



ln

ˇi 2 T˛,i



= const −

E˛ RT˛,i

(1)

where ˇi is the heating rate under ith temperature program, T˛,i is the temperature at which the degree of conversion ˛ is reached, E˛ is the activation energy of the process at the degree of conversion ˛ and R is the universal gas constant.

40

As shown in Fig. 2 the activation energy of PVB thermo-oxidative degradation increases monotonically with elevation of ˛ over a range between 10 and 40 wt%. This dependence is apparently a representation of sequential involving of more deep degradation stages which proceeds at higher temperatures and which are displayed clearly in Fig. 1. However the fundamental characteristic of the dependence E˛ on ˛ is the sharp change of the curve at ˛ ≈ 10 wt%. The more important peculiarity is the practically constant value of activation energy at 2 ≤ ˛ ≤ 6 wt%. Keeping in mind the data presented in Fig. 1 and knowing the temperature range in which at all heating rates ˇi the extends of conversions 2–6 wt% are reached it is possible to believe that the limiting constant value of E = 70 ± 4 kJ/mol is the true one of the 1st low temperature stage of PVB thermo-oxidative degradation. It is known [17] that the often used Kissinger’ method [19] allows the less accurate estimation of activation energy due to using of simplified models and rough approximations. Nevertheless the application of this method gives the possibility more clearly and simply to assess the activation energy of each main stage and hence to predict the change of their contributions when the testing or operation conditions are altered. The dependence of the maximum reaction rate on temperature is described in accord with the Kissinger’ method by Eq. (2) [19]:



Fig. 1 shows the typical dependence of the specimen mass loss on temperature at a low heating rate. Both the TGA curve and its first derivative clearly indicate the presence of three main macroscopic stages in the process, which proceed in the temperature ranges of 170–300, 300–420 and 420–480 ◦ C. As the heating rate increases, these stages shift to higher temperatures, and the low-temperature peak of the first stage in the DTGA curve becomes less pronounced. In accordance with recommendation of the Kinetic Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC) [17], one from the most accurate estimation of activation energy can be made by using Kissinger–Akahira–Sunose Eq. (1) [18]:

35

Fig. 2. Activation energies of PVB thermo-oxidative degradations at different conversion levels calculated in accord with Kissinger–Akahira–Sunose method.

3. Results and discussion 3.1. Mass loss during thermo-oxidative PVB degradation

30

ˇi 2 Ti,max



= ln

 AR   E



E RTi,max



(2)

where Ti,max is the temperature corresponding to the maximum reaction rate and E is the activation energy of the process. Fig. 3 shows that the dependence underlying Eq. (2) holds for all three stages of the thermo-oxidative degradation of PVB. Table 1 summarises the values of Ti,max determined experimentally at given heating rates and the activation energies E calculated from Eq. (2) for all three stages. The first stage of thermo-oxidative PVB degradation is usually associated with the oxidation of butyral units [1]. A mass loss during the second stage was estimated by difference between conversion degrees at temperatures corresponding to the first and second minimum of derivative curve (71% according to the data from [1] and ∼60% in the current case). The results at the low heating rate (2 ◦ C/min) were used when the individual stages are determined most clearly. The second stage contributes the most mass loss and also referred to oxidation. This stage is accompanied by the evolution of gaseous products [1]. The activation energy estimated here for second stage (222 ± 13 kJ/mol) is very similar to the literature values (184–208 kJ/mol) measured by using static [1] and dynamic [2] TGA methods. However, the activation energy of the third stage

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Table 1 Temperatures corresponding to the maximum reaction rates (Tmax ) and activation energies (E) of the main macroscopic stages of thermo-oxidative PVB degradation calculated by using Eq. (2). Stage

1

ˇ (◦ C/min) Tmax (◦ C) E (kJ/mol)

2 264

5 292

2 10 319

20 346

2 352

5 363

68 ± 2

(184 ± 11 kJ/mol) found here is significantly lower than the value given early [1] (260–273 kJ/mol). A possible explanation of this difference is that the values of 260–273 kJ/mol were measured at higher temperatures (460–650 ◦ C) due to relatively higher heating rates and hence more deep conversions. To forecast the change in the material properties based on PVB under normal conditions (20–40 ◦ C), the data measured for the first macroscopic stage seem to be the most important. There are two reasons for this: the relatively low temperature at which this stage is realised (264–346 ◦ C) and the low activation energy of the process (68 ± 2 kJ/mol). The activation energy of the first stage was also calculated by analysing the initial sections of the TGA curves. Supposing, as Kissinger [19], that the mass loss is described by the first-order reaction Eq. (3) and is stepwise, we get dm = −k(m − m1 ) dt

(3)

where m is the specimen mass at time t (and current temperature T), m1 is the residual specimen mass remaining after the completion of the first macroscopic stage of the thermo-oxidative degradation of the polymer and k is the degradation rate constant at temperature T. Taking into account the dependence of k on T in the Arrhenius equation:



k = k0 exp −



E RT

(4)

where E is the activation energy of the process and k0 is the preexponential factor, as well as relationship (5), dm =ˇ· dt

 dm  dT

,

(5)

3

10 373 222 ± 13

20 386

2 461

5 482

10 496 184 ± 11

20 518

or, in logarithmic form,



dm/dT ln m − m1



= − ln

k   E  0 ˇ

+

RT

.

(7)

As shown in Fig. 2 the first macroscopic stage is characterised by the relative small and constant activation energy. This peculiarity define the temperature range where the relationship (7) is consistent with linear dependence of ln[(dm/dT)/(m − m1 )] on 1/T at constant k0 and E. Analysis of the experimental data reveals that the linear dependence (7) is actually observed over a rather broad temperature range at physically reasonable values of the empirically tuned parameter m1 (Table 2). Fist-order kinetic model was used in the last case according to four main reasons: (1) this is one of a very common occurrence mechanism; (2) unlike the n-order kinetic model the only one parameter is varied; (3) the calculated values are consistent well with the experimental data (0.9936 ≤ R2 ≤ 0.9985); and (4) the agreement of the calculated value with the results determined by using other methods can be consider as an evidence that the initial stage of PVB degradation proceeds in accord with fist-order model. It is important that the activation energy of the initial stage of PVB degradation determined by using Eq. (7) does not depend practically on heating rate. Analysis on the basis of the dependence (7) may be extended on the more deep stages and allows constructing the complete dependence of the activation energy on the degree of conversion. However the problem in question is the PVB degradation at low degrees of conversion when polymer holds their mechanical and physicochemical properties and therefore the main effort is undertaken in the study of the first stage. The mean activation energy (61 ± 8 kJ/mol) at 172–361 ◦ C determined in this manner agrees rather well with the value obtained by the Kissinger–Akahira–Sunose (70 ± 4 kJ/mol) and the Kissinger method (68 ± 2 kJ/mol).

we get dm/dT =− m − m1

1  ˇ



· k0 exp −

E RT

 (6)

The high sensitivity of modern chromatographic methods has allowed the detection of the formation of volatile products during PVB heating at relatively low temperatures (80–120 ◦ C) for the first time. However, only one product, referred to as butanal, has been quantitatively characterised. Fig. 4 shows that the evolution of the product proceeds at a constant rate, which increases with temperature. The activation energy of this process is 60 ± 14 kJ/mol. Based on the temperature interval, this allows butanal formation to be assigned unambiguously to the first macroscopic stage of thermooxidative PVB degradation discussed in the previous section. The value obtained in this work is much lower than that of 226 kJ/mol reported in [1]. However, the latter value was determined from butanal evolution at 310–400 ◦ C. This difference suggests, following the authors of [1], that the current butanal evolution may be assigned to the second macroscopic stage.

-9,5 2

ln(β/Tmax ) -10,0

2

1

3

-10,5

-11,0

-11,5

-12,0

-12,5 1,3

1,4

1,5

1,6

3.2. Evolution of volatile products during low-temperature PVB oxidation

1,7

1,8

1,9

1000/T max

Fig. 3. Dependence of the temperature of the maximum degradation rate on the heating rate for three main stages of thermo-oxidative PVB degradation.

3.3. Functional group formation The formation of a single product, carbonyl groups, was detected (1715 cm−1 ) by the Fourier-IR analysis of the thermal ageing of

V.B. Ivanov et al. / Thermochimica Acta 589 (2014) 70–75

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Table 2 Activation energies (E) of the initial stage of thermo-oxidative PVB degradation calculated by using Eq. (7). ˇ (◦ C/min)

E (kJ/mol)

20 10 5 2

64.5 58.0 57.9 64.0

Mean activation energy E (kJ/mol)

61 ± 8

PVB films at 80–100 ◦ C. This is primarily due to the high extinction coefficients of these groups (∼200 dm3 /(mol cm)), which allows the measurement of their contents at low PVB oxidation rates at moderate temperatures. Fig. 5 shows that the carbonyl groups on the external surface of PVB films are accumulated at constant rates, which is weakly dependent on temperature. The activation energy obtained using these data is only 11 ± 1 kJ/mol, suggesting a complex multistage process. It is interesting that the internal PVB surface contiguous to the glass is barely oxidised under the same conditions (Fig. 5, lines 4 and 5). This occurrence is not associated with diffusion limitations, as the characteristic diffusion time  calculated from the Smoluchowski–Einstein relation (8) l2 4D

61 62 77 82

where l is the specimen thickness and D is the diffusion coefficient, is ∼1 min (at D ∼ 10−5 cm2 /s) at temperatures above the glass transition point. As follows from the data in Fig. 5, the typical reaction time is hundreds of hours, i.e., 5–6 orders of magnitude higher than the characteristic diffusion time. This effect is apparently due to the orientation and low molecular mobility of the polymer units near the glass surface. This hypothesis is supported by the increasing differences in the oxidation rates of the external and internal surfaces of PVB films with decreasing temperature (Fig. 5). Similar effects of the inert support on the thermal degradation of polymers have been reported, but the scope of this effect is usually small, contrary to the effects shown in Fig. 5. In contrast to the IR range, the UV–vis absorption spectra are complicated (Figs. 6 and 7).

(8)

18000

2

15000

A

12000 S/1000

m1 (%)

196–361 197–320 200–300 172–277

9000

3 1

6000

3000

1,4 1,3 1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 200

1,2

0,8

0,6

2

0,4

0,2

0,0 0

200

400

600

800 1000 1200 1400 1600 1800 2000 Time (h)

250

300

350

400

Wavelength (nm)

0 200

400

600

800

1000

1200

Time (min) ◦

Fig. 4. Butanal evolution during PVB heating at 80 (1), 100 (2) and 123 C (3) (based on the relative area under the chromatogram peak).

Fig. 6. UV absorption spectra of PVB film before (solid line) and after heating at 70 ◦ C (dash lines) for 90–1931 h. Inset: kinetics formation of dienes (absorption at 210 nm) during thermo-oxidative degradation at 90 (1) and 70 ◦ C (2).

3 0,5

2

2,0

0,6

1,8

0,5

1,6

0,4

1,4

0,3

A

0

0,4

A

0,0

0,8

1

2

0,1

1,0

0,3

1

0,2

1,2

A1715/A1104

1

1,0

A

=

Temperature interval (◦ C)

0

200

400

600

800 1000 1200 1400 1600 1800 2000 Time (h)

0,6

0,2

0,4 0,2

0,1

4 0,0 5

0,0 0

500

1000

1500

2000

Time (h) Fig. 5. Difference in the relative carbonyl group content (A1715 /A1104 ) on the external (1–3) and internal (4, 5) surfaces of PVB film at 100 (1), 90 (2, 4) and 80 ◦ C (3, 5).

200

250

300

350

400

Wavelength (nm) Fig. 7. UV absorption spectra of PVB film before (solid line) and after heating at 90 ◦ C (dash lines) for 19–1343 h. Inset: kinetics accumulation of trienes and diene carbonyls (absorption at 275 nm) during thermo-oxidative degradation at 90 (1) and 70 ◦ C (2).

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Table 3 Activation energies and temperature ranges of main processes of low-temperature thermo-oxidative PVB degradation. Process

Temperature range (◦ C)

Analysis method

Activation energy (kJ/mol)

Standard error (kJ/mol)

Mass loss Mass loss Mass loss Evolution of gaseous products (butanal) Accumulation of carbonyl groups Formation of diene and ␣,␤-unsaturated carbonyls Accumulation of trienes and diene carbonyls Formation of polyenes

184–300 264–346 172–361 80–120 80–100 70–90 70–90 80–100

TGAa TGAb TGAc GC IR-spectroscopy UV-spectrophotometry UV-spectrophotometry Spectrophotometry

70 68 61 60 11 78 137 201

4 2 8 14 1 – – 44

The value of activation energies determined by the Kissinger–Akahira–Sunose (a), Kissinger (b) methods and by Eq. (7) (c).

In the short-wavelength range (210 <  < 250 nm), the optical density first decreases slightly and only begins to slowly increase after longer heating times (Figs. 6 and 7). Absorption in this range is usually due to the presence of dienes and ␣,␤-unsaturated carbonyls [6]. The activation energy of the accumulation of these products, as assessed by the rate dependence on temperature, is 78 kJ/mol (at 210 nm, absorption maxima of dienes). In the longer-wavelength range, 250 <  < 350 nm, the PVB initially does not absorb, and the optical density increases monotonously (Figs. 6 and 7). This process proceeds at a nearly constant rate for a long time. The absorption bands in this range are usually attributed to trienes and diene carbonyls [6]. The activation energy of the formation of these products, as determined by the experimental data, is 137 kJ/mol (at 275 nm, absorption maxima of trienes). Only at the relatively high temperature of 100 ◦ C are significant changes in absorption in the near-UV range ( > 380 nm) and visible range (400 <  < 500 nm) observed (Fig. 8). The autoacceleration of this process is not unexpected because absorption in this range is associated with polyconjugated structures, which can only be formed from precursors with shorter conjugated chains. The activation energy of polyene formation as assessed by the difference in absorption at 400 and 435 nm is 201 ± 44 kJ/mol. 3.4. Comparison of TGA and other results Table 3 shows all processes studied in this work, their activation energies and the temperature ranges in which they were determined. Rather good correlation between the activation energy values calculated by all tree TGA methods (Table 3) is attributed primary that the reaction kinetics is analysed in the close temperature 0,5

1

0,4

Α

0,3

2

0,2

3

0,1

0,0 0

20

40

60

80

Time (days) Fig. 8. Absorption change at 400 nm during thermo-oxidative PVB degradation at 100 (1), 90 (2) and 80 ◦ C (3).

intervals 184–300, 264–346 and 172–361 ◦ C by using Eqs. (1), (2) and (7) correspondingly. It is important also that the one step is considered namely 1st low-temperature stage of thermo-oxidative degradation of PVB. Analysing these results, it is clear that there is a wide scatter of activation energies. At the same time, however, there is a relatively large group of processes with similar activation energies from 60 to 78 kJ/mol. Indeed, there are only two cases with particularly high deviations towards extreme values (11 kJ/mol and 201 kJ/mol). We attribute these deviations again to the fact that corresponding processes of carbonyl groups accumulation and polyenes formation are not of primary origin. It is commonly suggested that free-radical processes with the participation of vinyl butyral units that lead to butanal release are primary [1]. This, of course, leads to the mass loss detected by TGA as the first macroscopic stage. Trienes and diene carbonyls are accumulated at later stages as a result of the consecutive formation and decay of acyl radicals, and the effective activation energy is therefore noticeably higher. The qualitative correspondence of activation energies for thermo-oxidative PVB degradation obtained by TGA (the first stage) and the analysis of product formation by GC and spectrophotometry methods indicates that TGA data may be used for the assessment of this polymer stability at relatively low temperatures in addition to high temperatures. The principal consideration for this is the capability to resolve the macroscopic stages of the process and correctly to assess the parameters of the first, low-temperature macroscopic stage. The results shown in this work and some other known data [5,6] are related to the low-temperature range but this one is near or above the usual PVB glass transition point. However, it is known that when the glass transition point is exceeded, the molecular mobility of macromolecule units and the rate of chemical processes involving them change drastically. Therefore, it seems important to refine the lower-temperature border, at which established regularities should work. TMA investigations indicate the presence of fast relaxation processes in the cast PVB films in the range of 25–50 ◦ C. In this case, the inflection point of the TMA curve lies at 37 ◦ C. After preliminary heating at 140 ◦ C, the fast relaxation zone shifts towards higher temperatures (40–70 ◦ C), and the inflection point lies near 57 ◦ C, corresponding to the glass transition point of the studied PVB specimen. The lower glass transition point for the initial PVB film is apparently caused by the plasticising action of residual solvent (isopropanol) and adsorbed water. Preliminary heating eliminates the solvent and water, the content of which, as shown by special tests, can be up to 8.2% (at room temperature and 95% relative humidity). Therefore, based on the results presented, assessments based on PVB ageing results in the first macroscopic stage for cast films can be used up to +37 ◦ C and, with care, even up to +25 ◦ C. These results are also suitable for forecasting plasticised PVB ageing, as this material is most widely applied.

V.B. Ivanov et al. / Thermochimica Acta 589 (2014) 70–75

4. Conclusion Thus, using TGA studies of PVB, it is possible to discern the first, low-temperature macroscopic stage and to determine the activation energy of the corresponding process. In contrast with the second and the third stages, activation energy of the first stage closely fits those of the formation of gaseous products as well as dienes and ␣,␤-unsaturated carbonyls. Thus, its value can be used in the assessment of PVB stability at low temperatures. To assess and forecast PVB stability under common operational and storage conditions, the complementary accelerated testing at relatively low temperatures of 70–120 ◦ C with determination of gaseous products and ␣,␤-unsaturated carbonyls are preferable. References [1] L.C.K. Liau, Y.C.K. Thomas, D.S. Viswanath, Mechanism of degradation of poly(vinyl butyral) using thermogravimetry/Fourier transform infrared spectrometry, Polym. Eng. Sci. 96 (1996) 2589–2600. [2] M.D. Fernandez, M.J. Fernandez, P. Hoces, Synthesis of poly(vinyl butyral)s in homogeneous phase and their thermal properties, J. Appl. Polym. Sci. 102 (2006) 5007–5017. [3] A.K. Dhaliwal, J.N. Hay, The characterization of polyvinyl butyral by thermal analysis, Thermochim. Acta 391 (2002) 245–255. [4] R. Liu, B. He, X. Chen, Degradation of polyvinyl butyral and its stabilization by bases, Polym. Degrad. Stab. 93 (2008) 646–853. [5] N.N. Kolesnikova, S.G. Kiryushkin, P.S. Voskanyan, A.A. Aslanyan, A.P. Mar’in, On the role of hydroperoxide groups in yellowing of polyvinyl butyral, Polym. Sci. Ser. B 31 (1989) 146–148. [6] V.I. Grachev, I.B. Klimenko, L.V. Smirnov, A.F. Gladkikh, A spectroscopic study of the kinetics of thermal-oxidative degradation of polyvinyl butyrals (PVB), Polym. Sci. Ser. A 16 (1974) 367–373.

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