Polymer Degradation and Stability 91 (2006) 2595e2604 www.elsevier.com/locate/polydegstab
The reciprocal influence between ion transport and degradation of PA66 in acid solution Abastari a,*, T. Sakai a, H. Sembokuya b, M. Kubouchi a, K. Tsuda a a
Department of Chemical Engineering, Tsuda and Kubouchi Laboratory, Tokyo Institute of Technology, 2-12-1 S1-17, O-okayama, Meguro-ku, Tokyo 152-8552, Japan b Sembokuya Co., 41 Higashimatano-cho, Totsuka-ku, Yokohama-shi, Kanagawa 245-0065, Japan Received 6 April 2006; received in revised form 17 May 2006; accepted 23 May 2006 Available online 25 July 2006
Abstract Transport behavior of acid solution through polyamide was studied by measuring element distribution in cross section, pH, and ion concentration. Degree of degradation that related to the decreasing of molecular weight and flexural strength was observed in order to study the influence of acid solution on the polyamide 66 (PA66) degradation. The permeation mechanism of acid solution can be explained: at first water penetrates into polyamide and it is followed by acid. In this process, water does not affect the molecular weight at 50 C but only reduces the polyamide strength by plasticization. Moreover, proton (Hþ) has contributed to the anion transport and degradation of polyamide by the hydrolytic reaction. Proton attacks the polyamide chain, and scission of chain occurs, and reacts with anion to form other material substance. This process affects the decrease of molecular weight and the significant loss of polyamide strength. Analysis results from ion concentration measurement shows that the amount of proton and anion transport into deionized waterside was imbalance, which probably due to the different mobility between proton and anion or formation of other material substance by reaction of anion and PA66 bond. Such information is not only necessary for the investigation of hydrolytic degradation of polymer and prediction of lifetimes for a protective polymer lining/coating to chemical attack, but may also be helpful towards gaining a deeper insight into the processes of degradation of other polymer. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Diffusion; Permeation; Ion transport; Polyamide; Proton; Degradation
1. Introduction Polymeric materials are currently utilized in material technology for many aspects. It is encountered in almost every area of modern life. It has been utilized for micro-electronic, manufacturing in the industrial equipment, composite application, implanted components in human bodies, etc. This is attributed to the fact that polymeric materials offer good thermal stability, good mechanical properties, low dielectric constant and good chemical resistance [1,2]. One of the advantages of polymeric materials is its high resistance to chemical environments.
* Corresponding author. Tel./fax: þ81 03 5734 2124. E-mail address:
[email protected] (Abastari). 0141-3910/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymdegradstab.2006.05.018
Polymeric materials are used as lining for metal, concrete and others in order to protect a base material from the corrosion that is caused by environmental solution. During the application, thermal stress, permeation/penetration, absorption, inadequate surface preparation, operation and others, may reduce polymeric materials’ performance. However, corrosion resistance of polymeric materials in service is closely interwoven with the chemical stability of polymers [3e5]. The lifetimes of materials are directly related to the environments to which they are exposed. The behavior or permeability of environmental solution that passes through the polymer lining is one of the critical factor. Penetrants may enter a polymeresubstrate system via penetration/permeation (absorption, diffusion and sorption) through the polymer bulk and/or cracks and crazes. Once a penetrant is introduced into a system, it may lead to a variety of chemical and physical
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changes in the material, some of which include plasticization and swelling of the material and/or creation of a weak boundary layer between the lining and substrate. These changes may affect its performance [3e14]. The research that reported the kinetic study of comparison between penetration/permeation of environmental liquids and chemical degradation is insufficient. In the corrosion of a polymeric material, it is important to evaluate both penetration/ permeation of environmental solution and chemical degradation of polymeric materials, even into molecular level of ion mobility of the diffusion of electrolyte solution. On the other hand, in the combination of polymeric materials and environmental liquids, some environmental liquids may permeate without being accompanied by chemical degradation of material [14e20]. Although it is an important factor how environmental solution passes through the lining, researches about this topic are few until now. Therefore in this research, the study on penetration/permeation behavior of an acid solution in the molecular level was carried out and to be an objective in order to know the mechanism of how the electrolyte solution diffuses and reacts with polymer bulk. Permeation of environmental liquids is generally very slow in many cases of corrosion-resistant polymeric material. Thus, studying the combination of penetration/permeation and degradation becomes difficult. Almost all the polymeric materials that are used for lining have small permeability for the environmental solution, and it will take a long period to observe the permeation phenomena and degradation mechanism. Therefore the comparable level of diffusion and reaction rate of penetrant in polymer bulk are needed. For this reason, polyamide 66 (PA66) was used for investigating the penetration/ permeation mechanism of penetrant and degradation behavior of polymeric materials. PA66 is a convenient test material for studying corrosion process due to its hydrophilicity and degradability (e.g. in acid solution). Several studies have been published on the diffusion of environment solutions into polyamide and degradation of polyamide in acid environments [14e18,21e24]. The work presented here deals with transport behavior of acid solution through polymers (PA66) by measuring the diffusion rate of penetrant, pH, ion concentration and degree of degradation which corresponds to the decreasing of molecular weight and flexural strength. Quantitative analysis of acid transport and its reaction rate will be presented in other paper. Such information is not only necessary for the investigation of hydrolytic degradation of polymer and lifetimes of protective polymer lining/coating to chemical attack, but may also be helpful towards gaining a deeper insight into the processes of biological degradation of polymeric materials intended for use in medicine, e.g. artificial organs and surgical sutures [3]. Since different investigators use different definitions of permeation and penetration, definitions from ASTM F739 (for permeation) and ASTM F903 (for penetration) are used in this research. Permeation is defined as the process by which a chemical moves through a material on molecular level by the process of absorption, diffusion and desorption. Penetration is defined as the physical transport of chemical from one side of
the material to the other side of the material such as through imperfections, hole, tears, crack, etc. [25,26]. These two definitions are applied and generalized in this study. 2. Experimental procedure Penetrants/electrolytes diffusion in polymers may be determined by standard techniques conventionally used for investigating the solubility and diffusion of low-molecular weight compounds in polymers. Measuring the weight change of a sample is one of the common method and technique which is being used. The variations in sample weight will be due to the concurrent sorption of water and electrolyte molecules [3e5]. This technique was used in this research to observe the penetration/permeation behavior of penetrants or electrolytes. 2.1. Materials and conditions The polymer utilized in the present study as test material is a commercial PA66 (UBE 2020). The specimen geometry for permeation test was 80 80 mm with 2 mm or 1 mm thickness. Before permeation test, the specimen was washed with soap to ensure that remained release oil was removed from specimen. Specimen was dried in thermostat chamber at 50 C for at least 100 h to ensure that its weight reached a steady state condition. At this condition, it was assumed that most of water in PA66 has been evaporated during that time. PA66 was tested in this work under some acid conditions for several days. In addition Na2SO4 was also used in order to study the influence of proton on the anion transport. 2.2. Permeation test Permeation test was done by setting the specimen between stagnant acid solution and deionized water as shown in Fig. 1a and b. One side was contacted with the acid and the other side with deionized water. Temperatures at both sides were set to be same and controlled automatically to be at 50 C. 2.3. Permeation/diffusion analysis Penetration/permeation analysis was done by measuring weight change, penetration depth of sulfur (S)/chlorine (Cl) element and pH of deionized water. 2.3.1. Measurement of weight change Specimen was removed at regular time intervals, and carefully wiped to remove excess penetrant. Specimen was kept at room temperature for 1 h before its weight was measured. Specimen was weighed using microbalance. The penetrant uptake was determined by obtaining the change in mass of specimen at different times, relative to the initial mass. 2.3.2. pH measurement pH was also measured in the waterside by digital compact pH meter with 0.1 decimal in accuracy.
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2.4. Degradation analysis The degree of PA66 degradation was evaluated by observing the crack propagation using SEM, molecular weight analysis and flexural strength measurement. 2.4.1. Analysis of molecular weight In this research, SEC (size exclusion chromatography) system was used to evaluate degradation of PA66. The mixture of m-cresol/chloroform (35/65 weight ratio) was used as mobile phase for SEC system. PA66 was dissolved into this mixture. About 10 mg of PA66 sample was taken at the specific thickness (0.1e0.2 mm) for injection. This sample was dissolved into 10 ml of m-cresol/chloroform mixture with the same composition as mobile phase for almost 2 h to ensure that all of PA66 samples were dissolved completely and ready to be analyzed. 2.4.2. Strength evaluation by three point bending test Three point bending test of PA66 was done after permeation test. This test was done in two conditions; an acid side to be tensile and waterside to be tensile conditions, respectively. Specimen was cut to be 60 25 mm in size from the center of specimen for this test. 3. Results and discussion 3.1. Penetration/permeation behavior of acid solution
Fig. 1. Schematic apparatus of permeation test (a) permeation test condition, one side was contacted with penetrant (acid solution) and water at the opposite side and (b) complete schematic of instrument.
2.3.3. Ion chromatography measurement In order to detect the presence of anion and its concentration in deionized waterside, ion chromatography measurement was done. Ion concentration was measured in deionized water after permeation test at specific time interval. Due to the limitation of instrument ability which cannot measure the concentration of ion above 100 ppm or it has to be diluted, concentration of 5 wt% H2SO4 was decided to be used for permeation test in this analysis for the convenience. 2.3.4. Energy dispersive X-ray spectrometer (EDS) Penetration depths of sulfur (S) and chlorine (Cl) elements in this research were monitored by combination of scanning electron microscope (SEM) and X-ray analysis on cross section of PA66. EDS results described the distribution of sulfur or chlorine element in PA66, and penetration depth of both elements were determined from this profile. In addition, Electron Probe Micro Analyzer (EPMA) was also used to detect sulfur and chlorine elements. EDS and EPMA measurements gave the same results of element profile and distribution. Therefore, only EDS results were presented in this paper.
Penetration/permeation behavior of sulfuric acid solution has been studied systematically. Weight change and concentration profile of sulfuric acid in PA66 have been measured to discuss the mechanism. Weight change of PA66 after contacted with sulfuric acid solution is shown in Fig. 2. These figures show the weight uptake of PA66 after contacted with acid solution in different concentrations and deionized water system at 50 C. In Fig. 2a there are two saturation stages observed. It can be identified that the system reaches the first saturation around 100 h and after that the weight change increases significantly. On the other hand, from Fig. 2a, penetration depth of sulfuric acid in PA66 reaches about a half of thickness at 120 h (t1/2 y 11). The first saturation in Fig. 2a may be mainly obtained by water diffusion from both sides of surface. Water penetrates into PA66 at first and then it is followed by sulfuric acid. Main mechanism is that water diffuses and fills the free volume of PA66 until first saturation is reached. After 120 h, the weight change increases sharply. This phenomenon is also found in Fig. 2b for other H2SO4 and HCl concentrations and for the experiment using 1 mm thickness of specimen. The sharp increase in weight change can be caused by crack occurred after this time due to PA66 degradation. Thus, weight uptake will shift to second saturation stage. The weight change increases again due to acid diffusion. Results in Fig. 2a and b for PA66 immersed in H2SO4 and HCl, show the same trend in which two saturation stages are recognized. This behavior is not found for example when PA66 contacted in 0.5 M sulfuric acid solution where crack
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Fig. 3. Gradation in mapping data or slope line in line analysis shows the distribution of S element in PA66, and horizontal line is unpenetrated region of S element. The intersection point of both these lines was determined as penetration depth. Fig. 4 shows the change of distribution of S element in PA66 with time increase after permeation test in 10 wt% H2SO4 e deionized water system at 50 C. As can be observed in Fig. 4, concentration profile of S element in PA66 shows the trend of Fickian diffusion as shown in 72 h. Then, penetration depth of S element into PA66 increases gradually as permeation time increases. After 408 h immersion, crack or highly degraded regions are recognized at the surface of H2SO4 side. At this region, S element distribution is horizontal. It can be caused by the increase in permeability due to the degradation by sulfuric acid solution. Crack or craze reduces the resistance of PA66 to the diffusivity of solution. 3.2. Ion transport behavior of acid solution In case of electrolyte solution diffusion, proton is considered to contribute to the degradation of PA66 and anion transport. Many literatures have discussed about the degradation of PA by the mechanism of hydrolytic reaction where proton takes part in the reaction [3,5,7,15,16]. However, until now there is no sufficient information, which explained about the anion in their mechanism through the polymer and its effect to the degradation mechanism. In this research, PA66 was contacted with different of environmental solutions (H2SO4, HCl, and Na2SO4) in order to study the influence of proton to the anion transport. The pH of waterside or Na2SO4 solution
Fig. 2. (a) Weight change of PA66 and penetration depth of S element (2 mm thickness) after permeation test in 10 wt% H2SO4 e deionized water system (50 C) at different permeation times, where x ¼ penetration depth of S element and L ¼ overall thickness of PA66 and (b) weight change of PA66 (1 mm thickness) at different times after permeation test in H2SO4, HCl e deionized water system at 50 C.
does not occur as can be observed in Fig. 2b. When crack occurs the weight change will increase significantly due to poor resistance to penetration for sulfuric acid or hydrochloric solution and water [27]. Acid and water sorption in moderate hydrophilic polymers, such as PA66, is rather complex phenomenon due to interactions between water, acid solution and polymer [3,28]. However, from weight measurement, it shows that relationship between weight gain led initial proportionality to t1/2. Thus diffusion type of sulfuric acid solution into PA66 at the initial condition (before crack occurs) can be categorized following the Fickian diffusion theory [29e38]. Analysis results from EDS measurement of S element on cross section of specimens also show good agreement. Penetration depth of S element was determined visually from the EDS analysis as shown in
Fig. 3. Determining method for penetration depth of S element in PA66 from EDS results.
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was measured in order to detect the presence of proton. To detect the presence of SO2 4 ion and Cl ion in PA66, sulfur and chlorine elements were observed by EDS to get the penetration depth of the element into PA66. 3.2.1. Ion transport of acid solution Fig. 5 shows the measurement results of deionized water pH and its relation with penetration depth after permeation test in H2SO4 and HCl solutions. As can be seen, pH of deionized water changes with time. When the pH of deionized water decreases, it means that the acid solution (especially proton) passes throughout PA66. The relationship between decreasing of pH and penetration depth of S or Cl element may be compared in Fig. 5a and b. As seen in Fig. 5a and b, pH of water is
Fig. 4. Change of distribution of S element in PA66 with time increase that obtained from EDS after penetration test in 10 wt% H2SO4 e deionized water system at 50 C (highly degraded PA66 for 408 h or more that severe crack and some of them with surface lost observed, is describe as hatching region).
Fig. 5. pH of deionized water and penetration depth of S element after contacted with acid solution, where x is defined as penetration depth of S/Cl element and L is overall thickness of PA66 (a) 10 wt% sulfuric acid solution with 2 mm thickness and (b) sulfuric acid and hydrochloric acid solution with 1 mm thickness.
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found to decrease after sulfur (S) or chlorine (Cl) reaches into the waterside. Deionized water after permeation test of specimen in 5 wt% H2SO4 e water system was analyzed. The results are plotted in Fig. 6, which gives the information about SO2 4 content (in ppm) in deionized water obtained by ion chromatography after permeation test and then the comparison data that are obtained by calculation from pH of deionized water. In Fig. 6, the concentration of SO2 4 increases with the increase of pH in waterside. However, a interesting phenomenon has been observed in this measurement. Fig. 6 shows that, at early period, SO2 4 content of experimental data in water is always higher than calculated values and then gradually be lower than calculated values. If the mobility of proton and SO2 4 is in the same rate, SO2 4 content in water (from experiment/ion chromatography) should be close to the calculated values. The difference between experimental results and the calculated one for SO2 4 indicates that proton and SO2 ion probably have different 4 rates of mobility or SO2 ion interacts with PA66 bond to 4 form other material substance in their diffusion process in PA66.
3.2.2. Proton contribution to the anion transport Some experiments have been done to study the influences of proton to anion transport in polymer bulk. For this purpose, deionized water, hydrochloric acid and Na2SO4 were used as the environmental liquids. In order to check whether Na2SO4 is able to penetrate into PA66 or not, specimen of PA66 was examined in condition between 1.0 M Na2SO4 and 1.0 M HCl solutions as shown in Fig. 7aec. At this condition, Cl element penetrates into PA66. On the other hand, penetration of S element could not be identified at the other side even the Cl element has passed through all the thickness of PA66 after extended period of permeation time as shown in Fig. 7b and c. In addition, the other experiment was also done separately. Specimen was placed into 1.0 M Na2SO4/1.0 M HCl mixture and deionized water system with the same temperature condition as shown in Fig. 7d. In this case, both penetrations of S and Cl elements were observed in PA66 from the EDS analysis. From these results, we consider that proton has a contribution to the anion transport. Anion is not able to transport into PA66 without the presence of the proton. 3.3. Degradation behavior of polyamide
Fig. 6. (a) SO2 4 ion content and decreasing of pH in deionized water at different times after permeation test in 5 wt% H2SO4edeionized water system at 50 C and (b) expanded scale for low ppm data shown in (a).
3.3.1. Decreasing of molecular weight The influence of acid permeation on the molecular weight change of PA66 was investigated [15,16]. The decrease in molecular weight corresponds to the degradation of polyamide due to chemical reaction by acid hydrolysis [7,8,15e 18,24,35]. The mechanism of acid permeation and its influence on the molecular weight change were studied in more detail in this research. Fig. 8 shows the distribution of PA66 molecular weight at surface of PA66 specimen after contacted with 10 wt% H2SO4. There is a shift of curve with time which indicates a change in the molecular weight. The change in the breadth of the curves, which shows the molecular weight distribution, is quite significant. Average molecular weight decreases with time increase. The diffusion of acid and chemical reaction itself are mechanisms which result in a decrease in molecular weight of polymer by hydrolysis. Average molecular weight distribution along the depth of specimen is plotted by using the ratio of average molecular weight before (M0) and after (M ) penetration/permeation test as shown in Fig. 9. Fig. 9 shows the decrease in average molecular weight along the thickness of PA66 with time variable. Molecular weight of PA66 decreases from H2SO4 side as time increases. Reducing the molecular weight will affect not only to the loss of PA66 strength but also probably to the increase of the diffusion rate of acid solution. In crack region, it is assumed that there is an insignificant resistance for penetrant to flow into PA66, i.e. a very high diffusion coefficient. The diffusion rate of solution in this region may be assumed as infinite and predicted to be constant, as some scientists have observed [27,36]. In addition, in Fig. 9, average molecular weight is not found to decrease at waterside. Water does not affect the molecular weight of PA66 at 50 C. The decrease in molecular weight that observed at waterside for 610 h of permeation time was caused by the sulfuric acid permeation that diffused through the thickness of PA66 as shown in Fig. 4.
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Fig. 7. Distribution of S and Cl elements in PA66 after contact with (a) 1.0 M Na2SO4 and 1.0 M HCl at 50 C for 16 h, (b) 1.0 M Na2SO4 and 1.0 M HCl at 50 C for 70 h, pH of Na2SO4 was detected as 4.7, (c) 1.0 M Na2SO4 and 1.0 M HCl at 50 C for 240 h, and (d) 1.0 M HCl/1.0 M Na2SO4 mixture and deionized water at 50 C for 16 h.
Relationship between penetration depth of anion (SO2 4 ) and degradation of PA66, which in this case is defined by the decrease in molecular weight, is observed as shown in Fig. 10. For example in Fig. 10, for 236 h of permeation test, penetration depth of S element is shown around 1.35 mm from H2SO4 side, where at the same time decrease in molecular weight of PA66 is also observed at 0e1.35 mm of thickness. The decrease in molecular weight occurs at the region where sulfur element exists. Sulfur element might have contributed to the reaction mechanism. EDS analysis and pH measurement show the rational results that sulfuric acid solution passes into waterside for 408 h of permeation time. Furthermore, even though S element passes through the PA66 thickness, molecular weight of PA66 is not degraded by low concentration of S element as shown in Fig. 9. It might be degraded but reaction rate is very low due to low concentration of S element. Hydrolytic reaction is considered to occur at low reaction rate. Strong acids in relatively low concentration have relatively low effect on reaction rate [17].
Fig. 8. PA66 molecular weight distribution on the surface of PA66 specimen (0e0.1 mm) after penetration/permeation test in 10 wt% H2SO4 e deionized water system at 50 C.
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Scheme 1.
anion are considered to have different mobilities in this process. On the other hand, SO2 4 ion probably makes their way into amine terminal and forms other substance (Scheme 2).
Fig. 9. Average molecular weight distribution of polyamide 66 along the thickness after permeation test in 10 wt% H2SO4 solution (M ¼ molecular weight after permeation test, M0 ¼ molecular weight before permeation test).
From the explanation above, we have observed the relationship between anion and PA66 degradation. Proton and anion collaborate together in PA66 degradation. Some references give the schemes of hydrolytic reaction in PA by the acid solution. But until now, it cannot explain clearly about the interaction between acid ion and PA bond in the process of degradation [3,14,16,17]. Myagkov and Pakshver considered the ionexchange model (Scheme 2). In this model it is assumed that proton of solution does not make their way into the polymer; only anion diffuses and takes part into anion exchange [3]. Referring to the results which has been explained before, that proton and anion take part in PA66 degradation and the possibility of SO2 4 ion interacts with PA66 bond, PA66 degradation by acid solution probably occurs according to the reaction in Schemes (1) and (2). Proton makes reaction with amide group of PA66, and then SO2 ion comes into system and makes 4 bond with proton from amide group (Scheme 1). Proton and
3.3.2. Change of mechanical property Decrease in molecular weight will cause the loss of strength [18,38e40]. Flexural strength of PA66 was measured after permeation test in order to know the decrease in mechanical properties and its relation with the molecular weight. As has been explained before, deionized water did not affect the average molecular weight at 50 C. The decrease in molecular weight was started from acid side. Thus flexural strength of test pieces gave different results when the test was done in two tensile conditions: an acid side (degraded part) to be tensile and waterside (undegraded part) to be tensile. Fig. 11 shows the retention of flexural strength of PA66. Rapid decrease in flexural strength is recognized after the permeation of acid and water. When condition of waterside is tensile, the flexural strength decreases sharply due to plasticization by water permeation. Then the flexural strength shows constant after 120 h of permeation due to the uniformity of plasticization by water permeation in PA66. From EDS and pH measured data, sulfuric acid diffuses through the whole polymer for 408 h of permeation time, but flexural strength does not found to decrease. At the same time, in Fig. 9, the decrease in molecular weight of the waterside surface is also not found. The low concentration of sulfuric acid in polymer at waterside is not enough to degrade the polymer for 408 h. The flexural strength decreases again after 610 h due to the acid that penetrate through the whole thickness from the other side, degrade the polymer. The decrease in molecular weight is also recognized at this time as seen in Fig. 9. These flexural strength results show good agreement with molecular weight measured in Fig. 9. On the other hand at the opposite condition when acid side is tensile, the flexural strength decreases monotonously with increase in time. 4. Conclusion Permeation behavior of acid solution in terms of ion transport was studied and some results have explained about the
Fig. 10. Relationship between penetration depth of S element and reducing of molecular weight distribution of polyamide 66 along the thickness after permeation test in 10 wt% H2SO4 e water system for 236 h.
Scheme 2.
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Fig. 11. Comparison between retention of flexural strength of 2 mm thickness of PA66 at wet condition, where waterside and 10 wt% H2SO4 side are as tensile.
mechanism and phenomena. Permeation behavior of acid solution into PA66 can be explained as follows; at first, water penetrates into polyamide and then it is followed by acid. In this process, water does not affect the molecular weight but only reduces the polyamide strength by plasticization. Moreover, proton (Hþ) ion has contributed to the anion transport and degradation of polyamide by the hydrolytic reaction. Anion is able to diffuse into PA66 by interacting with proton. Proton attacks the polyamide chain and scission of chains occurs. Anion is observed to take part in this reaction process. The chain scission affects the reduction of molecular size and the loss of polyamide strength. Therefore when swelling occurs, crack will grow and propagate easily. This process will decrease the strength of polyamide significantly. In addition, from the ion concentration measurement, the amount of SO2 4 ion in deionized water was observed to be less than predicted by calculation. It might be caused by the interaction/bonding of SO2 4 ion with other PA66 bond to form other material substance or different mobility of SO2 4 ion and proton. Acknowledgements The authors would like to thank UBE Co. for supporting PA66 specimens (UBE 2020B). Additional thanks are also to Sho-bond Co. for supporting the EPMA and ion chromatography analysis in this research. References [1] Michael E, Bever B. Encyclopedia of material science and engineering. Cambridge: Pergamon Press Ltd.; 1986. p. 3728e51. [2] Kim H, Jang J. Corrosion protection and adhesion promotion for polyimide/copper system using silane-modified polymeric materials. Polymer 2000;41(17):6553. [3] Zaikov GE, Iordanskii AP, Markin VS. Diffusion of electrolytes in polymers. Oxford: Alden Press Ltd.; 1988.
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