Structure and properties of poly(ethylene-co-chlorotrifluoroethylene) and polyvinylidene fluoride exposed to water, hydrochloric acid, hydrobromic acid and tetrachloroethylene.
Fluoropolymers are used extensively as linings or coating materials to protect steel or glass-fiber rein-forced plastics (FRP) in metal-aggressive environments and often at elevated temperatures. Their excellent thermal resistance and chemical resistance make them attractive as protection for process components in the pulp and paper, metallurgical, chemical, petrochemical, pharmaceutical and electronic industries. Common environments here include hydrofluoric acid (1), wet chlorine gas (2), outlet brine (3), water and hydrochloric acid (4).
Despite the fact that fluoropolymers have been used for a long time, little is known about their long-term performance in severe environments. It is important to clarify the chemical-polymer interactions, e.g. the sorption and desorption characteristics of these polymers, in order to assess the long-term properties of the polymer products. Limited information exists on the mechanism and behavior of acid transport in polymers, see e.g. (5-7). Although the lining itself appears to be unaffected by the chemical, the underlying substrate may be attacked since the chemical may diffuse rapidly through the lining. For example the condensation of water on the inside of the lining can lead to debonding, void formation and early failure (8).
This study aims at exploring the transport properties of hydrochloric acid and hydrobromic acid in a dipolar fluoropolymer, poly(ethylene-co-chlorotrifluoroethylene) (ECTFE) (two grades), and a hydrogen bonding fluoropolymer, poly(vinylidene fluoride) PVDF (four grades) (Table 1). The acid transport properties are compared with the transport of water and tetrachloroethylene in order to reveal possible differences between acid and non-acid transport. For practical reasons, it is also important to see whether the polymers are affected physically and/or chemically by any of the chemicals at the elevated temperature. Size exclusion chromatography, infrared spectroscopy, tensile testing and differential scanning calorimetry were employed to obtain this information.
The characteristics of the materials are presented in Table 1. The polymers were kindly supplied by Ausimont S.p.A., Italy. Tetrachloroethylene (TCE) was a 99.5% purity grade (Kebo Lab., Sweden: [[rho].sub.TCE] = 1110 kg [m.sup.-3]). Deionized water, 35%HCl (Prolabo/Merck Eurolab; [[rho].sub.HCl] = 1180 kg [m.sup.-3] and 47%HBr (Kebo Lab., Sweden, [[rho].sub.HBr] = 1490 kg [m.sup.-3]) were used. ECTFE and PVDF were compression molded into 1-mm-thick and 1.5-mm-thick plates at, respectively, 260[degrees]C and 200[degrees]C. The samples were preheated between the plates for 5 min under a pressure of 0.2-0.3 MPa, followed by an off-gasing procedure involving 20 strokes from 0 to approx. 1-1.3 MPa for about 30 seconds. They were then exposed to a pressure of approximately 4 MPa for 2 min. The cycle was ended by water-cooling the plates for 2-3 min, with the pressure maintained at approximately 4 MPa. The reference and the exposed specimens were obtained from respectively rectangular and circular samples from different batches. The masses of the dry polymer samples ranged between 1 and 1.26 g.
Sorption and Desorption Measurements
The sorption experiment was performed on single specimens of each grade by immersing the specimen at 70[degrees]C in a bottle containing the liquid. The mass increase was recorded by intermittently weighing the surface-dried sample using a Sartorius balance with an accuracy of [+ or -]0.02 mg (the relative error of the measurements were 0.003% with a standard deviation of 1 X 1[0.sup.-5] g). The desorption experiment was performed by placing the solute-saturated specimen in a 70[degrees]C warm "air-conditioned" heating chamber. The mass decrease was recorded by intermittently weighing the specimen using the same balance. The sorption-desorption cycle lasted for between 175 and 376 days. The diffusivities and permeabilities were calculated from the desorption data.
Differential Scanning Calorimetry
The melting endotherms of the polymers were obtained by heating 5 [+ or -] 0.3 mg samples at a rate of 10[degrees]C mi[n.sup.-1] between -10[degrees]C and 300[degrees]C using a temperature- and energy-calibrated Mettler-Toledo DSC 820.
The stress-strain properties were measured on 25-mm-long desorbed and dry dumbbell-shaped specimens (thickness typically: 0.75-1.5 mm; width of narrow section: 2.2-3.25 mm; gauge length: 10 mm) at 25[degrees]C and 40% relative humidity using an Instron Testing Instrument Model 5566. The strain between gauges was recorded at a strain rate of 500 mm mi[n.sup.-1] and the Young's modulus was calculated as the initial slope of the stress-strain curve. The tensile tests on exposed material were obtained on specimens that had been subjected to a complete sorption-desorption run at 70[degrees]C, for 175-376 days depending on the specific solute, and subsequently stored at room temperature.
Size Exclusion Chromatography
Size exclusion chromatography (SEC) was performed by first dissolving 1 mg PVDF material at 70-100[degrees]C in 10 ml dimethyl formamide (DMF) for 2 min and subsequently exposing the solution to ultrasonic stirring for a few minutes. The procedure was repeated 3 times. The solution was subsequently filtered through nylon filters (pore size ~ 0.45 [micro]m), and the filtered solution was injected into a Waters GPC system using a solvent delivery system (model 510), automatic injector (WISP 712) and a differential refractometer (Waters 410) as detector. All measurements were performed at 70[degrees]C with a 10 [micro]m mixed B column from Polymer Labs. DMF was used as solvent at a flow rate of 1.0 mL/min. Linear polyethylene oxide was used for calibration.
A Perkin-Elmer 2000 FTIR-spectrophotometer, equipped with a Golden Gate accessory from Grasseby Specac, was used to obtain reflection-IR-spectra.
For a plate geometry. Fick's second law of diffusion (9) is given by:
[[[partial derivative]C]/[[partial derivative]t]] = [[[partial derivative]]/[[partial derivative]x]] [(D(C)[partial derivative]C]/[partial derivative]x]) (1)
where D is the diffusivity, x is the distance, t is time and C is the solute concentration in the polymer. Only half the plate thickness was considered and the inner boundary co-ordinate was described as an isolated point. During desorption, the surface solute concentration was assumed to be zero. The concentration-dependent diffusivity (D(C)) was expressed (10) as:
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII (2)
where [D.sub.co] is the zero concentration diffusivity and [[alpha].sub.D] is the "plasticisation power". This equation has been used extensively and it has been shown that it fits diffusivity data well (11), (12). In addition, it can be derived and motivated by applying free volume theories (13), (14). Equation 1 in combination with Eq 2 and the appropriate boundary conditions given above was solved using a multi-step backwards implicit method described in detail by Edsberg and Wedin (15) and by Hedenqvist et al. (16), (17).
RESULTS AND DISCUSSION
Prior to the analysis and discussion of the desorption data, the chemical and physical impacts of the different chemicals are determined and discussed.
Size exclusion chromatography revealed that exposure to [H.sub.2]O, TCE, 35%HCl or 47%HBr did not affect the molar mass of the PVDF grades. It was not possible to obtain size-exclusion chromatography data on ECTFE due to the difficulty of finding a solvent suitable for both ECTFE and the SEC instrument.
The infrared spectra of the exposed ECTFE materials were identical to the spectra of the unexposed materials. However, the infrared spectra of the PVDF materials that had been exposed to the aqueous solutions (water, 35%HCl and 47%HBr), contained many small peaks in the 3500-4000 c[m.sup.-1] and the 1450-1900 c[m.sup.-1] regions. These "disturbances" were absent in the unexposed and the TCE-exposed materials. Consequently these peaks seem to have originated from changes in the polymer hydrogen-bond structure imposed by the presence of water and/or simply peaks from the water itself. Even though the materials were desorbed, a small amount of water must have remained. The water uptake in PVDF3 is at the most 0.04% at ambient temperature (ISO 62. method 1, (18)). The solute exposure also discolored some specimens.
Differential scanning calorimetry revealed no changes in the two ECTFE grades upon chemical exposure. The only features observed were the glass transition temperature in the vicinity of 40-50[degrees]C and the melting region from 150[degrees]C to 250[degrees]C. The PVDF materials showed what is referred to as the upper glass transition temperature in the vicinity of 30-60[degrees]C (19). This transition more or less overlapped the onset of melting. A distinct shoulder also appeared, peaking slightly below 100[degrees]C, in all PVDF grades exposed to all chemicals. Since this shoulder was absent in all the unexposed grades, it may originate from an annealing effect. The solute sorption/desorption cycle at 70[degrees]C lasted for 175 to 376 days and it is probable that low-temperature PVDF crystals developed during this thermal treatment (20). Unfortunately, due to unsmooth baselines, it was not possible to quantify the crystallinity increase during the annealing, IR spectra also showed indications of the presence of both [alpha] and [beta] crystallinity and it seemed that the [beta] crystallinity had increased slightly relative to the [alpha] crystallinity in the annealed specimens, in accordance with what has previously been reported (21), (22).
Table 2 shows the mechanical properties of the unexposed and exposed materials. An increase in stiffness, sometimes coupled with a reduction in ductility, of exposed ECTFE1 was observed with all the solutes. Several of the exposed PVDF resins became stiffer and occasionally they also became less ductile. This phenomenon was observed with all the chemicals, suggesting that it is related to the long-term thermal treatment (annealing) during the sorption/desorption cycle, and that it may not be due to any chemical attack. The thermally induced crystal growth, observed in PVDF probably stiffens the polymer. A small increase in modulus and a small decrease in fracture strain were observed by El Mohajir and Heymans (23) on compression-molded PVDF specimens annealed at 80[degrees]C for 10 days.
Figure 1 illustrates the sorption characteristics. It shows sorption curves for the aqueous solutes and for TCE in ECTFE1 and PVDF3. All the sorption curves were characterized by an induction period/sigmoidal shape at short times. This sigmoidal shape in the case of TCE is suggested to be due to swelling-induced mechanical stresses (24). Since the degree of swelling was much lower with the aqueous solutes, the s-shape or induction period is not obviously related to stresses. Figure 1b shows that the mass increase showed a maximum ("overshoot") for 35%HCl in PVDF3. Such behavior was also observed, to various degrees, with the other PVDF grades, but not in ECTFE, at least not to any extent significantly greater than the large experimental scatter. The occurrence of a maximum could be due to extraction of material or due to an increase in crystallinity. A solute-induced crystallization may lead to a peak in the mass increase curve since the material pushes out solute molecules as the crystals develop. However, since the "overshoot" was smaller or absent for the other solutes, it seems reasonable to suggest that the cause was extraction. The 47%HBr sorption curves were complicated. Even though the experimental scatter was very large in this case it seemed that a maximum in mass increase also occurred here in all the PVDF materials (see Fig. 1b, PVDF3). Considering the large uncertainty in the data (experimental scatter) it was not possible to conclude whether there was a maximum in the sorption curve in the case of 47%HBr-ECTFE (Fig. 1a). The "overshoot" effect was small or absent for water and TCE in both PVDF and ECTFE.
The solute mass fractions in the polymer amorphous component are given in Fig. 2. The crystallinities are displayed in Table 1. The mass fractions were estimated from the last readings on the sorption and desorption curves, even though the curves had not always leveled out. By far the highest solubility in the polymer was observed for TCE, possibly because of its high condensability (boiling point: 121[degrees]C).
It is interesting to ascertain whether both components of the surrounding acid diffuse into the polymer. In order to obtain this information, it is assumed that the solute mass fraction in the polymer in contact with the liquid is proportional to the solute activity above the liquid. The mass fractions in the polymer were consequently plotted after being normalized with respect to the water activity estimated from refs. (25) and (26) (water: [a.sub.w] = 1.35%HCl: [a.sub.w] = 0.26, 47%HBr: [a.sub.w] = 0.28). To have the same units TCE data were also normalized with respect to the activity ([a.sub.TCE] = 1). The normalized aqueous mass fractions in the polymer did not collapse into a single curve, suggesting that the acid components (HCl/HBr) also diffused into the polymer. It appears that the PVDF 47%HBr data lie on the water curve. However, if only the "desorption solute mass fractions" are considered, the 47%HBr data lie above the water curve. The relative contents of HCl, HBr and water diffusing into the polymer was roughly estimated by considering the difference in the solute mass fractions, normalized with respect to the water activity, between the acid and the pure water [DELTA](C [a.sub.w.sup.-1]) relative to that of the acid (C [a.sub.w.sup.-1][).sub.acid.sup.-1].
The water contents (fractions) in the acid that actually diffused into the polymer were estimated to be: 35%HCl-ECTFE: 19-21%, 35%HCl-PVDF: 37-44% and 47%HBr-ECTFE: 38-56%, 47%HBr-PVDF: 53-71%. Again it must be emphasized that these values were calculated on the assumption that the water mass fraction in the polymer in contact with the acid liquid increases in proportion to the activity of water in the liquid (or water vapor activity). Conde and Taxen (4) reported a three times higher mass increase of non-polar fluoropolymers in contact with an aqueous 35%HCl solution than when they were compared with pure water at 70[degrees]C. They suggested that the mass uptake increases because the HCl vapor activity was higher than the water vapor activity under these conditions. They used a pressure of 760 mmHg as the standard state for the respective gas components. Based on the same reasoning, vapor pressure data from ref. (25), extrapolated to 70[degrees]C, yielded a higher water vapor activity than that of HBr over a 48%HBr solution. Thus, it would be expected that the acid that penetrated into the polymer contained more water than in the case of 35%HCl. This is in agreement with the calculations above and with most of the data from the two-component sorption model given below.
[FIGURE 1a OMITTED]
The extraction power of the different liquids is given in Fig. 3. The extraction power is not a clear function of the solute solubility. Interestingly, TCE yielded the highest extractability in ECTFE, but similar or lower extractability compared to the other solutes, in the PVDF samples. Surprisingly, the degree of extraction power was not obviously related to the shape of the mass increase curves, i.e. to an increase in the size of the overshoot, in Fig. 1.
[FIGURE 1b OMITTED]
[FIGURE 2 OMITTED]
Considering the low aqueous solute mass fractions in the polymer, the diffusivity may be considered to be approximately constant and independent of solute content. Data in Table 3 show that the improvement in the fitting of the PVDF-[H.sub.2]O desorption curves, when using a solute concentration-dependent diffusivity (Eq 2), was small, especially considering the scatter of the data. Consequently the modeling of the two-component systems was performed using concentration-independent diffusivities. The strategy when fitting the acid desorption curves was as follows: use the water diffusivity determined from the pure water system and use also the water content in the aqueous solution that actually diffuses into the polymer, previously calculated using the corresponding vapor activities (see Table 3). Thus the HCl/HBr diffusivity was the only adjustable parameter. The PVDF-35%HCl system was readily fitted in this way and the HCl diffusivities obtained are given in Table 3. This strategy did not work for the corresponding ECTFE systems, since the "desorption-modeling" water content had to be set much higher than the "vapor-pressure"-calculated water content to describe the desorption process (Table 3). In the case of 47%HBr the modeled water content, with one exception, had to be adjusted to fit the desorption data (Table 3). The adjustment was however relatively moderate for PVDF. The strategy when fitting the PVDF-47%HBr desorption data was to first adjust, by visual inspection (manually), the water content to fit the "knee" clearly observed in the PVDF desorption curves (Fig. 4). Subsequently, a HBr diffusivity was selected that corresponded to a minimum SSD.
[FIGURE 3 OMITTED]
To conclude, it should be mentioned, as observed in Fig. 4, that the scatter in the experimental desorption data was high, due to the low solubility of the aqueous systems in the polymers. Therefore, especially for ECTFE, the fits were qualitative rather than quantitative, and optimization was mostly not meaningful. Nevertheless the trends were clear. The water contents in the diffusing acid were generally different from those in the surrounding solution (65% in 35%HCl and 53% in 47%HBr) (Table 3). Interestingly, the water content in the polymer was lower (HCl) and higher (HBr) than in the surrounding solution. This is consonant with the fact that water has a lower and higher vapor activity than respectively HCl and HBr. For PVDF, the water desorption curves had a Fickian shape, the 35%HCl desorption curves were more "round" and the 47%HBr desorption curves contained a "knee." The fact that the 47% HBr "knee" was well modeled and that the 35%HCl and 47%HBr desorption curves could be fitted using a water diffusivity value from the pure water system strengthened the idea that HCl/HBr and water diffuse as two separate components in the polymer, each with a unique diffusivity. Before using the two-component approach, the 47%HBr desorption curves were fitted by a time-dependent surface boundary concentration condition: [C.sub.b](t) = [C.sub.ini][e.sup.-[tau]/[TAU]], which describes an instantaneous decay in surface concentration (mass fraction) from the saturation value to [C.sub.ini], followed by a slow further decay to zero, the rate being determined by [TAU]. This approach is based on the idea that the acid diffusion is described by a single effective value. However, at the surface, the two components (water and HBr) evaporate at different rates. This should be compared with the two-component model, which uses two separate diffusivities but a single evaporation rate. Although it was possible to fit the 47%HBr desorption curves by this time-dependent boundary approach, it was abandoned because the two-component approach seemed to be physically more correct. Note that the transport properties were calculated using dry initial thicknesses and that these could vary over the specimen body. It should be noted that the value to which the desorption curve was normalized was chosen manually, and it therefore yielded, in combination with the scatter in data, an extra uncertainty in the calculated diffusivity data (Fig. 4). In addition, several desorption curves, especially those in the water and 35%HCl-ECTFE systems, had some long-term data that deviated from the "normal curve shape." These were omitted when the desorption curves were normalized.
[FIGURE 4 OMITTED]
Figure 5 shows that the solute diffusivity (values from Table 3) did not decrease in a simple way with increasing solute size. The sizes were estimated by taking the average of the largest and smallest van-der Waal distances (diameters) of the respective non-ionized species. The Cl-size was considered to be the smallest distance of the TCE molecule. Data were collected from the CS Chem3D Pro[R]-program (CambridgeSoft Corp. USA). The diffusivity was generally lower in the "dipolar" ECTFE than in the "hydrogen-bonding" PVDF at comparable crystallinities (Fig. 5 and Table 3).
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
Since most practical problems concern permeability rather than diffusivity behavior, the transmission rate for each component in the diffusing liquid was calculated as the component diffusivity multiplied by the component saturation content in the diffusing liquid. The "average" transmission rate for TCE was calculated according to ref. (24) with data from the same reference. This is a crude approximation, considering the uncertainty in the diffusivity data presented in Table 3, especially for 47%HBr. Nevertheless, the permeabilities are presented in Fig. 6. HBr showed the lowest transmission rate in both polymers. ECTFE was most permeable to TCE whereas PVDF was most permeable to [H.sub.2]O. The permeabilities of the aqueous solutes in PVDF were significantly higher than the corresponding TCE values. The opposite was observed in ECTFE. The aqueous solute permeabilities were on the same level in both types of material, whereas, as shown previously (24), PVDF was a much better barrier than ECTFE to the non-polar but polarizable TCE.
Water and acid solubilities in the polymers indicated that both water and HCl/HBr diffused into the polymer. For several systems, both sorption and desorption curves deviated from the normally observed curvature. Sorption "overshoot" effects were observed for e.g. the 35%HCl-PVDF3 system. Especially for PVDF, it was possible to fit the 35%HCl and the abnormal 47%HBr desorption curves by considering that HCl/HBr and water diffused separately within the polymer.
The water diffusivity was obtained from the pure water system and this enabled the HCl/HBr diffusivities to be calculated. Because of the small solute up-take in the polymer, the diffusivities were assumed to be independent of the solute concentration. Fits with concentration-dependent diffusivities did not improve the results. The solute diffusivities decreased in a non-simple way as a function of solute size.
The solute exposure itself seemed not to cause any detrimental effect on the polymer properties, except for discoloration in some systems. The observed mechanical changes were probably a consequence of the thermal treatment and not of the chemical exposure itself.
Table 1. Characteristics of Samples. Sample Copolymer (a) X (b) (mol%) Melting point ([degrees]C) ECTFE1 - - 241 ECTFE2 - - 228 PVDF1 HFP 2.0 158 PVDF2 - - 170 PVDF3 - - 174 PVDF4 - - 167 Sample [W.sub.c] (c) Polarity (d) ECTFE1 25 1 ECTFE2 18 1 PVDF1 37 2 PVDF2 51 2 PVDF3 55 2 PVDF4 48 2 (a) PVDF modified with HFP: hexafluoropropylene. (b) Data from supplier. (c) Mass crystallinities from ref. (24). (d) 1) dipoles and 2) hydrogen bonds (27, 28). Table 2. Mechanical Parameters. Material * U (c) [H.sub.2]O (d) HCl (e) HBr (f) TCE (g) ECTFE1 [epsilon] 452 (34) 350 (75) 415 (28) 432 (16) 354 (81) (a) E (b) 425 (51) 535 (38) 527 (14) 551 (39) 569 (32) ECTFE2 [epsilon] - 340 (95) 344 (87) 296 (59) 362 (4) (a) E (b) - 564 (28) 614 (14) 606 (39) 559 (2) PVDF1 [epsilon] 255 (216) 281 (7) 128 (133) 52 (28) 126 (131) (a) E (b) 471 (59) 642 (2) 665 (1) 632 (7) 631 (2) PVDF2 [epsilon] 77 (113) 24 (1) - 21 (0) 37 (24) (a) E (b) 742 (32) 948 (26) - 683 (366) 937 (45) PVDF3 [epsilon] - 31 (7) 25 (3) - 24 (7) (a) E (b) - 999 (8) 983 (25) - 997 (15) PVDF4 [epsilon] 146 (151) - 24 (2) 24 (0) 19 (3) (a) E (b) 725 (55) - 899 (82) 933 (21) 922 (40) * Values within parantheses are the standard deviation ([+ or -]), measured on 2-8 specimens. (a) Fracture strain (%). (b) Young's modulus (MPa). (c) Unexposed specimen. (d) Specimen sorbed in water and then desorbed. (e) Specimen sorbed in hydrochloric acid (35%) and then desorbed. (f) Specimen sorbed in hydrobromic acid (47%) and then desorbed. (g) Specimen sorbed in TCE and then desorbed. Table 3. Transport Properties. Solute/Material D (a) SSD (b) [D.sub.co] (c) [H.sub.2]O ECTFE1 9*1[0.sup.-8] 0.02 3.7*1[0.sup.-8] ECTFE2 1.2*1[0.sup.-7] 0.02 3.5*1[0.sup.-8] PVDF1 3.7*1[0.sup.-7] 0.02 2.9*1[0.sup.-7] PVDF2 3.0*1[0.sup.-7] 0.02 1.7*1[0.sup.-7] PVDF3 3.0*1[0.sup.-7] 0.01 1.8*1[0.sup.-7] PVDF4 2.9*1[0.sup.-7] 0.02 1.5*1[0.sup.-7] D (g) [C.sub.w] (h) [C.sub.w] (i) 35%HCl ECTFE1 2*1[0.sup.-9] 0.65 0.21 ECTFE2 9*1[0.sup.-10] 0.7 0.19 PVDF1 1.2*1[0.sup.-7] 0.37 0.37 PVDF2 6*1[0.sup.-8] 0.44 0.44 PVDF3 6*1[0.sup.-8] 0.43 0.43 PVDF4 8*1[0.sup.-8] 0.44 0.44 47%HBr ECTFE1 9*1[0.sup.-10] 0.70 0.56 ECTFE2 8*1[0.sup.-10] 0.50 0.38 PVDF1 6*1[0.sup.-10] 0.73 0.53 PVDF2 8*1[0.sup.-10] 0.75 0.70 PVDF3 1.5*1[0.sup.-10] 0.64 0.64 PVDF4 5*1[0.sup.-10] 0.62 0.70 Solute/Material [alpha] (d) C (e) SSD (f) [H.sub.2]O ECTFE1 2000 0.0012 0.02 ECTFE2 3000 0.0012 0.05 PVDF1 500 0.0017 0.02 PVDF2 1100 0.0016 0.01 PVDF3 1000 0.0016 0.01 PVDF4 1500 0.0015 0.02 SSD (j) C (e) 35%HCl ECTFE1 0.03 0.0013 ECTFE2 0.05 0.0016 PVDF1 0.04 0.0013 PVDF2 0.05 0.0009 PVDF3 0.04 0.0010 PVDF4 0.07 0.0009 47%HBr ECTFE1 0.1 0.0005 ECTFE2 0.04 0.0007 PVDF1 0.09 0.0007 PVDF2 0.09 0.0005 PVDF3 0.05 0.0005 PVDF4 0.05 0.0004 (a) Diffusivity considered to be constant (c[m.sup.2]/s) and obtained by the numerical procedure described in the theory section. (b) Sum of squares differences between modeled and experimental desorption data using a constant diffusivity. (c) Zero-concentration diffusivity (c[m.sup.2]/s) obtained by the numerical procedure described in the theory section. (d) Plasticisation power (1/[w.sub.f]) obtained by the numerical procedure described in the theory section. (e) Saturation solute mass fraction in the modeling ([w.sub.f]), more decimals were used in the modeling. (f) Sum of squares differences between modeled and experimental data. Manual "visual" fitting using a solute-concentration dependent diffusivity. Not optimized fitting (g) HCl or HBr diffusivity considered to be constant (c[m.sup.2]/s). (h) Mass fraction water in the aqueous solution diffusing into the polymer, obtained from the fit of desorption data. (i) Mass fraction water in the aqueous solution diffusing into the polymer, calculated from the relative partial pressures of the vapor components. (j) Sum of squares differences between modeled and experimental desorption data using constant HCl and HBr diffusivities. The water diffusivity was obtained from the pure water systems given above. Not optimized fitting, except for the 35%HCl-PVDF systems where the HCl diffusivities were optimized using [C.sub.w] from the vapor pressure data
Financial support from the Swedish Foundation for Strategic Research (SSF) and from the Plastics Research Programme of the Swedish Corrosion Institute is gratefully acknowledged. Patrizia Maccone and Matteo Vecellio at Ausimont S.p.A., Italy, are thanked for experimental assistance.
(1) Also at The Swedish Corrosion Institute, Kraftriket 23A, SE-104 05 Stockholm, Sweden.
(2) Present address: Habia Cable AB, Box 5075, SE-187 05 Taby, Sweden.
(3) The Swedish Corrosion Institute, Kraftriket 23A, SE-104 05 Stockholm, Sweden.
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M. S. HEDENQVIST [dagger], J. E. RITUMS (1), M. CONDE-BRANA, (2) and G. BERGMAN (3)
Department of Fibre and Polymer Technology, Royal Institute of Technology S-100 44 Stockholm, Sweden
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|Author:||Hedenqvist, M.S.; Ritums, J.E.; Conde-Brana, M.; Bergman, G.|
|Publication:||Polymer Engineering and Science|
|Date:||Jan 1, 2004|
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