Subnanoscopic Mapping of Glass Transition Temperature around

Jun 18, 2013 - the ionic core (multiplet), whereas 10DND probe based on a nonadecane backbone reflected the Tg at the polyethylene (PE) matrix. The lo...
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Subnanoscopic Mapping of Glass Transition Temperature around Ionic Multiplets in Sodium-Neutralized Poly(ethylene-randommethacrylic acid) Ionomer Yohei Miwa,* Tomoyo Kondo, and Shoichi Kutsumizu Department of Chemistry, Faculty of Engineering, Gifu University, Yanagido, Gifu 501-1193, Japan ABSTRACT: A local glass transition temperature, Tg, around ionic aggregates in poly(ethylene-random-methacrylic acid) (E-MAA) ionomers neutralized with sodium has been studied by the combination of the position-selective spin probing and microwave power saturation method of electron spin resonance (ESR). 5DSA, 7DSA, 10DSA, and 12DSA spin probes based on stearic acid allowed us to determine the local Tg at different distances from the center of the ionic core (multiplet), whereas 10DND probe based on a nonadecane backbone reflected the Tg at the polyethylene (PE) matrix. The local Tgs at the ionic multiplet itself and matrix region were determined to be 320 and 281 K, respectively, in the quenched E-MAA ionomer from the melt. Moreover, it was found that the region around the multiplets is dynamically restricted, and the thickness of the restricted region is ca. 10 Å. In the restricted region, the Tg gradually decreased with receding from the ionic multiplet. The thickness of the dynamically restricted region was in good agreement with the persistence length of the PE at the theta condition. nance13−15 and electron spin resonance (ESR),16−18 showed the restricted mobility of chain segments adjacent to the multiplets. Nonetheless, detailed information on the restricted region, such as the thickness of the restricted region and the gradient of the restriction in the region, is experimentally unknown. The aim of the present work is to reveal the spatial distribution of the glass transition temperature (Tg) around the ionic multiplet in E-MAA ionomers. Spin labeling and spin probing are powerful techniques to evaluate local molecular mobility in the time scale 10−11−10−7 s and local polarities in soft matter through the shape analyses of ESR spectra. Paramagnetic molecules are chemically bonded to target molecules in the spin label method while they are dispersed in the materials without chemical bonding in the spin probe method.19 Spiess and co-workers studied the local dynamics and structure of ionic aggregates in ionomers of polystyrene, polyisoprene, and their diblock copolymer using spin probing with ionic nitroxyl radicals.18,20−23 They showed highly restricted mobility at the ionic multiplets by means of the spectral shape analysis and electron spin relaxation time measurements. Additionally, the size of the ionic multiplets and the distances between the multiplets were measured by double electron−electron resonance technique. On the other hand, Kutsumizu and Schlick et al. demonstrated the spatial distributions of the local polarity and dynamics around the ionic multiplets in the E-MAA ionomers using positionselective spin probe method.17,24

1. INTRODUCTION Ionomers composed of copolymers containing relatively few ions placed randomly along the chains currently have tremendous commercial utility, such as packages, coatings, selective ion-transport membranes, etc.1−6 Especially, poly(ethylene-random-methacrylic acid) (E-MAA) ionomers are the most industrially important ionomers because of their impact resistance, elasticity, melt strength, and adhesion induced by the combination of flexible polyethylene (PE) chains and rigid ionic moieties.5,6 In addition to the current applications, ionomers have potential for the next-generation polymeric materials available for polymeric electrolytes for fuel cell and battery applications,7 templates for well-defined nanocomposites,8 sensors,9,10 etc. It is now generally accepted that ionomers owe their unique properties to the aggregations of ionic groups, called multiplets.4,11 Therefore, controlling the morphology and dynamic properties of the ionic multiplets is a very important subject in order to maximize the unique properties of ionomers. From this view, Winey et al. synthesized novel poly(ethyleneco-acrylic acid) ionomers in which ionic moieties are precisely sequenced along the chain to impart well-defined morphologies.12 On the other hand, the precise control of the dynamic properties of the ionic multiplets is currently hard because microscopic information about the molecular dynamics of, and near, the ionic aggregates is limited. The most comprehensive and general model presented by Eisenberg et al. has predicted that the mobility of polymer segments surrounding the multiplets is generally restricted;4,11 this prediction is important to understand the phase behavior and dynamics in ionomers. Indeed, some techniques, including nuclear magnetic reso© 2013 American Chemical Society

Received: May 18, 2013 Revised: June 10, 2013 Published: June 18, 2013 5232

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Spin Probing. Ionomer films were cut into small pieces with ca. 10 mm × 2 mm × 2 mm and immersed into distilled water at a room temperature for 1 week. The spin probes were first dissolved into a small amount of acetone, and distilled water was added to make an aqueous solution with 0.1 mM. The swollen ionomer films were dipped into the aqueous probe solution for 4 days. The ionomer pieces were dried under vacuum at room temperature for 12 h and then additionally dried at 353 K for 48 h. The dried ionomers were quickly encapsulated into 5 mm o.d. quartz tubes for the ESR measurements and sealed under a vacuum following further drying in a vacuum at 393 K for 10 min. After that, the samples were annealed at 296 K for 3 weeks in an incubation oven. The concentration of the spin probes in the ionomer was adjusted to be low enough to avoid broadening of the lines by spin−spin interactions. Toluene containing a trace of 10DND was soaked into the purified LDPE powders, and the powders were dried under a vacuum at 353 K for 24 h. The dried LDPE powders containing 10DND were press molded at 423 K to make a film having the thickness of 1 mm. The film was washed with acetone to remove 10DND at the film surface. The LDPE film was encapsulated into 5 mm o.d. quartz tubes and sealed under a vacuum. 2.2. Measurements. Electron Spin Resonance. ESR spectra were recorded with JEOL X-band (ca. 9 GHz) FA100 spectrometers with 100 kHz field modulation. The modulation amplitude, magnetic field width, sweep time, time constant, and number of scan were typically 0.25 mT, 15 mT, 20 s, 0.01 s, and 3, respectively. The magnetic field and g tensor were calibrated with Mn2+. The microwave powers used for measurements with and without microwave power saturation were 16 and 0.02 mW, respectively. As shown in our previous paper, the microwave power used for the saturation does not affect the value of the Tg determined by the MPS method.25 The measurement was carried out on the second heating process. Namely, before the measurement, the sample was annealed at 373 K for 10 min and quenched to 203 K in the ESR cavity; the samples were heated stepwise from 203 to 373 K with the interval of 2.5 K. The measurements were carried out at a constant temperature on the heating controlled within ±0.1 K. In this experiment, an automatic measurement program was used. The tuning parameters (phase and detector current) of the ESR spectrometer and the sample position in the cavity were kept constant, and only the temperature was varied for the MPS measurement. Differential Scanning Calorimetry. DSC measurement was carried out using a DSC7020 differential scanning calorimeter manufactured by SII and calibrated with indium, zinc, lead, and tin standards. The DSC cell was purged with dry nitrogen gas during the measurement with the flow rate of 40 mL min−1. For LDPE, measurements were carried out on the heating from 173 to 423 K at a rate of 10 K min−1. On the other hand, E-MAA ionomers were heated from 253 to 393 K at a rate of 10 K min−1, kept for 5 min, cooled to 253 K at a rate of 10 K min−1, and heated again at a rate of 10 K min−1. X-ray Diffraction. X-ray diffraction (XRD) data were acquired on a RINT-2100 diffractometer using Cu Kα radiation generated at 40 kV and 30 mA and configured in a Bragg−Bretano focusing geometry. The scattering angle (2θ) was scanned at 2.00° min−1 in the range 2°− 40° using a step size of 0.02°. All measurements were carried out at a room temperature. The sample films were prepared via press molding above Tm. 2.3. Determination of Tg,ESR by the Microwave Power Saturation (MPS) Method. The principle of the MPS method has been described in detail in our previous papers.25−27 This method determines a Tg of spin-labeled and spin-probed polymers from the discontinuity in the slope of the natural logarithm of the saturation factor, S, versus the inverse of temperature, T−1. The relative signal intensity VR from X-band ESR spectrometer is given by

Recently, Miwa developed a novel method, called microwave power saturation (MPS) method, to determine a local Tg of spin-probed and spin-labeled polymers from monitoring the temperature dependence of the ESR signal intensity under saturating microwave power irradiation (typically more than 1 mW).25−27 This method allows us to measure the local Tg in polymers around the stable free radicals with very simple procedure using a common X-band ESR spectrometer without any equipment modifications. In the present work, these MPS and position-selective spin probe methods were used in combination to determine a local Tg in the E-MAA ionomers. The aims of this work are to reveal (1) the Tg at the multiplets and (2) the distribution of the Tg around the multiplets in the E-MAA ionomers.

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. Materials. The E-MAA ionomers are a gift from Technical Center, Du Pont-Mitsui Polychemicals Co. Ltd., Chiba, Japan. The starting polymer, with Mn = 19 kDa and Mw = 95 kDa, is containing 5.4 mol % MAA units in the backbone, and the melt index (MI) is 6 g min−1. The average number of backbone carbons between two neighboring COOH groups was therefore ≈36. In this work, the E-MAA whose 90% of the COOH group was neutralized with sodium was used. Low-density polyethylene (LDPE) is MIRASON from Mitsui Chemicals Co., Ltd., Chiba, Japan. The LDPE was purified via reprecipitations from hot toluene solution to acetone and dried under a vacuum at 353 K for 24 h. The spin probes used in this work are illustrated in Chart 1. Four probes (5DSA, 7DSA, 10DSA, and 12DSA) are based on stearic acid, and one (10DND) has a nonadecane backbone. They differ in their polarity and/or in the position of the nitroxide group with respect to the headgroup; the number in each probe notation represents the nitroxide group position. They were purchased from Aldrich Chemical Co., Ltd. and used as received.

Chart 1

VR =

0.5 γH1(TT 1 2) 2 2 1 + γ H1 TT 1 2

(1)

where γ, H1, T1, and T2 are the gyromagnetic ratio, microwave magnetic field, spin−lattice relaxation time, and spin−spin relaxation 5233

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time, respectively.28 The γ2H12T1T2 is defined as the saturation factor, S, in this work. Without the saturation the VR is proportional to H1 because the S is small enough to be ignored. In experiments, the VR obtained from a double integration of a spectrum is proportional to the square root of the microwave power, P0.5, because of the H1 ∝ P0.5. On the other hand, the deviation from the relationship of the VR ∝ P0.5 is observed when the P is large because of an increase in S. This phenomenon is called microwave power saturation. As an example, plots for the LDPE spin-probed with 10DND at 203 and 323 K are

Figure 2. XRD patterns of LDPE (a) and E-MAA ionomer (b).

23.2° are assigned respectively to (110) and (200) diffraction peaks of PE crystallites of orthorhombic type.29 On the other hand, a shoulder at 18° comes from the amorphous PE region.30 The crystallinities (Xcs) for the LDPE and E-MAA ionomer were determined to 38% and 19%, respectively. For the E-MAA ionomer, the “ionomer peak” at ca. 3.5° was observed.31 3.2. DSC Measurements. DSC trace for the LDPE and EMAA ionomer are shown in Figure 3. The Tg and Tm were observed for the LDPE at 252 and 383 K, respectively.

Figure 1. Plots of VR normalized by VR,0.01 mW against P0.5 for LDPE spin-probed with 10DND at 203 and 323 K. The straight solid line indicates the ideal relationship without the microwave power saturation. Saturated VR value, VR,S, and unsaturated one, VR,US, are shown with arrows. shown in Figure 1. When the P is constant, the S is determined from the ratio of the saturated VR value, VR,S, to the unsaturated one, VR,US,

VR,S VR,US

1 1+S

=

(2)

Therefore, the S is given by S=

VR,US VR,S

−1 (3)

In this work, the VR,S value was obtained from the double integration of the ESR spectrum measured at 16 mW. On the other hand, 0.02 mW was low enough to avoid the saturation as shown in Figure 1. Therefore, the VR,US value at 16 mW was calculated as follows:

VR,US =

⎛ 16 ⎞1/2 ⎜ ⎟ V0.02 mW ⎝ 0.02 ⎠

Figure 3. (A) DSC trace for LDPE. (B) DSC traces for E-MAA ionomer on first heating (a) and second heating (b).

(4)

where V0.02 mW was the double integration value of the ESR spectrum measured at 0.02 mW. The inflection temperature in the slope of the temperature dependence of the lnS was defined as Tg,ESR (see Figures 4 and 5). As demonstrated in our previous paper, the T2 does not affect the value of the Tg,ESR; the inflection of the temperature dependence of the S at the Tg,ESR is due to the decrease in the T1.27 It should be noted that the absolute value of S determined by the experiment is strongly influenced by many factors, such as the tuning parameters of the ESR spectrometer, the inserted sample position, the shape of samples in the cavity, etc.; therefore, the direct comparison of absolute S values should not be directly compared unless measurement conditions are very precisely controlled. However, we confirmed that the Tg,ESR is not influenced by such factors as long as the tuning parameters of ESR spectrometer and sample position were kept constant during the temperature variable measurement. In the present work, the sample position and tuning parameters for microwave irradiation were kept constant during the variable temperature measurements.

For the E-MAA ionomer, a large endothermic peak was observed at 324 K while this peak was disappeared on the second heating process. This additional endothermic peak is a unique property for E-MAA ionomers.32,33 When aged at a room temperature for more than several days, the additional endothermic peak appears; the size of this peak increases with the aging time. In the present study, the ESR measurements were carried out on the second heating process to avoid the influence of this additional transition at 324 K. 3.3. ESR Measurements. Polyethylene. Arrhenius plots of the S for the LDPE spin-probed with 10DND in the range 203−313 K are shown in Figure 4. The temperature at the inflection was defined as Tg,ESR whereas the data points below and above the transition were linearly least-squares fitted. The Tg,ESR for the LDPE was 255 K and experimental uncertainties are within 2 K. The Tg,ESR for the LDPE was in good agreement with the Tgs determined by DSC, 252 K (Figure 3), and dynamic mechanical thermal analysis, 251 K.34

3. RESULTS 3.1. XRD Measurements. XRD patterns for LDPE and EMAA ionomer are shown in Figure 2. Two peaks at 20.9° and 5234

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described above, the S is proportional to the T1; the T1 shows a minimum at the motional correlation time of nitroxides that is equal to ca. 2 × 10−8 s.35

4. DISCUSSION 4.1. Structure of Ionic Aggregates and Locations of Spin Probes. The structure of the ionic aggregates and the locations of spin probes in the sodium-neutralized E-MAA ionomers were previously studied by Kutsumizu and Schlick et al. using small-angle X-ray scattering (SAXS) and ESR, respectively.24 The ionic peak in SAXS was analyzed on the liquidlike model, which postulates that ionic aggregates in ionomers are spherical particles consisting of an ionic multiplet of radius R1 and a shell of hydrocarbon chains with outer radius RCA; the spheres are dispersed in the amorphous matrix region with a liquidlike order under the limitation of the closest approach, 2RCA.31 For the E-MAA ionomer with neutralized 90% of the COOH group, the R1 and RCA were determined to be 6.3 and 9.7 Å, respectively.24 As Kutsumizu and Schlick showed, the nitroxide groups of the nDSA act as “spin labels” located at different distances from the center of the ionic aggregates because carboxylic groups of nDSA probes are incorporated into the ionic multiplets.24 When the molecular motions of the probes are frozen at 77 K, the 2Azz value of ESR spectra reflects only the polarity of the local environment around nitroxides.36 If nitroxides are located in the ionic multiplets, significant increase in the 2Azz should be expected. In Figure 6, the 2Azz are plotted against r where r is

Figure 4. Temperature dependence of S for LDPE spin-probed with 10DND. The inflection temperature is defined as Tg,ESR.

E-MAA Ionomers. The temperature dependence of the ln S for the E-MAA ionomers on the second heating processes is shown in Figure 5. The plots are vertically shifted to avoid

Figure 5. Temperature dependence of ln S for E-MAA ionomers on the second heating process. The arrows indicate Tg,ESRs. The plots are vertically shifted to avoid overlapping.

overlapping in the figure. As shown in Figure 3B, the E-MAA ionomers show an anomalous endotherm at 324 K on the first heating process. Therefore, the ESR measurements were carried out on the second heating process to avoid the influence of this additional transition at 324 K. The Tg,ESRs for the E-MAA ionomers spin-probed with 5DSA, 7DSA, 10DSA, 12DSA, and 10DND are 320, 319, 310, 299, and 281 K, respectively. Here, the data points below and above the transition were linearly least-squares fitted. Experimental uncertainties for the Tg,ESR are within 2 K. The Tg,ESR for each spin probe are listed in Table 1.

Figure 6. Plots of 2Azz against the distance between nitroxide and carboxylic groups in each probe, r. Solid line and broken lines indicate the 2Azz for 10DND in E-MAA ionomer and LDPE, respectively.

Table 1. Distance between Nitroxide and Carboxylic Group in the Probe, r, and Tg,ESR for Each Spin-Probed Sample sample

spin probe

r/Å

Tg,ESR/K

E-MAA ionomera

5DSA 7DSA 10DSA 12DSA 10DND 10DND

5 8 12 14 N/A N/A

320 319 310 299 281 255

LDPE a

± ± ± ± ± ±

the distance between nitroxide and carboxylic group in each probe. These distances were determined on the basis of the Chem3D software. This result indicates that the nitroxide of 5DSA is located inside the ionic multiplet because the 5DSA showed significantly large 2Azz value. This is quite reasonable because the r of the 5DSA is smaller than the R1, 6.3 Å. On the other hand, the 12DSA showed the 2Azz value as small as the 10DND in LDPE. This was originally discovered by Kutsumizu and Schlick, and this is due to the existence of the ion-depleted zone around the ionic multiplets.24 The hydrophobic probe, 10DND, is expected to be excluded from both the ionic aggregates and PE lamellae regions. The structure of the ionic aggregates and the locations of the probes in the E-MAA ionomer are schematically presented in Figure 7. 4.2. Mapping of Tg around Multiplets. Eisenberg et al. first introduced an idea of dynamically restricted polymer segments surrounding the multiplets.4,11 Until now, this prediction is an important key to understand the phase behavior and dynamics in ionomers. The thickness of the

2 2 2 2 2 2

Neutralized 90% of COOH groups with sodium.

Interestingly, the spin probes located closer to the ionic multiplet showed broader glass transition. This result indicates that the ionic multiplets are dynamically heterogeneous because of their inhomogeneous composition. This must be an important fundamental property of the ionic multiplet. The 10DND showed a minimum of the S around 356 K, and the S increased again with an increase in temperature. As 5235

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Figure 7. Suggested locations of nDSA and 10DND probes in the EMAA ionomer based on the analysis of the ESR results; the carboxylate and carboxylic acid groups of the ionomer (○) and the acid group (●) and the nitroxide groups (■) of the probes are indicated. Dark shaded, semidark shaded, and gray-shaded regions represent the ionic multiplet, dynamically restricted region, and PE matrix region, respectively.

Figure 8. (A) Plots of Tg,ESR against r. Tg,ESR for 10DND is shown with solid line. R1, 6.3 Å, determined by SAXS is shown with broken line. (B) Plots of Tg,ESR vs (r − R1)2.

mechanical thermal analysis.39 Moreover, Kutsumizu et al. observed the Tg of the matrix region at 286 K for the amorphous E-MAA ionomers containing 13.3 mol % of the methacrylic acid moiety by DSC measurement.30 As shown in Figure 8B, the Tg,ESRs for the nDSA probes show a straight relation against the square of (r − R1) where the R1 determined by SAXS is 6.3 Å.24 The extrapolation of this relation intersects the line of the Tg,ESR for the 10DND at the (r − R1) of ca. 10 Å. This is the thickness of the restricted region around the multiplet; this length is correspondent with the persistence length of the PE, 10 Å, which is determined in 1dodecane solution with the theta condition.37 It should be noted that the all-trans conformation from carboxylic to nitroxide groups in nDSA probes and the location of the carboxylic group at the center of the ionic multiplet are assumed in our analysis. Therefore, the thickness of the restricted region determined by our method may be including uncertainties within a few angstroms. Nevertheless, our result is in extremely good agreement with the prediction of Eisenberg.4,11 Furthermore, as shown in Figure 5, the spin probes located closer to the ionic multiplet showed broader glass transition. This result indicates that the ionic multiplets are dynamically heterogeneous due to their inhomogeneous composition. This must be an important fundamental property of the ionic multiplets.

restricted region surrounding each multiplet is considered to be determined largely by the flexibility of the polymer backbone; the more flexible the chain, the thinner the “skin” of restricted mobility. The distance within which polymer segments experience an appreciable restriction in mobility is difficult to ascertain exactly, but Eisenberg et al. predicted that the distance may be assumed to be of the order of the persistence length of the bulk polymer. The persistence length is a measure of the distance within which local inflexibility in a polymer chain persists.37 Indeed, some techniques detected the restricted segmental motion adjacent to the multiplets.13−17 Furthermore, Wouters et al. determined the thickness of the restricted region surrounding multiplets in maleated ethylene−propylene copolymer based ionomers to ca. 10 Å from the spin-diffusion experiments of solid state NMR; however, the estimated size suffers from a large error because the calculation is based on several assumptions.15 In Figure 8A, the Tg,ESR are plotted against the r. The Tg,ESR decreased with receding from the multiplet. This is the first and direct evidence of the gradient of the Tg in the restricted region surrounding multiplet. The Tg,ESR for the 5DSA, 320 K, reflects the glass transition of the multiplet itself. This value is much lower compared to the Tg of poly(methacrylic acid) neutralized with sodium determined by DSC, 636 K.38 In the case of the EMAA, the methacrylic acid unit is connected to flexible ethylene units, and they must relax cooperatively at the glass transition; as a consequence, the Tg decreases. On the other hand, the Tg,ESR of the 10DND in the E-MAA ionomer reflecting the glass transition of the matrix region, 281 K, was higher than that of the LDPE, 255 K. In the E-MAA ionomers, the ionic aggregates act as physical cross-linkers, and some carboxylic and ionic groups may be isolated in the PE matrix; as a consequence, it is considered that the mobility of the amorphous region is restricted and the Tg of the matrix region in the E-MAA ionomer is elevated. This result is in good agreement with the disappearance of the original glass transition of the PE component around 253 K in E-MAA ionomers containing more than 5.4 mol % of methacrylic acid moiety by dynamic

5. CONCLUSION The glass transition temperature around the ionic multiplets in the E-MAA ionomers neutralized with sodium has been studied by the combination of the position-selective spin probe and microwave power saturation methods of ESR. The ESR measurements were carried out for the E-MAA ionomer quenched from the melt to avoid effects of the unique transition at 324 K generally observed in the DSC measurement for E-MAA ionomers aged at a room temperature. The Tg,ESRs at the ionic multiplet itself and matrix region were determined to be 320 and 281 K, respectively. Moreover, it was found that the region around the ionic multiplet is dynamically restricted and the thickness of the region was estimated to be ca. 10 Å. This value was in good agreement with the persistence 5236

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(29) Longworth, R.; Vaughan, D. J. Nature (London) 1968, 218, 85− 87. (30) Kutsumizu, S.; Tadano, K.; Matsuda, Y.; Goto, M.; Tachino, H.; Hara, H.; Hirasawa, E.; Tagawa, H.; Muroga, Y.; Yano, S. Macromolecules 2000, 33, 9044−9053. (31) Yarusso, D. J.; Cooper, S. L. Polymer 1985, 26, 371−378. (32) Marx, C. L.; Cooper, S. L. J. Macromol. Sci., Phys. 1974, B9, 19− 33. (33) Tadano, K.; Hirasawa, E.; Yamamoto, Y.; Yamamoto, H.; Yano, S. Jpn. J. Appl. Phys. 1987, 26, L1440−L1442. (34) Wakabayashi, K.; Register, R. A. Polymer 2005, 46, 8838−8845. (35) Robinson, B. H.; Haas, D. A.; Mailer, C. Science 1994, 263, 490− 493. (36) Griffith, O. H.; Jost, P. C. In Berliner, L. J., Ed.; Spin Labeling Theory and Applications; Academic Press: New York, 1976; pp 453− 523. (37) Strobl, G. R. The Physics of Polymers; Springer: Berlin, 1996; pp 20−53. (38) Kwon, Y. K.; Boller, A.; Pyda, M.; Wunderlich, B. Polymer 2000, 41, 6237−6249. (39) Wakabayashi, K.; Register, R. A. Macromolecules 2006, 39, 1079−1086.

length of PE at the theta condition. In the restricted region, the Tg,ESR gradually decreased with receding from the ionic multiplet. This is the f irst experimental result for the mapping of the local Tg around the ionic multiplet in the angstrom scale.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.M.). Notes

The authors declare no competing financial interest.

■

REFERENCES

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