Improved Dielectric Model for Polyvinyl Alcohol-Water Hydrogel at Microwave Frequencies

Transcription

1 Ameican Jounal of Applied Sciences 7 (2): , 2010 ISSN Science Publications Impoved Dielectic Model fo Polyvinyl Alcohol-Wate Hydogel at Micowave Fequencies 1 You Kok Yeow, 2 Zulkifly Abbas, 2 Kaida Khalid and 3 Mohamad Zaki Abdul Rahman 1 Depatment of Radio Communication Engineeing, Faculty of Electical Engineeing, Univesity Technology Malaysia, UTM Skudai, Malaysia 2 Depatment of Physics, 3 Depatment of Chemisty, Faculty of Science, Univesity Puta Malaysia, UPM Sedang, Malaysia Abstact: Poblem statement: The study descibed igoous dielectic modeling fo Polyvinyl Alcohol ()-wate hydogel mixtue at micowave fequencies. Appoach: A commecial openended coaxial senso was used to measue the dielectic constant, loss facto and ionic conductivity, σ of -wate hydogel mixtue anging concentation of % wate content. Results: The senso was opeating between 0.13 and 20 GHz at and above of oom tempeatue (25±1) C. Indiectly, the elaxation time, τ, activation enegy, Q and entopy change, ΔS of the hydogel mixtues ae detemined based on linea fitting of measued data using Debye and Ahenius appoaches. Conclusion/Recommendations: Two main elaxation pocesses wee found anging 2-10 and GHz, espectively. Dielectic dispesion is suggested to descibe by combination of Cole-Davidson (CD) and Debye (Dy) pocesses. The esults ae discussed qualitatively based on bound states of wate in hydogel mixtues. Key wods: Dielectic constant, loss facto, -wate hydogel, elaxation times INTRODUCTION Recently, the Polyvinyl Alcohol ()-wate hydogel was used on medical application, such as healing agent, due to the composition of the hydogel is vey simila to the human body skin. In addition, thee ae non-toxic, non-cacinogenic and bioadhesive chaacteistics. Because of those popeties, is capable of simulating natual tissue and can be eadily accepted by human body. In geneal, this medical application was inteest fo wate content in the hydogel is about 80% and the tempeatue is between C. In macoscopic obsevation, the mechanical chaacteistics, such as dielectic of polyme molecules ae often consideed. The dielectic popeties can be used to explain the oientation of the molecules o elaxation mechanism in the polyme hydogel (Sengwa and Kau, 2000). Howeve, the polaization molecules in polymes ae complex due to many body inteactions between binding molecules. Thus, a lot of the dielectic equation was modified fom the ideal Debye theoy, such as Cole-Cole (CC), Davidson-Cole Kohlausch-Williams-Watts (KWW) distibution function, in ode to epesent and descibe the popeties of the polyme hydogel. In this study, a detailed macoscopic dielectic elaxation behavio of wate in a hydogel was investigated and epoted. The vaiable of envionmental conditions consideed ae the wate content, m.c, fequency, f unde seveal tempeatue, T conditions. Then, the dielectic popeties as a function of fequency and pecentage wate content in hydogel wee fomulated. Finally, the bonding states of wate molecules in hydogel wee discussed based on elaxation time, τ and mean activation enegy, Q. MATERIALS AND METHODS Pepaation of -Wate mixtues: Up to 11 diffeent samples of Polyvinyl Alcohol (), Mn = weights (1-15 g) wee mixed with 60 g of wate in a small beake, espectively. Duing the pocess of pepaation sample, the wate was heating indiectly between C by mixing the continuously little by little until dissolution is (DC) and Haviliak-Negami (HN) as well as Coesponding Autho: You Kok Yeow, Depatment of Radio Communication Engineeing, Faculty of Electical Engineeing, Univesity Technology Malaysia, UTM Skudai, Malaysia 270

2 completed. Afte that, the mixtue samples wee kept at oom tempeatue (25±1) C. The pecentage of wate content in -wate mixtue is calculated fom the fomula: m Wate m.c = 100% m + mwate (1) whee, m and m Wate ae the weigh of and wate (in g), espectively. Dielectic measuements: The HP 85070B openended coaxial senso was used to detemine the dielectic popeties of -wate mixtues. The measuement appaatus consists of a compute contolled HP 8720B Vecto Netwok Analyze (VNA). In this study, ai, metal shot and deionized wate wee used as thee dielectic efeences fo calibation at apetue of open-ended coaxial senso anging GHz at (25±1) C. Afte calibation, the senso was immesed into the hydogel sample to measue its elative pemittivity. (c) Fig. 1: Vaiation in measued of dielectic constant, ε ; loss facto, ε with fequency at oom tempeatue (25±1) C fo vaious wate content, m.c in hydogel; (c) The measued pemittivity of Polyvinyl Alcohol () powde anging GHz 271

3 RESULTS AND DISCUSSION Analysis of data: In geneal, the elative pemittivity of wate ( ε 80 ) is fa geate than ( ε 1.6 ) (Fig. 1c), consequently, the dielectic popeties of wate content in -wate mixtue is dominated. Figue 1a and b show the vaiation in dielectic constant, ε and loss facto, ε of hydogel with fequency at oom tempeatue, (25±1) C fo vaious pecentage wate content, m.c. In geneal, the cuve of dielectic constant, ε of hydogel mixtues is dispese boade and showed lowe maxima of loss facto, ε compaed with pue wate. The decease in elative complex pemittivity of the hydogel mixtue is caused by the displacement of polyme molecules in wate. Dielectic modeling: The elative complex pemittivity, ε of hydogel may be calculated by using a sum of two elaxation pocesses, which is the combination of Cole-Davidson (CD) and Debye (Dy) pocesses. Howeve, dispesion also exists at vey low fequencies ( 2 GHz) fo dielectic constant, ε which has not been investigated in this study. Moeove, the loss facto, ε at lowest fequencies ( 3 GHz) is assumed entiely caused by conductivity, σ and chaacteized as ε =σ 2πε o f. Finally, the elative complex pemittivity of hydogel is expessed as: (ε s and ε 1 ) and elaxation time (τ 1 and τ 2 ) coesponding to vaious pecentage of wate content, m.c ae evealed in Table 1. Finding Optical Pemittivity, ε : In geneal, the optical pemittivity, ε is independent of fequency, f and tempeatue, T (Nyfos and Vainikainen, 1989). Thus, the ε of hydogel is assumed as mixtue expession: ( 1 ) ε =ν ε + ν ε (4) wate wate wate whee, wate ε = 4.9 and ε = 1.6 ae the infinite optical pemittivity of pue wate, dy and dy powde, espectively. The faction volume of pue wate, ν wate is calculated fom: v wate ( ρ ) m.c = 100ρ + m.c ρ ρ wate wate (5) ε ε ε ε jσ 1 j 2 f s 1 1 ε =ε + + A2 1+ ( jωa ) + ( ωτ2) πε 1τ1 o (2) whee, A 1 and A 2 ae the empiical constant, which ae detemined by optimized with measued data. Finding elaxation time, τ, static pemittivity, ε s and ε 1 : The static pemittivity, ε s and elaxation time, τ of hydogel mixtue can be pedicted easily by linea Eq. 2 (Robet, 1988): ε = ωε τ+ε (3) s Fom (3), we obseved that the gadient of vaiation in ε with ωε is epesented by the elaxation time, τ, as well as the point at ε -axis, when ωε = 0 gives the value of ε s. The height of the intemediate plateau fom the line in Fig. 2 epesented as ε 1. The intesection between the line and ε -axis gives the value of ε s. Howeve, the Fig. 2 contains two Fig. 2: The ε vesus ωε fo vaious wate content, linea slopes epesented two majo dispesions, which m.c, which plotting slope is epesented the is boad low-fequency dispesion and high-fequency elaxation time, τ of -wate hydogel at dispesion. The estimated values of dielectic constant (25±1) C 272

4 Table 1: The estimated values of dielectic static (ε s and ε 1 ), elaxation time (τ 1 and τ 2 ) and conductivity, σ fo vaious pecentage of wate content, m.c at oom tempeatue based on fitting data in Fig. 2 and 3 Wate (g) (g) m.c (%) σ(ω 1 m 1 ) τ 1 (ps) (1st fitting) τ 2 (ps) (2nd fitting) ε 1 ε s (1st fitting) *: 1st fitting of measued data is fom 2-10 GHz; 2nd fitting of measued data is fom GHz Whee: ρ wate = g ml 1 ρ = 1.26 g cm 3 ae the appaent density of wate and dy powde at oom tempeatue, espectively and m.c is the pecentage of wate content in the hydogel Finding conductivity, σ: The conductivity tem, σ is detemined by optimizing with measued loss facto, ε at low fequency ( 5 GHz) with (1). The estimated values of conductivity, σ ae listed in Table 1, as well as plotted as Fig. 3. The conductivity data inceases in linea fom with wate content, m.c in the mixtues as evealed in Fig. 3. Howeve, the appaent conductivity itself is independent of fequency. The linea scope may be calibated diectly in pecent of wate content, m.c. The obtained fitted paametes as a function of wate content, m.c (%) fo (1) ae listed in Table 2. Macoscopic analysis: The measuement esults by using HP coaxial senso and calculated values of (1) can be compaed between Fig. 1a and b and 4. Clealy, the calculated values in Fig. 4 ae quite consistent with measued data in Fig. 1a and b. The values of elaxation time, τ obtained fom Fig. 4 ae available in Table 1. The elaxation time, τ is highe at low fequencies (below 10 GHz) and decease with wate content m.c, in hydogel due to the oientation polaization of pola molecules is slowed down by the binding of wate molecules and in the mixtues. The wate molecules ae diectly attached by swelling into the goups of polyme molecule in the main chain and eplaces coss-links between molecules. It is a main facto to limit its movement and elaxation time, τ incease compae with fee wate molecules. In addition, the wate molecules can also be hydogen bonded with hydophilic goups (- OH) in the side chain of the molecule. This type of bond is caused by pedominantly Coulombic foces and has little effect on the igidity of the stuctue. 273 Fig. 3: Vaiation in conductivity, σ with pecentage of wate content, m.c in -wate hydogel with linea fit Table 2: The elationship between each of paametes in Eq. 1 with wate content, m.c (%) Dielectic paametes of -wate hydogel in Eq. 1 (80% m.c 98.5%; 100%); (0.13 GHz f 20 GHz); 25 C ε s = (m.c) (m.c) (m.c) ε 1 = (m.c) (m.c) (m.c) (m.c) wate ε =νwateε + ( 1 νwate ) ε wate whee: ε = 4.9 ε = τ 1 = ( m.c ) ( m.c ) m.c s 14 τ = ; s σ= m.c Ω m A 1 = (m.c) (m.c) A 2 = (m.c) Howeve, the elaxation time of hydogel is appoximately equal to the elaxation of fee wate (8.4 ps) fo fequencies above 10 GHz. Obviously, enegy above 10 GHz is lage enough to beak the hydogen bond between wate molecules and hydophilic goups of. In fact, the oveall effect on wate stuctue is extemely complex.

5 Fig. 5: The measued ε vesus ωε, which plotting slope is epesented the elaxation time,τ of wate at 10, 15, 20, 25, 30, 40, 50 and 60 C Fig. 4: Vaiation in calculated of dielectic constant, ε and loss facto, ε with fequency at oom tempeatue (25±1) C fo vaious wate content, m.c in hydogel Tempeatue effects analysis: Figue 5 shows the ε vesus ωε plot fo pue wate at vaious tempeatue, T. The measued elaxation time, τ of bulk wate anging C can be obtained fom fitting of Fig. 5 by using (2) ae tabulated in Table 3. It is expected that the hydogen bonds ae boken at high tempeatue, which leads to incease in mobility of side chains o deceases of the elaxation time, τ. The elaxation time, τ of wate and hydogel ae plotted as Ahenius (Hasted, 1973) plots in Fig. 6. The linea elationships in Fig. 6 indicate that the tempeatue dependence of the elaxation time can be descibed by (6): 1 ln ( τ ) = Q + ln τ R ( T + 273) o (6) 274 Table 3: The estimated values of elaxation time, τ fo pue wate and hydogel unde seveal tempeatue, T τ(ps) Kaatze, Hasted, Sample T ( C) This study (2005) (1973) Wate % m.c This study Hydogel GHz GHz % m.c This study hydogel GHz GHz % m.c This study hydogel GHz GHz Whee: h τ o = exp k T 273 ( + ) ( ΔS R) (7)

6 Whee: R = the gas constant (R = J mol 1 K 1 ) k = The Boltzman constant (k = J K 1 ) h = The Phanck constant (h = J sec 1 ) This condition will cause the elative pemittivity, ε of hydogel ae evident less sensitive to highe tempeatue (> 30 C), especially fo hydogel with low wate content (< 80% m.c) as shown in Fig. 7. The linea slope in Fig. 6 epesents the mean activation enegy, Q of bulk wate and gives 18.3 kj mol 1 compae with liteatue (Nyfos and Vainikainen, 1989) value 18.8 kj mol 1. While, the estimated value of In(τ o ) is o τ o = sec. Indiectly, the entopy change, ΔS can be detemined fom τ o. The simila pocedues ae implemented in hydogel and the mean activation enegy, Q fo 96.8 and 80.0% m.c hydogel ae estimated between 12.1 and 5.45 kj mol 1 fo 2-10 GHz and 14.2 and 5.84 kj mol 1 fo GHz, espectively, as listed in Table 4. This mean that the enegy, Q eleased (o absobed) pe mole fo the hydogen bond ae fomed in hydogel, ae less than the hydogen bonds fomed in pue wate fo entie fequency. In othe wod, the lowe value of Q, the moe stable of the hydogel. In additional, a negative value of ΔS indicates a decease in entopy, the less andom in satuated hydogel system. Figue 7 shows the vaiation in elative pemittivity, ε of hydogel with fequency fo vaious tempeatue, T. As mention ealie, the binding between chain and wate molecules ae vey stable fo high concentated hydogel, thus the slight highe tempeatue o enegy is not significant to polaize the molecules in the hydogel compaed to the pue wate. Table 4: The estimated values of mean activation enegy, Q and elaxation coefficient,τ o fo pue wate and hydogel fo fequency ange of 2-20 GHz f Q T Δ S Sample (GHz) (kj mol 1 ) ln(τ o ) (ps)(τ o ) ( C) (J (K mol) 1 ) Wate % m.c hydogel % m.c hydogel % m.c hydogel (c) Fig. 6: Ahenius plots fo bulk wate and hydogel

7 CONCLUSION In this study, a linea fitting method was used to eplace complicated numeical outine fo finding out the calculating dielectic paametes. The linea polynomial fitting is used to estimate the values of dielectic static, ε s elaxation time, τ and mean activation enegy, Q as well as entopy change, ΔS. The igoous dielectic model which is consists of two elaxation pocesses, is ceated successfully to descibe the electic popeties of the hydogel mixtue. REFERENCES Hasted, J., Aqueous Dielectics. Chapman and Hall, New Yok, ISBN: , pp: 302. Kaatze, U., Electomagnetic Wave Inteactions with Wate and Aqueous Solutions. In: Electomagnetic Aquamety, Kupfe, K. (Ed.). Spinge, New Yok, ISBN: , pp: Nyfos, E. and P. Vainikainen, Industial Micowave Sensos. Atech House, Nowood, MA., ISBN: , pp: 351. Robet, P., Electic and Magnetic Popeties of Mateials. Atech House, Nowood, MA., ISBN: , pp: 458. Sengwa, R.J. and K. Kau, Dielectic Dispesion studies of poly(vinyl alcohol) in aqueous solutions. Polyme Int., 49: DOI: / (200011)49: 11<1314::AID-PI479>3.0.CO;2-8 Fig. 7: Vaiation in elative pemittivity, ε of wate and 80% m.c hydogel with fequency fo vaious tempeatue, T 276