Analysis of mobile ionic impurities in polyvinylalcohol thin films by thermal discharge current and dielectric impedance spectroscopy

Analysis of mobile ionic impurities in polyvinylalcohol thin films by thermal discharge current and dielectric impedance spectroscopy Analysis of mobile ionic impurities in polyvinylalcohol thin films[.]

current and dielectric impedance spectroscopy

M Egginger and R Schwödiauer,

Citation: AIP Advances 2, 042152 (2012); doi: 10.1063/1.4768805

View online: http://dx.doi.org/10.1063/1.4768805

View Table of Contents: http://aip.scitation.org/toc/adv/2/4

Published by the American Institute of Physics

Analysis of mobile ionic impurities in polyvinylalcohol thin films by thermal discharge current and dielectric

impedance spectroscopy

M Egginger1,2and R Schw ¨odiauer1,a

1Department of Soft Matter Physics, Johannes Kepler University, Altenbergerstraße 69,

4040 Linz, Austria

2isiQiri interface technologies GmbH, Softwarepark 37, 4232 Hagenberg, Austria

(Received 15 August 2012; accepted 9 November 2012; published online 21 November 2012)

Polyvinylalcohol (PVA) is a water soluble polymer frequently applied in the field of organic electronics for insulating thin film layers By-products of PVA synthesis are sodium acetate ions which contaminate the polymer material and can impinge on the electronic performance when applied as interlayer dielectrics in thin film transistors Uncontrollable voltage instabilities and unwanted hysteresis effects are regularly re-ported with PVA devices An understanding of these effects require knowledge about the electronic dynamics of the ionic impurities and their influence on the dielectric properties of PVA Respective data, which are largely unknown, are being presented

in this work Experimental investigations were performed from room temperature

to 125◦C on drop-cast PVA films of three different quality grades Data from ther-mal discharge current (TDC) measurements, polarization experiments, and dielectric impedance spectroscopy concurrently show evidence of mobile ionic carriers Results from TDC measurements indicate the existence of an intrinsic, build-in electric field of pristine PVA films The field is caused by asymmetric ionic double layer formation at the two different film-interfaces (substrate/PVA and PVA/air) The mobile ions cause strong electrode polarization effects which dominate dielectric impedance spectra From a quantitative electrode polarization analysis of isothermal impedance spectra temperature dependent values for the concentration, the mobility and conductivity together with characteristic relaxation times of the mobile carriers are given Also shown are temperature dependent results for the dc-permittivity and the electronic resistivity The obtained results demonstrate the feasibility to partly remove contam-inants from a PVA solution by dialysis cleaning Such a cleaning procedure reduces

the values of ion concentration, conductivity and relaxation frequency Copyright

2012 Author(s) This article is distributed under a Creative Commons Attribution 3.0 Unported License [http://dx.doi.org/10.1063/1.4768805]

I INTRODUCTION

Polyvinylalcohol (PVA) is an attractive dielectric polymer in the field of organic electronics Since the first successful application of PVA as a gate dielectric for an all-organic field effect transistor (OFET), in the year 1990,1 the material became increasingly popular over the years

By 2006, PVA was considered as “ one of the most widely used polymer dielectrics for organic

electronic applications”.2Today, PVA is still wide spread and a commonly used polymer dielectric

in the research field of organic electronics.3 6 Much of this attraction is due to easy processing in combination with desirable dielectric characteristics: Very good insulating properties and notably

a fairly high dielectric permittivity qualified PVA as a favorable organic material for interlayer dielectrics The widespread use of PVA however, revealed also a serious disadvantage as the material

a Electronic mail: reinhard.schwoediauer@jku.at

2158-3226/2012/2(4)/042152/15 2, 042152-1 Author(s) 2012

was found to be responsible for uncontrollable voltage instabilities in OFETs Those instabilities, which cause a hysteresis in the device’s transfer characteristic, have been frequently reported for PVA and other dielectrics alike (see7,8and the references within), but a generally accepted explanation for the cause has not yet surfaced

As the device problems are obviously related to the interlayer dielectric it appears to be necessary

to dedicate further research work towards a better characterization of the dielectric materials involved The electrical nature of many insulating materials, including PVA, is only partially understood Only the most common electrical properties are well known Standard parameters like the dielectric permittivity and the dielectric loss factor, conductivity and dielectric strength, though important, often give insufficient information when it comes to electronic applications Equally important, but more subtle, are properties related to charge injection, charge trapping and charge storage Also the effect of impurities, especially the presence of mobile ionic carriers, often have a crucial impact on the electronic performance Thus, knowledge about related parameters, like temperature dependent concentration and mobilities of ionic impurities, are most relevant

For pure PVA - a material which is predominately produced and used for non-electronic ap-plications - the respective data are largely unknown This work is a first step towards a more comprehensive characterization of PVA to gain a better understanding of the electrical properties beyond already tabulated standard parameters The paper presents a series of experiments with three different grades of PVA: A standard off-the-shelf product, a special-purpose PVA material for electronic applications, and a dialysis cleaned special-purpose material are being discussed Thermal discharge current (TDC) measurements with all three grades, and additional polarization experiments demonstrate the presence of mobile ionic carriers Pronounced effects of electrode polarization appear already in pristine PVA films The electrode polarization of all samples has been investigated in detail by dielectric impedance spectroscopy (DIS) A quantitative fit of the measured spectra allow to deduce the temperature dependent concentration of the mobile ionic carriers and the related mobility, conductivity and relaxation time Further parameters like the dc-permittivity and the dc-resistivity are also given with respect to temperature

The results reveal that the dielectric properties of PVA are generally affected by the ionic impurities Dialysis cleaning of the polymer solution can reduce the concentration of impurities which lead to a lower ion conductivity and to a longer ion relaxation time

II EXPERIMENT

A Materials and sample preparation

A 7% solution of “normal grade” PVA was prepared with 1.75 g of PVA from Sigma Aldrich with tradename MowiolR 40–88 (average molecular weight M

W∼ 205000 g/mol) This off-the-shelf polymer was submerged and dissolved at 80◦C in 25 ml ultra pure, 18 M-cm water from a

Millipore Ultra Pure Water System In the same way a similar 7% solution of “electronic grade” PVA was prepared from a MowiolR 40–88 special-purpose material (for electronic application), received directly from the manufacturer: “Kuraray Specialties Europe GmbH” From this 25 ml solution approximately 2×5 ml were filled in two dialysis tubings (Sigma–Aldrich, D0530) and submerged into a 500 ml beaker with ultra pure, 18 M-cm water Dialysis proceeded under constant stirring

for more than 24 hours at room temperature The final obtained “dialysis grade” PVA solution was poured into a volumetric flask and stored for further use at 4◦C; the same happened also with the

“normal grade” and the “electronic grade” solutions Small amounts of the solutions were further passed through a 0.45μm PE filter and stored at 4◦C as well The filtered solutions were taken for

PVA film casting

The quantitative analysis of experimental data require samples of a certain minimum thickness Films with thicknesses between 20 and 70μm were fabricated from all three PVA grades via

drop-casting on a specially prepared PEEK substrate A schematic of the substrate is depicted in Fig.1(a) The 2 mm thick disc with a diameter of 30 mm has a polished surface with a shallow circular groove

of 15 mm in diameter The groove serves two purposes: First it marks and defines the area which

is to be filled with a predefined volume between 150 and 600μl of PVA solution, and second the

FIG 1 PEEK substrate for PVA drop-cast films with sub-surface contact of the bottom gold electrode (a) Cross sectional view of the substrate, the drop-cast PVA film, and the gold coated stainless steel top electrode (b) Geometric capacitor model

of a drop-cast PVA film with an air gap between the non-uniform film surface and the top electrode (c)

groove works as a kind of “drop stop” which hinders the PVA-water solution to form a spherical drop under the strong force of surface tension As a result the coated area remains coated during the slow drying process, and, as sketched in Fig.1(b), the final film dries into a plano-concave shape with maximal thickness at the rim, and a thinner central area with only a moderate thickness variation Within this area the films are electrically contacted by a small, gold coated stainless steel disk of 5

mm diameter and 1 mm height The electrical counter-contact at the bottom is realized with a 13

mm diameter gold electrode evaporated on top of the PEEK substrate Prior to evaporation a 0.5

mm interconnect-hole, perpendicular through the substrate, and positioned 5 mm off the center, is filled with silver paste to contact the open end of an insulated wire which is fed through a second bore parallel to the surface This embedded contact wire is designed to avoid any unwanted surface leakage-currents between top- and bottom electrode as they may occur in high-voltage polarization experiments

Samples were drop-casted from filtered PVA solutions with a variable volume pipette Slow drying was carried out at room temperature beneath a protective dome under constant flow of nitrogen The dried PVA films are hygroscopic and were thus stored in an evacuated desiccator for

a number of days before being installed in the experimental setup

B Experimental setup and procedure

A custom made sample chamber has been designed and used for all measurements A scheme

of the sample chamber together with the installed PVA sample and the instrumentation is presented

in Fig.2 The aluminum chamber can be evacuated and/or filled with inert gas The PEEK substrate

is sticked to a Linkam THMSB heating element via a thin layer of heat conductive paste On the substrate is the PVA film with the top electrode centrally positioned and firmly held in place by a thermally and electrically insulated clamping bar Both, the top- and the bottom electrodes are wired

to BNC feed-through connectors The connected instrument for TDC measurements is a Keithley

6514 System Electrometer, an additional (Rhode & Schwarz NGK 280) voltage source in series is used for polarization experiments, and DIS is performed with a Novocontrol measurement system consisting of an Alpha-A mainframe and a ZG4 test interface Together with a Linkam TSM 90 temperature controller the instruments are connected to a personal computer for instrument control and data storage Reference data of the temperature gradient across the PEEK substrate were recorded from room temperature to 170◦C with a 100μm thin NiCr-Ni thermocouple embedded in a ∼150

μm thin epoxy-film on a dummy-substrate.

A sample was removed from the desiccator and installed instantly in the chamber The bottom electrode-wire was soldered to the BNC ground and the top-electrode was positioned and held by the attached rigid signal wire at some distance above the PVA film The gap between film and top-electrode remained during a following 24 hour film-drying procedure where a reduced

chamber-FIG 2 Experimental setup for thermal discharge current measurements and dielectric impedance spectroscopy on drop-cast PVA films.

pressure of<20 mbar was maintained by a continuously operating pump The sample temperature

was set to 52◦C A stronger drying was avoided because temperatures above 55◦C were already found to introduce irreversible changes in the dielectric properties of PVA After 24 hours, heating was switched off and the chamber was flushed with nitrogen The chamber was opened quickly and the top-electrode was now placed onto the PVA-film and firmly fixed with the clamping bar Immediately after, the chamber was closed again, evacuated and flushed with nitrogen several times All measurements were performed under nitrogen atmosphere with ca 200 mbar overpressure

III RESULTS AND DISCUSSION

A Thermal discharge current (TDC) measurements

Strong TDCs in the range of several nA/cm2have been measured from pristine PVA samples at ramped temperature heating and during isothermal condition The pristine PVA samples, prepared, installed and directly connected to our ammeter as described, have neither been poled nor charged, but produce nevertheless a pronounced current upon first heating!

Examples of such spontaneous discharge currents from all three PVA grades are given in Fig.3 The TDCs were recorded during linear heating from room temperature (∼22◦C) to a final PVA

film temperature of about 120◦C with a constant rate of 10◦C/min, followed by a long isothermal period of several days During the whole period the temporal evolution of the currents show a number of features which are visible in the log-linear representation of Fig.3(a)and in the log-log representation of Fig.3(b) In the log-log representation only a low increase in current is observed below the supposed glass transition temperature of about 60◦C As the temperature increases all samples and all grades of PVA show a pronounced kink between 80◦C and 100◦C This kink seems

to be characteristic for the material; a comparable feature has also been observed earlier elsewhere9 with thermally stimulated discharge current (TSDC) experiments of strongly polarized PVA layers With further increase of temperature the discharge currents rise sharply, and at the final temperature

of ca 120◦C some fairly high values in the range of several nA can be observed Within two minutes from the beginning of the isothermal period the discharge currents increase to maximum values The maximum current values do not correlate with the quality grade, but seem to depend on the film thickness in a non-trivial way Thicker films (> 10 μm) were found to produce higher currents,

but also much thinner spin-casted films (<2 μm) produced current peaks of comparable magnitude.

The transient discharge current of the samples follow the universal Curie-von Schweidler power

law function, I(t) ∝ t n , with a common exponent of n 11 for rising currents (driven by

ramped-temperature) and n −0.9, for decreasing currents during the first period of isothermal discharge This first period ends as the discharge currents deviate from the power law and pass through zero

0.0 1.0 2.0

-40 0 40 80 120

time t (min) -14

-12 -10

(a)

(b)

FIG 3 Thermal discharge current vs time at constant rate heating and isothermal conditions from a 33μm thick “normal

grade”, a 40 μm thick “electronic grade” , and a 25 μm thick “dialysis grade” , PVA film in log-linear (a), and log-log

(b) representation Arrows indicate the polarity reversals.

towards another extremum with opposite polarity Such a change in polarity can be observed more than once with reduced currents and growing time intervals

Polarity reversal of a TDC demonstrates the simultaneous existence of dipolar- and unipolar charges Dipolar charges can be directly related to the hydroxyl (OH) groups in the chemical structure

of PVA The origin of unipolar charges must be ascribed to the ionic sodium acetate (NaAc) ash which is a by-product of PVA production and which is always present in the material in some amounts.7,10The ash content of both PVA materials used for this study has been measured explicitly

by the manufacturer with 0.13% and 0.14 % Na2O for the “normal grade” and the “electronic grade” respectively As the ash content measurement requires a substantial amount of undissolved polymer,10 the ash content of the dissolved “dialysis grade” PVA was not measured Compared

to the “electronic grade” PVA a reduced ash content in the “dialysis grade” film can be expected Taking dissociated Na+/Ac−ions into account the built-up of an inhomogeneous charge distribution across the film thickness must be expected for all solution processed layers The electrode/polymer solution interface in particular cause a multiple double layer formation due to metal polarization and ion accumulation.11For a watery PVA solution, drop-casted onto a gold surface, a Helmholtz-layer of hydrated Na+ions must be considered at the Au/PVA solution interface According to the Gouy-Chapman theory, beyond the Helmholtz layer, an additional excess charge of positive polarity

is accumulated within a diffusive space charge region having an extension in the order of the Debye

length, LD

The electrical conditions at the opposite air/polymer-solution interface is different Theoreti-cal models strongly suggest a net surplus of polarizable anions which have a propensity for the interface.12 Because of this, and also because of the additional requirement for charge neutrality, a

non-zero electric field must act beyond LD, across the bulk of the polymer solution, where NaAc and

OH groups with a net dipole moment shall experience a polarization As the liquid polymer solution dries to a solid thin film the charge distributions at the interfaces are being fixed and a persistent

polarization, P, in the bulk is being stabilized.

Thermally stimulated discharge currents of charged and polarized electrets - dielectric mate-rials with quasi-permanent charges - have been investigated and analyzed by van Turnhout.13 Van Turnhout showed that charged electrets with intrinsic space charges and polarized dipoles produce a

transient current density, i(t), which is directly related to the difference in decay rates between a po-larization, P(t), and a space charge related surface charge density, σ(t), at the electrodes: i(t) ∝ d[P(t)

0 2000 4000 6000 8000 10000 12000

time t (min) -0.3

-0.2 -0.1 0.0 0.1 0.2 0.3

-100 -50 0 50 100

FIG 4 Ionic depolarization current, I, showing the transit time of ionic carriers from “normal grade” PVA at 80◦C, caused

by multiple polarization experiments with alternating voltage steps of ±100 V.

− σ (t)]/dt This relation is being derived under the assumption of an air-gap between the electret

surface and one electrode An air-gap is crucial to observe a current reversal The experiments reveal such polarity reversals of the TDCs only because all drop-cast PVA samples dry to a plano-concave shape, where an air-gap indeed exists between the plano-concave PVA surface and the planar top electrode

In view of van Turnhout’s analysis, the TDCs in Fig 3 reflect the motion of dipolar and unipolar charges towards a new equilibrium under short circuit condition at elevated temperature

As explained in13 σ and P decay not independently, but the decay rate of the space charge is

slowed down by the polarization that weakens the field created by σ The discharge starts with

reorientation of dipoles which have short relaxation times and which are present in large amounts This gives rise to strong discharge currents With some delay to the dipole relaxation the ionic space charges at the bottom Au/PVA interface start to drift and establish a long lasting current with opposite polarity that eventually reverses the total TDC The TDC experiment always show the technical current directed from the bottom- to the top electrode for the fast polarization current,

˙

P, and the long lasting space charge current, ˙ σ , is always directed from the top- to the bottom

electrode This observation agrees with the assumption that the positive Na+ cations are initially located near the bottom electrode and they slowly move through the dielectric under short circuit condition at elevated temperatures After several days the second reversal of the current direction with already very low currents indicate a still unstable and ongoing interaction between dipoles and ions

B Polarization and transient current measurements

The dynamics of mobile ionic carriers in solid polymer electrolytes is usually investigated with transit time-of-flight (TOF) polarization experiments.14–16A high-field TOF polarization experiment

for electrolytes with a lower ion conductivity has been introduced by Kohn et al.17Similar experi-ments with drop-cast PVA films also show an ion current maximum with a characteristic time lag after polarization reversal Figure4 show recorded data of a TOF polarization experiment with a

ca 40μm thick “normal-grade” PVA sample at 80◦C and with polarization steps of±100 V The experiment was preceded by thermal discharge under short circuit condition as described above for more than 1000 minutes The final discharge current was in the order of 10−11A The first poling step had a duration of 80 min and was too short for a sufficient ion repolarization The subsequent voltage reversal resulted in two current peaks appearing at transit times of 12 and 220 minutes past polarization reversal After a much longer polarization for more than 1000 min the next polarization reversal caused a single current peak at a transit time of 270 min With repeating polarity reversals, transit times between 100 min and 300 min were observed The shape and the maximum values of the current peaks are not reproducible but change with every new polarization step This change indicates a change of the material which will be discussed later below In general, the accuracy and

106

109

1012

103

106

109

1012

100

103

106

109

10-2 100 102 104 106

frequency (Hz)

10-2 100 102 104 106 frequency (Hz)

10-2 100 102 104 106 frequency (Hz)

103

106

109

103

106

109

1012

103

106

109

1012

(a, i)

(a, ii)

(a, iii)

(a, iv)

FIG 5 Isothermal dielectric impedance spectra from drop-cast PVA films of “normal-” (a,_), “electronic-” (b,_), and

“dialysis grade” (c,_), with recorded real (_, i) and imaginary (_, ii) components at 19 different temperatures between ca.

22 ◦C and 125◦C, together with fitted imaginary and real impedance data related to 125◦C (_, iii) and 70◦C (_, iv).

the reproducibility of the polarization and transient current measurements were low for all PVA samples and grades For a quantitative analysis much more reliable and accurate data could be obtained with dielectric impedance spectroscopy

C Dielectric impedance spectroscopy (DIS)

Impedance spectra of all PVA samples were recorded with an effective signal amplitude of 50

mV in the frequency range from 10 mHz< f < 10 MHz at isothermal conditions in 18 temperature

steps from room temperature to 125◦C PVA film temperature Examples of the impedance spectra are displayed in Fig 5 with three columns from left to right for “normal-”, “electronic-”, and

“dialysis grade” PVA films respectively The first two rows show the real, Z, and the imaginary, Z, components of the impedance spectra for the total of 19 temperatures Connected data points by solid lines indicate the first spectra at room temperature and the last spectra at 125◦C At room temperature,

below frequencies of f  30 mHz, the impedance of all samples are in the order of >1011, and both

impedance components show a decrease which is almost proportional to inverse frequency This frequency behavior follows an empirical impedance function, known as “constant phase element”

(CPE) which takes the form ZCPE = Z0(iωτ) −β, where i=√−1 represents the imaginary unit,

ω = 2πf denotes the angular frequency, and Z0,τ and β ∈ (0, 1] are temperature dependent

parameters A CPE appears in the majority of experimental data on solid and liquid electrolytes.18 The CPEs of drop-cast PVA samples at room temperature are reasonably well described with a common exponent ofβ ≈ 0.98.

With increasing temperatures the impedance,|Z| =√Z2+ Z2, decreases and deviate from

the CPE response A maximum in the imaginary part of the impedance, near 30 mHz, is already clearly visible at about 50◦C for the “normal grade” PVA For the “electronic-” and “dialysis grade” PVA the maximum appears at ca 60◦C The maxima shift to higher frequencies with further elevated temperatures, and the impedance in the lower frequency range decrease substantially

At the final film temperature the low frequency impedance values have dropped by five orders

of magnitude and the maxima have shifted into the kHz range In general, the high temperature impedance data over the whole frequency range resemble very much spectra that are dominated by

strong electrode polarization effects Such spectra have been frequently observed with ion-blocking electrodes connected to electrolyte systems.19–23

The ac-characteristic of electrode polarization (EP) had been investigated and analyzed by Chang and Jaffe.24The work was continued by MacDonald25,26and also by Coelho.27,28The general theory

of EP was simplified for less complex situations by Klein et al.21Klein’s description of EP for single ion conductors has been used for this work to fit the PVA impedance data Examples of the fitted data are given in the third and the fourth row of Fig 5 with a spectra at maximum temperature and a second spectra at 70◦C All spectra together with the related fit functions are presented in the supplemental material.29

D Data Analysis

The fitting model for data analysis describes a PVA sample, according to Fig.1(c), as parallel

plate capacitor with a total area A, and an overall thickness L, together with a thin air-gap located underneath the electrode and defined by an effective gap-area, Ag, and an effective gap-thickness, Lg Both air-gap parameters were estimated experimentally The dielectric material response is based on

an elementary impedance description with an ohmic, temperature dependent PVA film resistance,

˜

R, and a dispersive capacitor in parallel The corresponding impedance is

1+iω ˜R C0εEP(ω)β (1)

where C0= ε0A/ ˜L expresses the geometric capacitance defined by a PVA surface area ˜A, and a˜ corresponding film thickness ˜L; ε0 denotes the vacuum permittivity The temperature dependent exponent,β, is related to the CPE which describes the power law characteristics of the spectra The

dielectric permittivity,εEP(ω), is assumed to be determined by electrode polarization which can be

modeled with a Debye-like permittivity:25εEP(ω) = εs+ (εs, EP− εs)/(1+ i ωτEP);εsandεs, EPare the temperature dependent high- and low frequency limits, andτEP is the temperature dependent relaxation (build up and decay-) time for the EP due to mobile ionic carriers The applied fitting model uses a modified formula based on the dielectric function proposed by Cole and Cole30

εEP(ω) = εs+ εs,EP − εs

The temperature dependentα-parameter allows for an improved fitting of the Zextrema It was

found close to a Debye characteristic (α = 1), ranging between 0.9 < α < 1, and it can be associated

with a distribution of relaxation times.18The EP relaxation time,τEP, is related to the transit-time of ions from one interface to the other and it scales directly with the drift length, ˜L A distribution of

τEPcan be expected due to the different and inhomogeneous interface regions and related trapping mechanisms, and also because of the irregular thickness of the drop-cast film

The drift length and its relation to the Debye length is crucial in the theory of EP The relation was introduced and defined by Macdonald25denoted with the symbol M≡ 1

2L˜/LD This parameter

is related to almost all dielectric properties and it also relates the high frequency permittivity, εs, with the low-frequency permittivity21

The parameter M can therefore be obtained, in principle, from experimental data via the high- and low frequency limits (M  εs, EP/εs 1) of the real permittivity, ε = Re(εEP) Alternatively, the

parameter M can be obtained also via the frequencies f εand f δassociated with the maximum of the imaginary permittivity,ε= Im(εEP), and the maximum of the loss angle, tanδ = ε/ε, respectively;

the relation is M = ( f δ /f ε)2.21

However, the spectra of PVA in permittivity representation, ε(ω) = ε(ω) − i ε(ω), do not

show any evident saturation with high- and low frequencyε −limits, and the maxima of ε are

not clearly expressed either, but superimposed by conduction processes Important characteristic

values can be extracted more easily from the impedance representation, Z( ω) = Z(ω) + i Z(ω), as

displayed in Fig.5 The mid-frequency minimum and the high frequency maximum of Z(ω) are

clearly expressed and separated Thus, in a good approximation, the associated frequencies, fmand

fh, can be directly related to f ε ≈ f2

m/fh, and f δ ≈ fm These two frequency values allow to estimate the parameter

with a better accuracy The Z(ω) data also allow to determine directly the temperature dependent β-parameter via simple power-law fits, since at sufficient distance from the extrema Z(ω)∝ω −β.

For solid and liquid electrolytes the CPE relatedβ-parameter is generally known not to be constant

over the entire frequency range.18 For PVA at elevated temperatures, β was also found to be

slightly higher in the high frequency regime, f > fh, compared to the mid- to low frequency range,

fl < f < fm All PVA Z( ω) spectra were fitted with the high frequency β values throughout the

full frequency range Of course, in the low frequency range, and especially at lower temperatures, the data are less accurately described But fits with low frequencyβ values produce even stronger

deviations in the higher frequency- and higher temperature range as shown with dashed lines in Fig.5(a, iii) and (a, iv) Nonetheless, fits with low frequency β values are helpful in case of a low

frequency Z-maximum Such a maximum could be confirmed for the Z(ω) spectrum of “normal

grade” PVA at the highest experimental temperature The apparent saturation of Z(ω) towards

the lowest frequencies constitutes one branch of the low-frequency maximum, at fl 10 mHz,

which can be directly related to an effective sample resistance R A simple analysis of Eq.(1)at fl

yields

Z(2π fl) 1

2R

sin (πβ/2)

The knowledge of R for a spectra at a specific temperature determines the corresponding fit function

to a large extent The best-fit parameters for that spectra can thus be taken as a reliable reference

for all successive fits of data without a fl-maximum at lower temperature levels Unfortunately, low-frequency maxima could not be measured for “electronic grade” and “dialysis grade” PVA samples Measurements at even lower frequencies and/or higher temperatures were not evaluated because the additional thermal load accelerates permanent changes of the material due various effects such

as degassing of water vapor and molecular fragments,10 increased crystallization and oxidation

and softening effects So, any distinct values of R are not available for “electronic-” and “dialysis

grade” PVA, and because of the product ˜R εEP(ω) in Eq.(1)the fit parametersεsandεs, EPcannot

be determined without ambiguity Therefore, impedance data fitting of “electronic-” and “dialysis grade” PVA started with an initial educated guess of parameters which were chosen reasonably similar to the “normal grade” parameters

E Fit Results

Data fitting has been performed manually with routines and tools encoded in MathematicaR. Much effort was made to find all fit parameters close to sufficiently smooth functions with reasonable

physical values Following the work of Klein et al.21 the fit parameters can be directly converted (see Appendix) into characteristic material properties The basic non-ionic dielectric properties are given with Fig.6showing for all three PVA grades the temperature dependent electronic resistivity,

ρ, and the the static permittivity, εs, of an ion-free PVA material The “electronic-” and “dialysis grade” spectra below 70◦C cannot be fitted reliably because of disappearing Z(ω)-minima, and

hence related data are not given Results for the fitted spectra suggest a higher electronic resistivity for the special-purpose “electronic grade” PVA compared to the standard “normal grade” PVA The highest resistivity shows the “dialysis grade” PVA which is on average by a factor of 1.9 above the

“electronic grade” PVA The static dielectric permittivities of all grades are very similar and show practically no difference within the fitting accuracy

The amounts of mobile ionic impurities are displayed in Fig.7, and numerical values at selected temperatures are given in TableI At temperatures above 85◦C all grades of PVA show a

concen-tration, p, of mobile Na+ions in the order of 1024m−3with a somewhat higher concentration close

to 1025m−3 in the “electronic grade” PVA This matches with the measured Na O ash content of

The amounts of mobile ionic impurities are displayed in Fig.7, and numerical... fragments,10 increased crystallization and oxidation

and softening effects So, any distinct values of R are not available for “electronic-” and “dialysis

grade” PVA, and because of. .. εEP(ω) in Eq.(1)the fit parametersεsand< i>εs, EPcannot

be determined without ambiguity Therefore, impedance data fitting of “electronic-” and