Dielectric Spectroscopy for Polymer Melt Composition Measurements.
Laboratory and in-line dielectric spectroscopy studies of molten polymers revealed the ability to make composition measurements of the comonomer concentration along the polymer chains. The dielectric permittivity or capacitance was found to be proportional to the polymer sidechain composition. The length of the polar sidegroup dictated the optimum measurement frequency; i.e., a short sidechain, such as the C-Cl bond in chlorosulfonated polyethylene, required a high measurement frequency (short relaxation time) due to the rapid mobility of the sidechain, whereas a longer sidechain, such as the vinyl ether sidegroup in Nafion(r), required a much lower frequency (longer relaxation time) to orient the sidechain to a measurable extent. For in-line process studies, a new cylindrical, interdigitated dielectric sensor and associated electronics were developed to make measurements on molten polymers at the exit of an extruder up to 400[degrees]C and 3000 lbs/[in.sup.2]. In-line studies of molten polymers revealed a d irect relationship between the dielectric signal and the polymer comonomer composition. The sensor represents a non-invasive, real-time process composition measurement and can be integrated to provide closed-loop process control.
Composition analysis of molten polymers has long been a highly desirable yet extremely elusive measurement. The processing of most polymer melts normally involves high temperatures and pressures, corrosive and erosive environments, and multiphase systems, which make in-line measurements challenging. In addition, the theoretical understanding of polymer melts is in its infancy, allowing at best speculative data interpretation. The desire is to extend the range of known analytical techniques used for composition evaluation from a low temperature regime, where variables can be independently separated and studied, to a high temperature regime, where many variables contribute simultaneously to the signal. The method discussed in the present paper involves measuring the electrical properties of a polymer to uncover the polymer's physical and chemical properties using dielectric spectroscopy. A limited number of research papers exist on dielectric composition measurements of polymers dealing mainly with the motion o f dipoles at or below the glass transition temperature ([T.sub.g]). With the possible exception of high temperature cure monitoring of composites, applications of dielectric studies to polymer melts in chemical processes are virtually nonexistent.
Dielectric spectroscopy imposes a sinusoidal voltage (or electric field) across a stationary or flowing polymer and measures the resultant alternating current produced from the movement and energy associated with dipole orientation and ionic conduction. These dielectric measurements are then related to the physical and chemical structure of the polymer.
In low temperature dielectric experiments, the orientation of localized dipoles is measured in the presence of an alternating electrical field over a range of temperatures. For a copolymer, where the two repeating units have different dipolar behavior, the concentration of comonomer units can be measured with dielectric spectroscopy. An example of this type of measurement was shown for Nafion(r) (DuPont) copolymers . Nafion(r) is a copolymer of tetrafluoroethylene and a sulfonate or carboxylate vinyl ether. The vinyl ether sidechain displays [alpha] and [beta] transitions from -100 to 20[degrees]C, which were used to determine the comonomer content or equivalent weight of the polymer.
Sub-glass and glass transitions can be readily detected in polymers with dielectric spectroscopy. When the temperature is raised above the [T.sub.g], however, ionic conduction plays a progressively more dominant role in the measurement and tends to mask the dipolar signal contribution. Higher frequencies are required to suppress the ionic contribution. At lower frequencies, however, the ionic mobility provides an additional measurement of polymer rheology, as is shown in a companion publication .
Hedvig  and Nagy et aL  pioneered the study of the electrical properties of polymers with dielectric spectroscopy. All analyses were limited to temperatures below the glass transition temperature of the polymer; in this temperature range, the ion mobility was very small and the motion of permanent dipoles was observed. Sub-glass and glass transition temperatures were obtained accurately using dielectric spectroscopy. Nagy developed many of the original dielectric measuring devices for analytical measurements.
The application of dielectric spectroscopy to high temperature polymer melts has been limited by both a lack of fundamental knowledge of polymer melt behavior and the difficulty of developing a rugged sensor to make dielectric measurements in harsh environments. Unfortunately, basic knowledge of molten polymers is lacking. Dielectric sensors, developed in the past [3-5] for in-process use, have limited application to polymer measurements because of temperature and pressure limitations, inadequate geometrical design, poor signal to noise ratio, and/or inappropriate materials of construction. The sensor described in the present paper eliminates these limitations and allows direct in-line measurements of flowing molten polymers up to 400[degrees]C and 3000 psi .
Much of the fundamental understanding of the dielectric behavior of matter can be traced back to the pioneering work of Debye  in the 1920s. Although "capacitance" measurements were crudely made before Debye's time, Debye's basic studies on the motion and energy of dipoles and ions created the foundation to interpret these and future measurements. Later, extensions of the Debye theory were put forth by Onsager , Kirkwood , and Frohlich ; a comparison between these methods and experimental data of liquids is given by Smyth . MacDonald  presents a good overview of polarization in many different materials whereas a thorough mathematical treatment is given by von Hippel . Unfortunately, although these theories yield accurate results for liquids, they are inappropriate in many polymer applications.
In the early 1980s, Senturia and co-workers  designed and built a fringing field dielectric sensor probe as opposed to the parallel plate sensor used up until this time. The new sensor made measurements at very low frequencies (0.05 Hz), enabling the cure monitoring of epoxies. Recent applications of this technique are given by Fodor and Hill  while a general background on the subject of dielectrometry of polymers is also available .
The present study examines the electrical properties of polymers above the melting temperature ([T.sub.m]). Very few studies to date attempt to examine the properties above even the [T.sub.g] let alone [T.sub.m] mainly because the analysis becomes increasingly more difficult at the higher temperatures. Ions, permanent dipoles, and induced dipoles may all play significant roles in affecting the response at these elevated temperatures. This paper presents experimental data backed by theoretical arguments for a variety of polymers above [T.sub.m].
Dielectric measurements are based on applying an alternating electric field across a material and examining the orientation of permanent and induced dipoles and the separation of positive and negative ions in the material. The motion of dipoles and ions can be represented by a complex admittance (Y in [[omega].sup.-1] defined as
Y = I/V = [I.sub.in] + [iI.sub.out] = [I.sub.o]sin[delta] + [iI.sub.o]cos[delta]/V (1)
where I is the total current (Amps), V is the voltage (Volts), [I.sub.in] is the in-phase current with the voltage (Amps), [I.sub.out] is the out-of-phase current with the voltage (Amps), [I.sub.o] is the amplitude of the total current (Amps), and [delta] is the phase angle (degrees).
The complex capacitance (C in Farads) is composed of a real capacitance (C in Farads) and an imaginary capacitance or dissipation (Din Farads) and related to the real and imaginary components of the complex permittivity ([[epsilon].sup.*]) by the capacitance in a vacuum ([C.sub.o] in Farads).
[C.sup.*] = C + iD = [C.sub.o][[epsilon].sup.*] = [C.sub.o]([epsilon]' + i[epsilon]") (2)
Knowledge of the sensor geometry allows the computation of the absolute dielectric permittivity ([epsilon]') and the dielectric loss factor ([epsilon]") and, therefore, the complex permittivity ([epsilon].sup.*]). The dielectric permittivity is a measure of the motion and/or orientation of dipoles and ions in an AC field, whereas the loss factor represents the energy expended during dipole or ion movement. For a parallel plate geometry, the computation of [epsilon]' and [epsilon]' is trivial; however, for a more complex geometry, such as the interdigitated cylindrical geometry used for the in-line sensor described in the present paper, the computation is much more involved. The temperature and applied frequency also affect the measured [epsilon]'. For molten polymers, [epsilon]' generally increases with temperature and decreases with frequency. At extremely high frequencies, [epsilon]' is generally independent of frequency.
The experimentally measured quantities (C and D) are related to the desired dielectric variables ([epsilon]' and [epsilon]") by
C =[I.sub.out]/[omega]V = [C.sub.0][epsilon]' (3)
D = [I.sub.in]/[omega]V = [epsilon] [C.sub.0] = 1/[omega][R.sub.p] (4)
where [omega] = 2[[pi]f and f is the frequency (Hz) and is the parallel resistance ([omega]).
The dissipation factor (tan[delta]) is the ratio of the imaginary component to the real component of the dielectric data.
Tan[delta] = [I.sub.in]/[I.sub.out] = D/C = [epsilon]"/ [epsilon]' = 1/[omega][R.sub.p] [C.sub.p] (5)
The last term in Eq 5 is only valid for a parallel equivalent circuit where [C.sub.p] is the parallel capacitance (Farads).
When a voltage is applied across a material, the electrical energy is absorbed by dipoles and ions in the material resulting in degrees of polarization and various atomic and molecular relaxations. A relaxation is the movement of a dipole and/or ion to its lowest energy state (lowest impedance); the relaxation time is the elapsed time taken to achieve this relaxed state. At low frequencies or high temperatures, the dipole/ion has sufficient time or enough thermal energy to fully relax, but at high frequencies or low tempera-hires the dipole/ion either cannot keep up with the applied high frequency field or does not have enough thermal energy so that the dipole/ion never attains a fully relaxed state but may attain a steady unrelaxed ("frozen") state.
The relationship between polymer composition and either capacitance or dielectric permittivity is given below. The dielectric properties of a material placed between two capacitor electrodes is given by
[epsilon]' - Q + P/Q = C/[C.sub.0]
where Q is the charge per unit area on the capacitors in a vacuum (Coulombs/[m.sup.2]) and P is the additional charge per unit area on the capacitors with a polymer present (Coulombs/[m.sup.2]). The value of Q is a constant for a given system, but P varies with the concentration or type of material present. The classic method of obtaining P (typically called the polarization when written as a vector) is to relate it to concentration by the following equation (19)
P = [n.sub.d][alpha][E.sub.L] (7)
where [n.sub.d] is the concentration of dipoles per unit volume (moles of dipoles/[m.sub.3]), [alpha] is the polarizability of the material (F-[m.sup.2]), and [E.sub.L] is the local electric field strength (V/m). Equations 6 and 7 show the relationship between the dielectric permittivity and the concentration, but the polarizability and electric field strength are not always straightforward to evaluate.
Alternatively, the polarization can be expressed in the following manner
P = [n.sub.d][N.sub.A][[micro].sub.d] + [n.sub.i][N.sub.A][[micro].sub.i] (8)
where [N.sub.A] is Avogadro's number (6.023 X 1[0.sup.23] dipoles/mol), [[micro].sub.d] is the dipole moment along the polymer sidechains (C-m), [n.sub.i] is the concentration of ions present per unit volume (moles of ions/[m.sup.3]), and [[micro].sub.i] is the dipole moment of an ion-ion pair (C-m).
The dipole moment for the ion-ion pair is simply expressed as
[[micro].sub.i] = [q.sub.e][l.sub.i] (9)
where [q.sub.e] is the elemental charge (1.6) + [10.sup.-19] C), and [l.sub.i] is the distance between ions (m).
The dipole moment for the covalently bonded dipoles along the polymer sidechains requires a more rigorous calculation, such as using the Fri5huich modification of Onsager's equation (20)
[[[micro].sup.2].sub.d] = 3KT/[4[pi]n.sub.d]g ([[epsilon].sub.r] - [[epsilon].sub.u]) ([2[epsilon].sub.r] + [[epsilon].sub.u]/[3[epsilon].sub.r]) [(3/[[epsilon].sub.u + 2]).sup.2] (10)
where k is Boltzmann's constant (J/K), T is temperature (K), g is the Kirkwood factor (21), [[epsilon].sub.r] is the relaxed permittivity, and [[epsilon].sub.u] is the unrelaxed permittivity.
Therefore, substituting Eq 8 into Eq 6 gives a direct relationship between the concentration and dielectric variables.
[epsilon]' = Q + [N.sub.A] ([n.sub.d][[micro].sub.d]
Note for the special case of ionomers where the equivalent weight (EW in g/equiv) is desired, [n.sub.d] is expressed as [rho]/EW, where [rho] is the polymer density (g/[m.sup.3]).
Equation 11 shows that the dielectric variables ([epsilon]'and C) are directly proportional to the polymer dipole concentration (comonomer content) and the length of the measured dipole (sidechain length). Experiments were performed to evaluate this relationship by varying the polymer comonomer concentrations and sidechain lengths as well as various dielectric parameters.
APPARATUS AND PROCEDURES
In-Line Dielectric Sensor
The sensor was made (R&D Consultants, Phoenix, Ariz.) via a process combining photolithography, electroless plating, and electroplating. An alumina ceramic was first machined into a hollow cylinder measuring 7.6 cm OD, 4.5 cm ID, and 3.8 cm in length. A photoresist (Riston(r), DuPont) was applied to the inside surface area of the cylinder. A fringing field circuit mask was then placed on the inside cylinder area over the photoresist. The exposed photoresist was etched with ultraviolet light to form the circuit pattern consisting of 27 pairs of electrode fingers each having a width of 1.2 mm and a gap of 1.2 mm between electrodes. The underlying alumina, now exposed through the photoresist, was etched with hydrofluoric acid to form grooves into which nickel was electroless plated. Nickel was applied to the inside, and a ground conductor (electrostatic shield) was applied to the outside of the ceramic by electroless plating. The photoresist was removed with a solvent, and the inside area was honed to a smooth finish. The entire part (with the exception of the exposed alumina) was then electroplated with gold. Finally, the sensor was coated with a thin layer of either silicon dioxide ([SiO.sub.2]), silicon nitride ([Si.sub.3][N.sub.4]), or sputtered alumina ([Al.sub.2][O.sub.3]) for protection. The fabricated sensor is shown in Fig. 1.
The metallization associated with each active electrode extends around the inside diameter edge of the sensor and is electrically connected to metallization covering one of the end faces of the sensor. In this way the sensor was connected to external measurement equipment by connecting wires to washershaped contacts pressed against the sensor body on the upstream and downstream faces. The sensor was bolted in place between a pair of flanges on the extruder using annealed gold-plated copper shims and elastomer seals (Kalrez(r), DuPont) as gaskets. The gaskets were of sufficient thickness to avoid capacitive coupling to the housing. The electrostatic shield was grounded.
The electrode pattern was such that the electrodes were oriented lengthwise inside the cylinder so the polymer flow was parallel to the length of the electrodes. The critical factor in the design was to space the "fingers" (line spacing) of the fringing field pattern far enough apart to allow significant penetration of the electric field into the polymer melt while at the same time keeping the electrodes close enough together to obtain a measurable capacitance ([greater than]40 pF). Based on these factors, the dimensions have been specffied so that the line spacing and the electrode width are both 1.2 mm; therefore, the measurable electric field extends roughly 5 times this dimension into the polymer or 0.6 cm. This penetration effectively measures about 46% of the polymer volume. The measured capacitance of the alumina sensor is on the order of 70 picofarads (pF) in the absence of polymer.
Note that the sensor dimensions may be changed depending on the application. It should be kept in mind, however, that smaller inside diameter, shorter sensors would have a smaller electrode area and, to maintain a measurable capacitance, would require a smaller gap between electrodes. When the inside diameter is smaller, the problem of patterning the electrodes on the inside of the conduit becomes more difficult, especially when the conduit is some shape other than circular in cross-section. With a larger diameter for a given measurement depth, a smaller portion of the total flowing fluid will be analyzed, and the measured sample may not be fully representative of the entire sample.
The thickness of the sensor is sufficient to permit safe operation at temperatures and pressures of the application in which the sensor is employed and will vary with the materials of construction. The pressure rating of the sensor is 21 MPa (3000 lbs/[in.sup.2]).
Two types of extruders were used. The first was a 22 mm single screw Killion extruder where the sensor assembly was positioned at the exit of the static mixer section downstream from the screw. The second was a twin screw Haake 90 extruder where no static mixer was used, and the sensor was positioned downstream from the screw directly upstream from the die. The sensor was encased between two hastelloy flanges and bolted to the extruder. The polymer flowed from the screw section, through the ceramic sensor, and exited from the extruder. The processing temperatures used varied between 160 and 400[degrees]C. Electrical measurements are taken on the polymer in the region from the wall (surface of the sensor) to approximately 0.635 cm (0.25 inches) radially into the polymer stream.
The electrical connections and equipment needed to make an in-line dielectric measurement are described below. A signal generator (Hewlett-Packard HP 3326A) sends a voltage sine wave, the frequency of which is set by a personal computer (IBM PS/2, Model 80), to drive the sensor. Because of the resistive and capacitive components of the polymer flowing through the sensor, the incoming voltage generates an alternating current (the measured signal). The current is sent back through a current (I) to voltage (V) converter (Ithaco, Model 1641 preamplifiers), which amplifies the signal either [10.sup.0], [10.sup.2], or [10.sup.6] times, depending on the frequency, while converting a current signal to a voltage signal. A switching unit (Cytec, Model LXB/128) is used to facilitate changing to the proper converter based on frequency.
The signal from the I to V converter is fed to a two-phase lock-in amplifier (Ithaco, Model 3961B), which filters out noise, selects the signal component at the reference frequency, and segregates the in-phase and out-of-phase portions of the current. The personal computer, attached to the sine wave generator and the lock-in amplifier through a general purpose interface bus (GPIB cable), is used to calculate the capacitance (C), dissipation (D), and dissipation factor (tan[delta]) based on the amplitude and phase angle of the resultant current.
The computer is connected to the instruments with GPIB cables. A 50 [omega] terminator is connected to channel A of the signal generator. An electrical BNC tee is placed on the terminator; one end of a BNC cable is connected to the tee and the other end to the sensor. A second BNC cable connects the tee to the reference input of the lock-in amplifier. The sensor is connected to the Cytec with a BNC cable, and then from the Cytec to the A signal input of the lock-in amplifier. A 10 pF reference standard capacitor (GenRad, 1404-C) was used to calibrate the instruments.
A pressure/temperature (P/T) box (Dynisco) interfaces to the computer through a switching box and then to the computer via a ribbon cable. A measurement of pressure and temperature is made by connecting the switching box to the P/T probe located at the sensor flanges and measures the polymer melt properties. Dielectric measurements were made over a range from 0.5 Hz to 200 kHz at 160 to 400[degrees]C.
The phase angle shift and gain measured by the sensor could be converted to a real and complex permittivity by solving Poisson's equation with the appropriate boundary conditions based on the sensor geometry. The mathematics are lengthy and time consuming, and beyond the scope of this paper.
All sensors used in laboratory experiments were commercially available (Micromet Instruments, Inc., Cambridge, Mass.). Four types of sensors were used: low conductivity (model S-20, [10.sub.-16] to [10.sup.-6] [[omega].sup.-1] [cm.sup.-1]), high conductivity (model S-40, [10.sup.-8] to [10.sup-1] [[omega].sup.-1] [cm.sup-1] thin film, and ceramic (model S-50). The low conductivity sensor was used for most polymer runs while the high conductivity sensor was used primarily for runs involving solvents and water.
The low conductivity sensor (16) consists of two interdigitated electrodes fabricated on a single-surface integrated circuit. The sensor was connected to a dielectrometer (Micromet, Eumetric System II) interfaced to a PC (Compaq). The commercial sensors were not amenable to in-line applications due to fragility and thermal limitations. The voltage was sent to the sensor setting up an electric field through the first 20 to 60 [micro]m of the polymer. The resulting current was sent back to the dielectrometer, and the gain and phase shift were used to compute [epsilon]', [epsilon]", and other dielectric properties.
To obtain dielectric data, a polymer pellet was placed onto a dielectric sensor and sandwiched in between two 3 mil Kapton(r) (DuPont), Teflon(r) (DuPont), or aluminum sheets. The assembly was then placed in a vacuum oven (VWR). A glass insulator and 440 g stainless steel weight were placed on top of the upper sheet to control the rate of heat transfer to the polymer and to insure intimate contact between the polymer and electrodes. To perform an experiment, the polymer was first dried overnight under 20-25 inches of vacuum and a nitrogen purge. The drying temperature varied depending on the polymer used. Then the temperature was quickly ramped up to above the polymer's melting point, and the polymer was allowed to cool at a controlled rate. Dielectric data were obtained throughout the temperature cycle.
The following polymers were chosen: chlorosulfonated polyethylene (CSPE), Elvax(r), and Nafion(r) (sulfuryl fluoride form). The reasons for using these particular systems is explained in the Discussion of Results section.
Polyethylene (HD-178 powder) was chlorosulfonated in a batch suspension process to various extents. All chlorine compositions were analyzed in triplicate by a weight gain measurement, an in-house IR spectrophotometer, and the Schoniger Combustion Method (a modified IR technique). The sulfur compositions in the chlorosulfonated powders ranged from 0.27 to 0.6%. Unlike commercial chlorosulfonated PE such as Hypalon(r) (DuPont), where Cl groups exist opposite other Cl groups along the polymer backbone, the polymers used here have uncompensated Cl groups. The polymer powder was placed upon the Micromet laboratory sensor, and the oven temperature was ramped up to above the melting point of the polymers ([greater than]130[degrees]C) and then allowed to cool to room temperature at a constant rate. All data were taken from the decreasing portion of the temperature curve; thus, the thermal history of each sample was identical.
Elvax(r) (DuPont) is an ethylene-vinyl acetate copolymer. The properties of the Elvax(r) samples were measured analytically and are shown in Table 1. Compositions were measured with FT-IR (Nicolet), rheological properties by a capillary viscometer, and thermal properties by DSC. Molten Elvax(r) measurements were carried out using the laboratory dielectrometer (using a procedure similar to that used for the CSPE samples) as well as in-line using the new ceramic sensor mounted on a twin screw extruder (Haake).
Nafion(r) (DuPont) is a copolymer of tetrafluoroethylene (TFE) and a sulfonate vinyl ether, the polymeric structure of which is
The polymer composition is expressed in terms of the equivalent weight (EW) defined as the weight in grains of polymer containing one equivalent of acid or, alternatively, the comonomer molecular weight plus l00n, where 100 is the molecular weight of TFE and n is the number of moles of TFE per mole of comonomer. Thus, the lower the EW, the lower the TFE concentration and the higher the vinyl ether concentration. The polymer is semicrystalline since the backbone TFE segments tend to crystallize the structure while the sidegroups hinder crystallization. In laboratory studies, Nafion(r) samples were heated to 220[degrees]C in a vacuum oven to soften the polymer and then pressed onto a single-surface dielectric sensor. Next, the polymer was cooled at a controlled rate (1[degrees]C/min) to obtain the dielectric data. Frequencies used ranged from 0.1 to 10,000 Hz.
DISCUSSION OF EXPERIMENTAL RESULTS
High temperature dielectric spectroscopy was used to measure the composition of a variety of polymer melt systems with use of laboratory single-surface sensors and with the new in-line dielectric sensor. The studies are detailed below.
The dielectric response of chlorosulfonated polyethylene (CSPE), made by randomly chlorinating and chlorosulfonating polyethylene (PE), was determined using single-surface laboratory dielectric sensors. Figure 2 shows that the dielectric permittivity was found to be a direct function of frequency, temperature, and chlorine concentration. The data display an exponential relationship between the chlorine concentration and the dielectric permittivity such that small fluctuations in the chlorine level result in large variations in the dielectric permittivity. Also, the higher the temperature, the greater the slope and the greater the deviation from linearity.
The trends observed in Fig. 2 are consistent with existing knowledge of dielectric behavior. During an experiment an alternating voltage of a prescribed frequency is applied which sets up an alternating electric field across the polymer. Permanent dipole orientation and ion movement further distort the atomic structure giving rise to induced dipoles within the polymer. The extent of orientation and the amount of energy expended during orientation of the dipoles and ions is a measure of the dielectric permittivity and the dielectric loss factor.
At low frequencies, the polymer dipoles can more readily follow the alternating electric field. As the frequency is increased, the dipoles cannot reorient fast enough or to the same extent to keep up with the changing field. Thus, the dielectric permittivity decreases at higher frequencies, which is observed by comparing Fig. 2a (1000 Hz) with Fig. 2b (10,000 Hz).
Because of the symmetry of the polyethylene chains, the polymer is essentially nonpolar (entanglements and crank shaft mechanisms, though, do yield some polarity). Since the main contribution to the orientation is from induced PE dipoles, the measured dielectric permittivity is small ([epsilon]'2) at [Cl] = 0. As the temperature is increased, the vibrational and translational motion of the PE molecules is increased as is the translational motion of any ionic species so the dielectric permittivity is also increased. As chlorine is substituted for hydrogen along the polymer backbone, the polymer becomes more polar. Permanent C-Cl dipoles in the chlorosulfonated samples cause larger dipole moments within the polymer leading to larger dielectric permittivities than for polyethylene, as shown in Fig. 2. Note that due to steric hindrance, a chlorine radical most likely will not attach to the polymer chain opposite another already attached chlorine atom; however, if the chlorine concentration in the suspension is increased even further, the steric hindrance may be overcome, and the dielectric response may then actually decrease as a result of canceling dipoles.
In addition to the above explanation, one other factor must be mentioned. During chlorination, for every chlorine free radical which attaches itself to a polymer chain, a second free radical forms HC1 which readily dissociates into [H.sup.+] and [C.sup.-] ions. As more chlorine free radicals are attached to the chain, more free chlorine ions are left in the polymer. Since no special procedures were employed to "wash" the ions from the polymer, the [C1.sup.-] ions remaining in the polymer may have contributed to the increase in the dielectric response.
The dielectric permittivity of Nafion(r) in the sulfonyl fluoride form was measured at elevated temperatures as a function of the equivalent weight (EW) or comonomer composition of the polymer. As the EW increases, fewer polar -[OCF.sub.2]CF([CF.sub.3])[OCF.sub.2][CF.sub.2][SO.sub.2]F side groups are available to contribute to the dielectric signal. In addition, the polymer crystallinity increases with increasing EW since the larger number of TFE segments enhance crystallization. Both of these factors cause a decrease in the measured charge on the electrodes; thus, the dielectric permittivity ([epsilon]') decreased with increasing EW, as shown in Fig. 3.
The data at low EW vary as a distinct function of temperature and frequency. As the EW is increased, the data decreased as explained above until at a high enough EW, the contribution of the small number of sidechains is negligible, and the curves reach an asymptote. The EW at which the asymptote occurs decreases with increasing frequency. The asymptotic behavior at high EW (as the EW [right arrow] [infinity]) approximately represents the dielectric response of poly-TFE ([epsilon]' = 2.04 at 100[degrees]0 (22)) where no sidegroups contribute to the dielectric signal. A low EW limit would also be expected corresponding to the [epsilon]' of a vinyl ether homopolymer. Furthermore, as the temperature is increased, the activity of the side groups is increased therefore increasing the dielectric permittivity. Note also from Fig. 3 that the sensitivity of the measurement (given by the slope) increases with temperature.
Elvax(r) Laboratory Measurements
Elvax(r) (ethylene vinyl acetate copolymer) is produced over a wide range of vinyl acetate to ethylene monomer ratios. The uncompensated acetate group has a strong dipole moment and is detectable in a capacitance measurement. The goal is to measure the polar vinyl acetate side group concentration [VA]. Note that the melting points of these polymers range from 50[degrees]0 at high [VA] to 100[degrees]0 at low [VA].
Elvax(r) samples, ranging from 9% to 40% [VA], were measured using the single surface laboratory sensor. Although data were taken from 25 to 200[degrees]0 and from 0.1 to 10,000 Hz, only data for three temperatures and one frequency are plotted for clarity versus the measured dielectric permittivity in Fig. 4. All data were fitted to sigmoidal regressions.
In general, the dielectric permittivity increased with [VA] since the larger number of polar vinyl acetate groups induce a greater charge on the electrodes during polarization leading to a higher measured dielectric permittivity. The curvature in the data regressions, though, is similar to the trends reported earlier in this paper for Nafion (R) and for chlorosulfonated polyethylene. At low [VA], very few dipoles contribute to the dielectric signal and the curves tend to asymptote. At high [VA], the large concentration causes dipoles to sterically interfere with each other during polarization so that although more dipoles are present, their polarization is more limited leading to a leveling of the measured dielectric permittivity.
The [epsilon]' data at 1 Hz increase with temperature as expected due to the greater thermal energy aiding the extent of polarization. Also, as the frequency is increased, the measured [epsilon]' decreases, which was also observed with other polymers in this paper. Even at 1 Hz, though, the [epsilon]' values are reasonable so that electrode polarization does not seem to play a major role in the measurement even at these high temperatures.
In order to compare the dielectric behavior of the systems studied, a composite plot was generated, as shown in Fig. 5. All polymer data are plotted at 1 Hz and 160[degrees]C, and all concentrations are given as a weight percent of the comonomer.
In each case, a sigmoidal relationship (solid curves) exists between the measured dielectric permittivity and the sidegroup concentration. The only deviation from this relationship is at extremely high concentrations where the dielectric permittivity tends to decrease (dashed curve). The magnitude of the measured signal and the inflection point depend on the polymer studied.
To explain the shape of the curves, consider the schematic representation shown in Fig. 6. At very low sidegroup concentrations, very few dipoles (sidegroups) are present and each act independently of one another. The dielectric permittivity, being proportional to both the orientation and concentration of dipoles, is therefore very small. As more and more dipoles are added to the polymer chain, the concentration increases while the orientation is roughly constant; therefore, the dielectric permittivity increases readily with the sidegroup concentration. However, at a high enough concentration, the motion of the sidegroups is sterically hindered; therefore, the increasing dipole concentration is offset by the sterically hindered motion, and the curve levels off. At even higher concentrations, dipoles may exist in an antiparallel configuration, thus forming canceling dipole moments. At these high concentrations, the dielectric permittivity thus decreases.
The sidechain length plays a major role in determining the shape and magnitude of the dielectric curves, as shown in Fig. 7. The error bars in the figure indicate the accuracy and reproducibility of known data on the length of the sidegroups. The C-C1 group length is straightforward while the Nafion(r) sidegroup length is debatable depending on the measurement or computational method used to determine the length.
As the sidechain length increases, the dielectric relaxation time increases. Therefore, a lower frequency is required to orient a longer sidegroup to the same extent as a shorter sidegroup. The data shown in Fig. 7 indicate the dependence of [nabla][epsilon]'. (the difference between the low and high asymptotic values) and the "optimum" concentration (inflection point of a curve) on the chain length. As the chain length increases, the dipole motion is more limited thereby decreasing Ac'. Also, longer sidechains tend to sterically hinder each other's motion. Therefore, larger "optimum" concentrations are needed for longer sidechain polymers.
Elvax(r) In-Line Measurements
Using the in-line alumina sensor on a Haake 90 twin screw extruder, the capacitance of various grades of Elvax(r) was measured over time at various frequencies. Figure 8 illustrates the measurement at two frequencies. The pressure of the molten polymer is measured by the P/T probe located near the sensor and also plotted in Fig. 8. Initially the extruder was empty, and at time = 0 the background signal was measured to be 73 to 94 pF in the frequency range of 0.5 to 200,000 Hz (these values include the air, ceramic, and stray capacitances). Elvax(r) 310 (25% VA) was added 20 min into the run. The polymer took approximately 5 min to flow from the hopper, through the screw section, and to the sensor at which point the measured capacitance (dielectric signal) increased dramatically. After 10 min a plateau value was achieved. The absolute plateau value was a direct function of the applied frequency. At 93 min, Elvax(r) 40W (40% VA) was added and another plateau was obtained. Finally at 194 min, Elvax(r) 760 (10% VA) was added and a lower plateau was achieved. The changes in capacitance are consistent with measurements taken on individually run Elvax(r) samples. In the frequency range examined (0.5 to 200,000 Hz), below 100 Hz the aforementioned trends were still present but the plateau value was not as stable. At frequencies at or above 100 Hz, the signals were very stable and consistent.
The measured dielectric capacitance (C), as given by the plateau capacitance values, was found to be proportional to the percent vinyl acetate in Elvax(r), as shown in Ftg. 9. Three duplicate experiments were run in real-time with two different dielectric sensors, made of either Macor or alumina; all data trends were reproducible after accounting for the different substrate properties.
During most of the run, data were taken at three frequencies (0.1, 1.0, and 100 kHz) to record the realtime transients as closely as possible. Once a plateau was achieved, a complete set of frequencies over the entire frequency range was measured which took about 15 mm. Breaks in the data in Fig. 8 indicate when the full frequency range was measured; these data are shown in Fig. 10. The curves show that below 100 Hz, ionic conduction plays a large role in the measurement so that the measured capacitance is large. One would expect that at extremely low frequencies, the curves would merge when ionic conduction overwhelms dipole motion. Above 100 Hz, dipole motion controls the capacitive signal. The curves are plotted as [1/1nf] in the inset plot to show the reciprocal behavior. In all cases, the percent vinyl acetate in the polymer was monitored directly by the measured capacitance.
The traditional way of generating a Cole-Cole plot is to use the real ([epsilon]') and imaginary ([epsilon]") components of the complex permittivity. The resultant semicircle then yields the relaxed and unrelaxed dielectric permittivities. During a measurement with the in-line sensor, the geometiy was too complex to compute the components of the permittivity so that only the capacitance and dissipation were obtained. A variation on a Cole-Cole plot with these data is shown below.
For a capacitor (C) and resistor (R) in parallel, the dielectric permittivity and loss factor are given by (23)
[epsilon]' = C/[KC.sub.o] (12)
[epsilon]" = G/[omega][KC.sub.o] (13)
where K is a geometrical constant and G = 1/R is the polymer conductance ([omega].sup.-1]). By dividing Eq 13 by Eq 12, the dissipation factor is obtained.
Tan[delta] = G/[omega]C (14)
Therefore, by plotting G/[omega][Kcsub.0] vs. C/[KC.sub.0], a Cole-Cole plot can be generated. To simplify the analysis further, [KC.sub.0] is a constant and can be factored out of the plot. In addition,
D = C tan[delta] = G/[omega] (15)
so a variation on a Cole-Cole plot could be generated by plotting D vs. C; the x-axis intercepts would then give the unrelaxed and relaxed capacitances.
The dielectric properties of Nafion(r) XR (1149 g/equiv, sulfonyl fluoride form) were measured with the in-line dielectic sensor. The temperature was ramped and held at 225, 245, 265, and 280[degrees]C while the frequency was varied between 1 and 100,000 Hz. A variation on a Cole-Cole plot, as described above, was generated from the in-line data and presented in Fig. 11. Classical behavior suggests that the dipolar relaxation should appear as a semicircle at high frequencies and ionic conduction should occur at lower frequencies as a vertical line. The data in Fig. 11 (inset) display a quarter circle at high frequencies (small capacitances) before ionic conduction begins to dominate the signal. The unrelaxed capacitance ([C.sub.u]) is 79 pF while the relaxed capacitance ([C.sub.r]) is approximately 82 pF by extrapolation making the strength of the relaxation [C.sub.r] - [C.sub.u] = 3 pF. It may be possible to draw a correlation between the dielectric strength and the polymer composition. In the high capacita nce (low frequency) range, the data were influenced by not only ionic conduction (which would form a straight vertical line) but also by electrode polarization causing the curve to have a positive slope.
Dielectric measurements of thermoplastic copolymers, measured at or above their DSC melting regions, revealed a direct relationship between the comonomer concentration and the measured dielectric permittivity. The relationship is based on the difference in dielectric polarization between the two monomer units in the polymer chain. The polarization is in turn due to the chain length, morphology, and chemical structure of the polymer groups.
A new sensor was developed to make in-line dielectric measurements of molten polymers at high temperatures and pressures. The in-line data, taken on various polymer systems, were found to show similar trends to off-line laboratory dielectric data. The measurement frequency was the critical factor dictating the accuracy of the data. Measurements below the optimum frequency resulted in ionic conduction masking the dipolar response; if the frequency was too large, the relaxation time of the sidechains was too short to be an accurate indicator of comonomer concentration.
Molten polymer measurements are critically needed in most polymer processes. The ability to measure comonomer concentrations will, it is hoped, lead to other in-line measurements, such as reaction rates, molecular weight, morphological changes, and rheological properties.
Our most sincere thanks to Darrell J. LaShomb and Thomas N. Norton for their laboratory work and to Robert L. Todd and Glenn W. Morris for performing the extrusion operations.
(*.) To whom correspondence should be addressed.
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Elvax(R) Analytical Data. Elvax(R) Number Composition (wt% VA) MW (g/mol) Intrinsic Viscosity 760 9 234,000 2.8 310 25 55,600 1.04 40W 40 84,300 1.44 Elvax(R) Number Melting Point ([degrees]C) 760 102.3 310 68.2 40W 50.2
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|Author:||PERUSICH, STEPHEN; MCBREARTY, MICHAEL|
|Publication:||Polymer Engineering and Science|
|Article Type:||Statistical Data Included|
|Date:||Jan 1, 2000|
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