AD-R123 597 UNDERSTANDING DIELECTRIC CURE MONITORING(U) iMASSACHUSETTS INST OF TECH CAMBRIDGE CENTER FORMATERIALS SCIENCE AND ENGINEERING S D SENTURIA

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MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS-1963-A

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OFFICE OF NAVAL RESEARCH

Contract N00014-78-C-0591

o Task No. NR 356-691

TECHNICAL REPORT NO. 5

UNDERSTANDING DIELECTRIC CURE MUNITORING / N

By

Stephen D. Senturia

Article prepared for publication in

The Adhesion Society Bulletin

MASSACHUSETTS INSTITUTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science

and Center for Materials Science and EngineeringCambridge, Massachusetts

October 5, 1982

A

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This document has been apprc, ed for public release and sale;C-. its distribution is unlimited.

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Understanding Dielectric Cure Monitoring Technical Report6/82 - 9/82

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Technical Report No. 57. AUTIOR(s) I. CONTRACT OR GRANT NUMBER(*)Stephen D. Senturia N00014-78-C'0591

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1. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on rever*e aide If neceesaery ad Identify by block number)

Dielectrometry, cure monitoring, microdielectrometry, conductivity,permittivity, loss factor, resins

20. ABSTRACT (Continue on reverse side If necaeeay and identify by block number)

An elementary description of the dielectric properties of curing systems,how they are measured, and how they can be interpreted.

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7a UNDERSTANDING DIELECTRIC CURE MONITORING

Stephen D. SenturiaProfessor of Electrical Engineering

Massachusetts Institute of Technol rCambridge MA 02139 "

\V Introduction kAn ideal process monitoring method is one which does not per-

turb the process, yet somehow provides conplete documentation ofwhat is going on. Like all ideals, it is rarely approached in prac-tice, but nevertheless serves to guide the development of suitablemethods. The monitoring of the cure of thermosets is a good example.The continuous transition from viscous liquid to rubbery gel to

vitreous solid characteristic of thermosets produces such largechanges in properties that almost any method of physical measurementcan be expected to yield a useful result.-In practice, however,techniques such as calorimetry, infrared spectroscopy, and dynamicalmechanical measurements, all of which yield highly useful informa-tion, tend to be confined to carefully controlled laboratory situa-tions because of the difficulties of in-situ use. For cure monitor-ing in the manufacturing environment, alternative techniques areneeded.

Electrical measurements offer an attractive possibility. Duringthe past decade, various in-situ methods for examini.ng changes inthe electrical conductivity of resins during cure have been devel-oped, as have methods for studying changes in dielectric properties.It is useful to group "electrical conductivity" and "dielectricproperties" under the common heading "dielectric properties",because, as will be shown below, measurements of the frequencydependence of dielectric properties can yield information both onthe conductivity and on the dielectric properties usually associatedwith hindered dipole rotation.

Parallel Plate Measurements

The most common form of dielectric measurement involves a pairof parallel plates or foils either placed in contact with orembedded into the specimen. The electrode pair form a circuit ele-nent which can be represented as a capacitor in parallel with aconductor. The capacitance of the capacitor depends on the area ofthe plates, the spacing between the plates, and on the dielectricpermittivity c' of the medium between the plates. If the permittiv-ity is dispersive (i.e., frequency dependent), then the measuredcapacitance would also depend on frequency. The conductance of theconductor in parallel with the capacitor depends similarly on theplate area and spacing, and also depends on the conductivity of themedium a. If a depends on frequency, then the conductance wouldalso. A conventional way of relating the permittivity and conduc-tivity contributions to one another is to define a quantity with thesame dimensions as c' , but proportional to conductivity. From basic

theory, the correct corresponding quantity, called the loss factorand denoted'by e", and is equal to a/w, where w is the angular fre-quency at which both e' and e" are measured. Both e' and e" areusually reported in units of the permittivity of free space co,which has the value 8.85x0 -14 Farads/cm. In this case, the e' valuecorresponds to the conventionally defined dielectric constant, and amaterial with an e" value of U9 iVty at a frgquency of 1 Hz has aconductivity equal to 5.56x10l (Ohm cmr .

Because both the capacitance and conductance measured fromparallel plates depend directly on plate spacing, and because thisspacing typically changes during a cure cycle either by shrinkage ofthe curing material or through the application of pressure part-waythrough the cure cycle, one usually finds reports of the ratio of e"to E', called the loss tangent (or, conventionally, tan6). Otherauthors report the dissipation factor D of the capacitor, which isexperimentally equivalent to tanS. In either case, the reason forreporting tan6 or D is that the plate spacing and area both cancelout in the ratio. This has the benefit of yielding a result that isrelatively insensitive to geometric changes, but has the disadvan-tage of preventing simultaneous separate measurements of e or e'.When tan6 is observed to change, one does not know a priori whetherto attribute that change to e', to e" or to both.

Measurements on parallel plate electrodes involve some form ofcapacitance bridge. Since the measurement apparatus is separatedfrom the plates by cables, the very tiny currents that charge anddischarge the cable capacitances coupled with electrostatic noisepickup on the cabling ultimately limit the lowest frequency at whichsatisfactory measurements can be performed. Typical values of thislow-frequency limit are on the order of 100 Hz, although someextensions to lower frequencies are possible with extremely carefuldesign. At the high frequency end, cable inductance eventuallylimits measurement accuracy, typically in the 100 kHz - 1 Mhz range.

Mi crodi el ectrometry

An alternative to the parallel plate approach to dielectricproperty measurements has recently been developed in our laborator-ies at MIT. The electrodes form an interdigitated pair, or combpattern, on the surface of a 2x4 mm integrated circuit (or "chip").The sample is placed directly on these electrodes; alternatively,the chip is embedded in the material undergoing cure. One of theelectrodes is driven with a sinusoidal signal, and field-effect-transistor amplifiers within the chip detect the amount of chargereaching the other electrode through the sample medium. For a givenchip geometry, calibration tables which relate the magnitude andrelative phase of this charge to the e' and c" values for the mediumhave been developed. The electrode geometry does not depend on tem-perature, pressure, or on shrinkage during cure. Furthermore, giventhe precision of modern microelectronic fabrication methods, dif-ferent chips are sufficiently identical to one another so thatindividual calibration is not required. Because of the built-in

amplification, there is no Ic-q-frequency limitation to the measure-ment other than the intrinsic reaction rate of the medium beingstudied, which represents a significant advantage over parallel

IU

plate methods. A seliiconductor diode temperature sensor is alsobuilt into the chip, so that extremely local temperature changesduring cure call be monitored. The chip is connected through finewires to electronic instrumentation which, under control of a desk-top calculator, sequences the measurement frequency, performs themeasurement, inteprets the data to yield e' and e" (and, if desired,temperature), loys the data onto magnetic cassette, and generatesreal-time display of the data.

Using the Microdielectrometry system, we have studied the cureof a number of thermosetting systems as functions of time, tempera-ture, and frequency. We consistently find that the frequency depen-dence of both c' and e" must be examined in order to provide mean-ingful interpretation of the data. A general model for how e' and e"change is described below.

Understanding the Data

In our most elementary model, the pernittivity is representedas consisting of a constant e. (the equivalent high-frequencydielectric constant) plus a Debye-like dipole orientation term,

( s - )+* 1 +( )

where es is the permittivity one measures at low frequency, and isthe dielectric relaxation time. Note that forwT=1, e' falls at themidpoint between Es and e.. Corresponding to the dipole term in 'there is a frequency dependent contribution to e" which exhibits apeak at wr=1. We also add a bulk conductivity term, o/w, where inthe elementary model, a is frequency-independent, yielding a totalC" of the form,

_ W + (WT 2

The parameters e,,, es, and T characterize the permittivity, and aplus the other parameters characterize the loss factor. In particu-lar, the frequency dependence of e" can provide immediate insightinto whether one's measurements are dominated by the conductivityterm or by the dipole term. An example will be helpful.

If we assume that the bulk conductivity of a curing systemfalls exponentially with time due to an increase in viscosity pro-duced by crosslinking, and if we also assume that the dipole relax-ation time grows exponentially with time for the same reason, thenfor typical initial values of a and T, the "Theory" curves of ' ande" versus time shown in Figure 1 would be expected. Note the char-acteristic decrease in c' at successively lower frequencies as Tgrows with time (a classic relaxation), and note the correspondingloss peaks in e". At 1000 Hz in the example, the loss factor drops,then increases, then drops again during cure. Further, note thatearly in cure, c" decreases monotonically with increasing frequency,but when the point is reached where the dipole loss peaks show up,the frequency dependence becomes complex. Since as one approachesthe loss peaks, e' is also changing with frequency, if one can only

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measure the ratio of e" to e', one cannot easily assign an origin toobserved frequency variation. There is a distinct advantage, there-fore, in obtaining separate measurements of both e' and e".

To illustrate the reasonableness of the elementary model, the"Experiment" side of Figure 1 shows actual data from an isothermalcure of an amine-epoxy system. The only major differences betweenthe Experiment and the Theory in Figure 1 are the dispersion earlyin cure in 0, which is attributable to ionic conduction withblocked electrodes, and the persistance of relatively high lossfactors at the end of cure, which is attributable to the drop inreaction rate due to vitrification of the sample.

The model outlined above represents a useful starting point forinterpreting dielectric data during cure. Rate of change of lossfactor can be related to reaction rate. The detailed shape of thedipole orientation peaks can be related to the distribution ofrelaxation times within the sample, which can, in principle atleast, be related to properties of the network being formed bycrosslinking. In every case, however, measurements of both e' and e"over a wide frequency range are required to pemit meaningfulinterpretation of the results.

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