Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-TR-2441 March 2001 

Vinyl-Ester (VE) Cure Characterization 

Via Direct Current Sensors 

Bruce K. Fink 

Weapons and Materials Research Directorate, ARL 

Mahendra EL Dorairaj and John W. Gillespie, Jr. 

University of Delaware 

Approved for public release; distribution is unlimited. 
Abstract 

High-performance thermosetting composites typically consist of a high-modulus 

fibrous material embedded in a thermosetting polymer matrix. The behavior of the 

resulting composite depends on the properties of the reinforcement, the interphase, and 

the matrix. Vinyl-ester (VE) resins are relatively low-cost matrix resins used in liquid 

moldtig of large structures such as contiguous vehicle hulls. In liquid-molding 

processes, quality-control sensors can ensure resin impregnation of the preform and 

cure of the resin after infiltration. For these purposes, SMARTweave (SW), based on 

direct current (DC) sensing, is used as an in-situ flow-front detection and curemonitoring system. SW measures change in the ionic conductivity with cure, which can 

then be related to the material properties like viscosity and degree of cure. This enables 

in-situ measurement of degree of cure and viscosity development during cure from SW 

measurements. This report builds on previous modeling work that assumed a direct 

dependence of DC resistance on the resin viscosity, limiting the use of such models 

beyond gelation. This report presents a continuum model based on free volume theory 

to describe ionic conductivity through gelation to vitrification. 

5 

ii 
Contents 

List of Figures Vii 

List of Tables xi 

1. Introduction and Background 1 

1.1 Motivation ..,.._..._....._.___.................,..,..,....... .._..f..................f..._.....__........... 1 

1.2 Objectives . . . . . . . . . . . . . . . . _ .. , __ .. . . . . . . . . . . . . . . . . . . . . . ..*. . . . . . . . . . _ ._ .. . . . . . . . . . +.. . . . . . . . . . . . . , . . . . . . . _. .1 

1.3 The SMARTweave System _.______._...f... + .. . . . . . . . . . . . . . .._____._._____.. e .. . . . . . . . . . . . . . ..-. 2 

1.4 Previous Work on Ionic Conductivity Modeling . . . . . . . . ..f...._.____________._ . . . . . . 6 

1.4.1 Review of England’s Model [4] .._. .._________....................... .._...._...... 7 

1.4.2 The Need for a Continuum Model . . . . . . . . . . . . . . . .._..._...____.._................ 9 

1.5 Report Overview.. . . . .*. . . . . __. . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . __. . . . . . . . . . . . . . . . . . . , , . . . . . . . . . . . . . . . .9 

1.6 Section Summary . . . . . . . . .._._f..f...._.................__._.___._.....................f......_.....f.. 13 

2. Experimental Methods 14 

2.1 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

Introduction .............................................................................................. 14 

Materials .................................................................................................... 14 

2.2.1 Backgromd on VE Resins ........................................................... 14 

2.2.1.1 VE Resin Systems .......................................................... 14 

2.2.1.2 Free Radical Chain Growth Copolymerization ........... 15 

2.2.2 Resin Compositions. .................................................................... 17 

Viscosity Experiments. ............................................................................. 17 

2.3.1 Sample Preparation.. .................................................................... 17 

2.3.2 Instrumentation ............................................................................ 18 

SW Experiments.. ...................................................................................... 18 

Dielectric Cure Monitoring.. .................................................................... 20 

FTIR Experiments ..................................................................................... 21 

2.6.1 Instrumentation and Sample Preparation ................................. .21 

2.6.2 IR Spectra of VE ............................................................................ 22 

DSC Experiments ...................................................................................... 23 

. . . 

111 
2.8 DMA Experiments.. ............................ .: .................................................... 25 

2.9 Liquid Chromatography ......................................................................... .25 

2.9.1 Sample Preparation.. .................................................................... 26 

2.9.2 HPLC Instrumentation ................................................................ 26 

2.10 Atomic Force Microscopy (AFM) ............................................................ 26 

2.10.1 Background ................................................................................... 27 

2.10.2 Instrumentation and Sample Preparation .................................. 28 

2.11 Section Summary ..................................................................................... .28 

3. Cure Kinetics of VE Resins 30 

3.1 Introduction .............................................................................................. 30 

3.2 Cure Kinetics Using FTIR ......................................................................... 30 

3.3 Effect of Styrene Concentration .............................................................. .32 

3.4 Effect of Temperature ............................................................................... 34 

3.5 Autocatalytic Kinetics Model Parameters ............................................... 36 

3.6 Section Summary ...................................................................................... 36 

4. Cure Monitoring of VE Resin 38 

4.1 Introduction .............................................................................................. 38 

4.2 SW Cure Data ............................................................................................ 38 

4.2.1 Effect of Styrene ............................................................................ 38 

4.2.2 Effect of Temperature .................................................................. 42 

4.3 Dielectric Cure Monitoring. .................................................................... .43 

4.3.1 Effect of Styrene.. .......................................................................... 44 

4.3.2 Effect of Temperature .................................................................. 46 

4.4 Section Summary.. .................................................................................... 46 

5. Characterization of Microgels 50 

5.1 Introduction .............................................................................................. 50 

5.2 Background ............................................................................................... 51 

5.3 Results. ....................................................................................................... 52 

5.3.1 Comparison of Microgel Growth Kinetics with SW Data.........5 2 

5.3.2 Separation of Microgels ............................................................... 54 

5.3.3 AFM Analysis of Microgels ......................................................... 57 

iv 
i 

5.4 Percolation Model ..................................................................................... 57 

5.4.1 Modeling Approach.. ................................................................... 59 

5.4.2 Percolation-Based Continuum Model ...... 

. ................................. 61 

5.4.2.1 Conductivity Model ...................................................... 61 

5.4.2.2 Viscosity Model ............................................................. 63 

5.5 Summary ............... .’ ................................................................................... 64 

6. Mathematical Model of the Ionic Conductivity Behavior 65 

6.1 Introduction .............................................................................................. 65 

6.2 Free Volume Model .................................................................................. 66 

6.2.1 Background.. ................................................................................. 66 

6.2.2 Theory.. ......................................................................................... 67 

6.2.3 Conductivity Model. ................................................................... 

.68 

6.2.4 Viscosity Model.. .......................................................................... 71 

6.3 Predictive Capability of the Free Volume Model.. ................................ 

.75 

6.3.1 Conductivity Model ..................................................................... 77 

6.3.2 Viscosity Model ............................................................................ 77 

6.4 Section Summary.. .................................................................................... 79 

7. Conclusions and Future Work 80 

7.1 Introduction .............................................................................................. 80 

7.2 Conclusions. .............................................................................................. 80 

7.3 Sununary of Free Volume Methodology ................................................ 81 

7.4 Recommendations for Further liesearch.. ............................................... 82 

7.4.1 Fundamental Understanding of T ga. Relationship .................. 

.82 

7.4.2 Positron Annihilation Studies ..................................................... 82 

8. References 83 

Appendix A. Dielectric Cure Monitoring 89 

A.1 Basis of Dielectric Behavior.. ................................................................... 

.89 

A.2 Dielectric Measurements for On-line Cure Monitoring.. ...................... 

-90 

A-2.1 Ionic Resislivi~ ............................................................................ 90 

A.2.2 Dielectric Constant and Dielectric Loss. ..................................... 91 
Appendix B. Calculation of the Volume Fraction of Microgels 93 

Appendix C. Determination of L/A Ratio of Single Node Test Cell 

(SNTC)-3 95 

Appendix D. Doping Results 99 

D.l Introduction ............................................................................................ ..9 9 

D.2 Cure Monitoring ...................................................................................... .99 

D.3 Cure Kinetics ........................................................................................... 100 

Appendix E. Percolation Model 103 

E.l Introduction ............................................................................................ 103 

E-2 Theory ...................................................................................................... 103 

E.3 Percolation and Conduction .................................................................. 105 

E.4 Evidence of Percolation in VE system ................................................... 106 

Appendix F. Analyzing Diffusion in the Pregel and Postgel Stage 109 

F.l Pregel Stage.. .*,,~.~~................*............................*....*....*.*......~.-...-......*..*.. 109 

F.2 Postgel Stage . ..*.......f............f......**....................*...*.........I.........,............. 110 

Appendix G. Differential Scanning Calorimeter (DSC)-Based Free Volume 

Modeling 113 

G.l Introduction ............................................................................................ 113 

G.2 Cure Kinetic Model ................................................................................. 113 

(2.3 Tga Model .............................................................................................. 113 

G.4 Conductivity Model ................................................................................ 114 

G.5 Viscosity Model ....................................................................................... 114 

Distribution List 119 

Report Documentation Page 139 

vi 
List of Figures 

Figure 1. Schematic illustration of an SW system and its components.. ................ 

.3 

Figure 2. SW system in operation. ............................................................................. 3 

Figure 3. Experimental setup of SW sensors. ............................................................ 4 

Figure 4. Circuit diagram of a single node cell. ........................................................ 5 

Figure 5. Typical SW signal of a curing resin mixture. ............................................ 6 

Figure 6. Schematic representation of England’s model [4] ..................................... 8 

Figure 7. Schematic of continuum model. .............................................................. .11 

Figure 8. Chemical structure of VE and styrene monomers. ................................. 16 

Figure 9. Schematic illustration of a Brookfield viscometer and small sample 

adapter .................................................................................................................. 19 

Figure 10. Typical viscosity profile of a curing VE resin.. ...................................... 19 

Figure 11. SNTC-3 single node test cell. ................................................................ ..2 0 

Figure 12. Typical dielectric signal of a curing VE sample. ................................... 21 

Figure 13. FTIR experimental setup.. ..................................................................... 22 

Figure 14. FTIR spectra of VE825 at the beginning of cure at 40 “C cure 

temperature. ........................................................................................................ .23 

Figure 15. Degree of conversion of VE 411-C-50 at 30 “C as obtained from 

PIRSA ................................................................................................................... . 24 

Figure 16. Schematic illustration of DMA setup. .................................................. ..2 5 

Figure 17. Schematic illustration of HPLC experimental setup.. .......................... .27 

Figure 18. AFM micrograph of microgels in VE 411-C-50 at a cure 

temperature of 70 “C [21]. ................................................................................... 28 

Figure 19. Block diagram for tapping mode operation. ......................................... 29 

Figure 20. Typical profiles of VE and styrene double-bond conversion.. ............. 31 

Figure 21. Fractional conversion of VE double bonds in Derakane 441-400 

cured at 40 “C. ..................................................................................................... 33

Figure 22. Fractional conversion of styrene double bond in Derakane 441-400 

cured at 40 “C.. ................................................................................................... .33 

Figure 23. Fractional conversion of VE double bonds in Derakane 411-C-50 

cured at isothermal temperatures of 30”, 40”, and 50 “C. ................................. 35 

vii 
Figure 24. Fractional conversion of styrene double bonds in Derakane 411-C50 cured at isothermal temperatures of 30°, 40°, and 50 “C.. ............................ 35 

Figure 25. SW behavior of Derakane 441440 cured at 40 “C. ......................................... 40 

Figure 26. Initial DC signal vs. styrene concentration in Derakane 441400. ..... ..4 0 

Figure 27. Initial viscosity vs. styrene concentration in Derakane 441-400. ....... ..4 1 

Figure 28. Viscosity development in Derakane 441-400 cured at 40 “C. ............... 41 

Figure 29. Fractional double-bond conversion vs. styrene concentration in 

Derakane 441-400 at DC signal cutoff. .............................................................. .42 

Figure 30. Glass transition temperature vs. styrene concentration for 

Derakane 441400 resin.. ...................................................................................... 43 

Figure 31. SW signal vs. time for Derakane 411-C-50 at different isothermal 

cure temperatures ................................................................................................ 43 

Figure 32. Viscosity development in Derakane 411-C-50 at different 

isothermal cure temperatures. ........................................................................... .44 

Figure 33. Effect of styrene on Derakane 4-N-400 cured at 40 “C using 

dielectric cure monitoring at (a) 28 weight-percent styrene, and (b) 47 

weight-percent styrene concentration. .............................................................. .45 

Figure 34. Dielectric cure monitoring of Derakane 411-C-50 at isothermal 

temperatures of (a) 30”, (b) 40”, and (c) 50 “C. ................................................... 47 

Figure 35. Ionic conductivity from dielectric measurements on Derakane 411- 

C-50 at 30 “C isothermal cure temperature. .....................................................48 

Figure 36. Comparison of SW behavior of ionic conductivity with dielectric 

behavior of Derakane 411-C-50 at 30 “C cure temperature. ............................. 48 

Figure 37. Illustration of cross-linking polymerization (a) at beginning, (b) 

initiation, (c) reaction in progress, and (d) possible gel&ion schemes.. ........ ..5 2 

Figure 38. Influence of rnicrogels on SW behavior of 411-C-50 for (a) 30” and 

(b) 40 “C, respectively. ........................................................................................ .53 

Figure 39. DLS data showing influence of microgels on SW response of 441- 

400 at (a) 28% and (b) 57% styrene. .................................................................... 54 

Figure 40. HPLC response (in pV) of pure styrene.. .......................... *. ................. ..5 5 

Figure 41. HPLC response (in pV) of pure unreacted VE825 with 28 weightpercent styrene.. ................................................................................................... 55 

Figure 42. HPLC response (in pV> of fractionated microgels. ............................... 56 

Figure 43. FTIR spectra of VE825 (a) at the beginning of cure and (b) at 9 min 

at 40 “C cure temperature.. .................. . ............................................................... 56 

Figure 44. FTIR spectra of fractionated microgels formed in the first 9 min of 

isothermal cure of VE825 at 40 “C. .................................................................... .57 

Vlll 
Figure 45. AFM pictures of microgels as observed on a fractured surface of 

411-C-50 sample cured at an isothermal temperature of 40 “C. . . . . . . . . . . . . . . . . . ._.__ 58 

Figure 46. AFM pictures of microgels as observed on a fractured surface of 

411-C-50 sample cured at an isothermal temperature of 50 “C. . . . . . . . . . . . . . . . . . . . . . . . 58 

Figure 47. 2-D percolation behavior of a continuous conducting medium 

[41]. . . . . . . . . . . . . . . . . . . .._.___.____..._..______.._..~____..__._ +..e ..____.......................~.____..__..._..._._._._.___ 60 

Figure 48. 2-D percolation behavior modeling using resistor network [40] _ . . . _ ._ _ .60 

Figure 49. 3-D percolation modeling using non-zero resistor values [35] _ _ . . . . . . , . . .60 

Figure 50. Development of resistor network model for curing VE resin at (a) 

time t=O, (b) time t=tl, and (c) time t=SW cutoff. The left side illustrates 

different stages of cure and the right side illustrates equivalent resistor 

network . . . . . . . . . . . . ..f.........f.........................f...........f._.___.___.___..._................................ 61 

Figure 51. Normalized DC signal vs. microgel volume fraction of Derakane 

411-D-50 at different isothermal cure temperatures. . . . . . . . . . . . . . . . . . .._.._................. 62 

Figure 52. Normalized DC signal vs. microgel volume fraction of Derakane 

441-400 at different styrene concentrations. _.__._....................,....._.__.____.___......... 62 

Figure 53. Experimental vs. theoretical fluidity of Derakane 411-C-50 at 

isothermal cure temperature of 30 “C. .___..________f.._..._...................__._______f_........., 64 

Figure 54. SW behavior prediction using free volume theory at 30 “C. 

(Degree of conversion obtained using FTIR.) _.....I~..~~.............._______.__.f__............ 71 

Figure 55. SW behavior prediction using free volume theory at 40 “C. 

(Degree of conversion obtained using FTIR.) ____................ .. . . . . __. ____. . . _. . . . . . . . . . 71 

Figure 56. Viscosity prediction using free volume theory at 30 “C. (Degree of 

conversion obtained using FTIR.) . . . . . . . . . . . . . . . . . . . . . ..__._. ._____._. . . . . . . . . . . ..*... . . . . ._______.... +. 72 

Figure 57. Viscosity prediction using free volume theory at 40 “C. (Degree of 

conversion obtained using FTIR.) . . . . . . . . . . . . . . . . . . . . ..__._.__.___.................................... ..73 

Figure 58. Schematic of viscosity and cure sensing using SMARTweave 

signal as the model input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..___.________................_....._..f........... 73 

Figure 59. T, (K) development with cure time as predicted by the free 

volume model. . . . . . . . . . . . ..f.............__.______. _. . . ..f_..___...............f.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 

Figure 60. Degree of cure prediction from SW data at 30 “C using free 

volume theory. . . . . . . . . .._._._. .._._.___.._._._.._f. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ._._........ ........f....... . . . . . 74 

Figure 61. Degree of cure prediction from SW data at 40 “C using free 

volume theory. . . . . . . . . . . . . . . . . . . . . . ..f.... e .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .._....... . . . . . . . . . . . .._............... 75 

Figure 62. Effect of deviation of ionic conductivity on degree of cure 

prediction from the free volume model at 40 “C for 411-C-50. ..__________.ff....,_... 76 

Figure 63. Effect of deviation of ionic conductivity on viscosity prediction 

from the free volume model at 40 “C for 411-C-50. . . . . . . . . . . . . . . . . ..f..............._......-. 76 

ix 
Figure 64. Free volume modeling of ionic conductivity using average WLF 

parameters. ___................ .. . . . . .....f...._... . . . . ..____.._.... * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .,., 78 

Figure 65. Free volume modeling of viscosity using average WLF 

parameters. ___..........................................._.....................................................,f._.._ 78 

Figure C-1. SNTC3 single node test cell. ............................................................... .95 

Figure C-2. Circuit diagram of a single node cell. .................................................. .96 

Figure C-3. Experimental cell for conductivity studies.. ....................................... .96 

Figure D-l. Comparison of SW response of TI-doped 411-C-50 against 

TA- doped and undoped 411-C-50 at an isothermal cure temperature 

of 40 “C . . . . . . . . . . . ..____.......................... * . . . . . . . . . . . * . . . . ** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 

Figure D-2. SW response of undoped 411-C-50 at an isothermal cure 

temperature of 40 “C . .._____.__._..............................____......_..........................,........ 100 

Figure D-3. Degree of conversion comparison between doped and 

undoped resin at 40 “C isothermal cure temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 

Figure E-l. Illustration of increasing volume contribution of the 

rnicrogels with cure. ._.......................~..._.________................................._._____.__________ 104 

Figure E-2. Normalized DC signal vs. microgel volume fraction of 

Derakane 411-C-50 at different isothermal cure temperatures. .....___............f 106 

Figure E-3. Normalized DC signal vs. rnicrogel volume fraction of 

Derakane 411-C-50 at different isothermal cure temperatures. ,.,...._._.__________ 107 

Figure G-2. SMARTweave (SW) behavior prediction using free volume 

theory at 30 “C.. .................................................................................................. 115 

Figure G-3. SW behavior prediction using free volume theory at 40 “C. ........... 115 

Figure G-4. Viscosity prediction using free volume theory at 30 “C.. ................. 116 

Figure G-5. Viscosity prediction using free volume theory at 40 “C.. ................ -116 

Figure G-6. Schematic of viscosity and cure sensing using SW signal as 

the model input .................................................................................................. 117 

Figure G-7. Degree of cure prediction from SW data using free volume 

theory at 30 “C . . . . . . . . ..*................................................................. I _._.._................. 117 

Figure G-8. Degree of cure prediction from SW data using free volume 

theory at 40 “C. ._..___..........,.........---................,.........,-....-.................................... 118 
List of Tables 

Table 1. List of compositions of the reacting resin mixture used in this study. . ..12 

Table 2. Autocatalytic parameters for the degree of conversion as observed 

using DSC. . ..___.__.......................f._.... . . . . . . . . ..f_.._.. _. ___...__.__.................~.._._..___........... 24 

Table 3. Tapping mode specifications. . . ..___.__._._______.................f.......f._..__..._............ 29 

Table 4. Kinetic parameters corresponding to VE 411-C-50 FTIR data. .,.._........__.. 37 

Table 5. Autocatalytic parameters for FTIR data of VE 441-400 cured at 40 “C. ..37 

Table 6. DMA results for Derakane 411-C-50 ..f.............._________._...... . . . . . . . . . . . . . . .._.. ..44 

Table 7. Maximum conversion of 411-C-50 from DC and AC cure monitoring....49 

Table 8. Maximum conversion of 441-400 from DC and AC cure monitoring.. . . . .49 

Table 9. T, -a model parameters for 411-C-50 corresponding to DSC. . .._.. .._..+... 69 

Table 10. T,a parameters for Venditti’s relationship for 411-C-50 

corresponding to FTIR . . . . . . . . . . . . . ..__________.._....f.ff................._...___.____........................ 70 

Table 11. WLF Parameters for conductivity model ,...,.___..................___......._.....f... 70 

Table 12. WLF parameters for viscosity modeling. . . . . . . . . . . ..__._................................ 72

Table E-l. Percolation thresholds .._.......................ff....__. ._.. .._.+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 

Table G-l. T,-a model parameters. ........................................................................ 113 

Table G-2. WLF parameters for conductivity model. ........................................... 114 

Table G-3. WLF parameters for viscosity modeling.. ........................................... 116 

Xi 
Xii 
1. Introduction and Background 

1.1 Motivation 

High-performance thermosetting composite materials typically consist of a highmodulus fibrous-reinforcing material embedded in a thermosetting polymer 

matrix. The behavior of the resulting composite depends on the properties of the 

reinforcement, interphase, and the matrix [lJ+ Vinyl-ester (VE) resins are one of 

the most important matrix resins used in liquid-molding processes such as resintransfer molding (RTM), vacuum-assisted RTM (VARTM), and Seemann’s 

composite resin-infusion molding process (SCRIMP) [2]. These processes have 

proven to be cost-effective methods for room temperature near net-shape 

manufacturing of large composite structures for naval, infrastructure, and 

military systems. Consequently, there is an increased demand to improve the 

quality and to further reduce the cost of manufacturing. In liquid molding 

processes, quality control requires sensors to ensure resin impregnation of the 

preform and cure of resin after infiltration. To address these needs, research 

laboratories have begun to develop and refine new sensor technologies for flow 

and cure monitoring. In this work, the focus is on the study of neat VE resin 

using two such monitoring systems. One is based on direct current (DC) sensing 

known as SMARTweave (SW). SW is a patented system developed jointly by the 

U.S. Army Research Laboratory (ARE) and the University of Delaware Center for 

Composite Materials (UD-CCM). The other method is the more commonly used 

dielectric monitoring, which is based on altematig current (AC). A structured 

attempt is made to study the various parameters relevant to- cure kinetics and to 

obtain an insight into the structure of cured VE resins. This work also attempts to 

model, characterize, and relate ionic conductivity, viscosity and degree of cure to 

sensor response. 

1.2 Objectives 

The purpose of this research is to investigate how the SW signal can be utilized 

to in-situ monitor the viscosity and cure of a reacting polymer. Previous studies 

toward this direction have been successful only up to the gel point of the resin [3, 

41. A primary reason is limitation due to these models’ assumed dependence of 

ionic conductivity on the macroscopic viscosity. This poses problems since the 

macroscopic viscosity rapidly increases to infinity at gelation. However, the 

ionic mobility continues resulting in continuation of an observed SW signal. This 

necessitates the use of a different model, one that does not exhibit a direct 

dependency on the macroscopic viscosity. Another concern specific to VE resin 

systems is that there is an offset between the time when the viscosity reaches a 

1 
minima and when the ionic conductivity reaches a maximum, thereby 

introducing inaccuracies in the previous models adopted for VE. 

The objectives of this work are to: 

l Develop a theoretical understanding of the ionic conductivity of the 

reacting -VE resins, based on the molecular events such as network 

formation, homopolymerization of the individual monomers, and 

molecular mobility. 

l Develop a continuum model for ionic conductivity that extends through 

gelation to vitrification. 

l Monitor viscosity and degree of conversion in composite liquid molding 

processes as a function of ionic conductivity using DC-based sensors. 

1.3 The SMARTweave System 

SMARTweave (Sensors Mounted as Roving Threads) (SW) was developed and 

patented in 1990 by ARL [33 as a flow front detection system and is well suited 

for use in conjunction with liquid molding processes. Figure 1 shows the basic 

components of an SW system, while Figure 2 shows an actual photograph of the 

system in operation. The flow front is obtained by sensing the changes in DC 

conductivity of the overlapping grid of insulated conductors embedded in the 

preform prior to injection molding as shown in Figure 3. One set of the grid 

serves as the excitation leads and the orthogonal set laid out in the parallel plane 

serves as the sense leads. The presence of resin at a node is detected by the step 

change in conductivity upon resin arrival. Continued monitoring of the 

conductivity provides information about the cure behavior of the resin at a point. 

SW offers a specific advantage over the conventional alternating current sensors 

by allowing for use of a large array of sensors in multiple planes (multiplexing) 

enabling a three-dimensional (3-D) visualization of flow fronts and cure from the 

DC signal. 

The underlying principle behind the SW system is that when a resm is injected 

into the preform carrying the SW sensors, the resin acts as the conductjng 

medium between the sensors. Therefore, the signal obtained from the SW sensor 

is sensitive to the resin conductivity providing insight into the material 

properties that affect the ionic conductivity. Owing to its low conductivity, the 

resin acts as a resistor and, under an applied voltage, current is induced in a 

circuit containing a sense resistor (Rs).. Prior to the arrival of the resin between 

the sensing grids, the resistance between them is infinite. Upon the infiltration of 

the resin between the sensing planes, a step change in resistance to a finite value 

occurs. Subsequent data reduction enables flow visualization and the 

identification of defects such as dry spots. The distribution of the orthogonal sets 

of sensing and excitation leads ensures that defects do not exceed the area of 

E 

2 


!$itch 

Junction Resistor (Rr) 

(Resistance of the Resin) 

Sense Resistor (I&) 

Figure 4. Circuit diagram of a single node cell. 

The junction resistance is the resistance of the resin infiltrating the fiber preform. 

During a test run, in the presence of the resin between the sense plane and the 

excitation plane, a voltage is created across Rs. Changes in Rj(t) are then recorded 

as changes in Vm(t) by the SW National Instruments-based Labview. software. A 

detailed explanation of the working of SW and its application to commercial 

projects is discussed elsewhere [4]. A typical SW signal obtained during a single 

node test is shown in Figure 5. Point A corresponds to the point along the tie 

scale when the resin reaches the node under consideration. Following the arrival 

of the resin, the junction resistance undergoes a step change from a value of 

infinity to a finite value as marked by the point B. The region between points I3 

and C is when the reaction starts to occur. As the reaction proceeds, the 

exothennic nature of the reaction increases the local temperature, forcing resin 

viscosity to decrease, resulting in the increase in the DC signal between point C 

and D. Subsequently, the viscosity of the resin continues to increase due to cross 

linking and network formation. This forces the viscosity to rapidly increase to 

infinity corresponding to the onset of gelation. This phenomenon is reflected on 

the DC signal as a pronounced decrease in the observed voltage value 

represented by the curves inflection at point E. The reactive mixture eventually 

reaches a glassy state (vitrification) thereby severely restricting molecular 

mobility at point F. Vitrification is said to have occurred when the glass 

transition temperature, Tg equals the cure temperature, T. This results in the DC 

signal tapering off to zero, represented by point G. This is designated as the 

“cutoff point” for the sensor. 

SW vs. Dielectric Cure Monitoring. One of the widely used online cure 

monitoring methods is AC sensing or dielectric cure monitoring. A 

comprehensive review of AC sensing is presented in Appendix A. Dielectric 

cure monitoring presents multiple problems in the areas of isolating ionic 

5 
Voltage 

Figure 5. Typical SW signal of a curing resin mixture. 

conductivity from dipolar contributions and obtaining relaxation time and 

experimental results in the right set of frequencies. 

The mathematical steps involved in extracting ionic conductivity are 

cumbersome and involves numerous approximations, limiting its use. Dielectric 

sensors are point sensors, providing information at specific locations in the parts. 

The cost of dielectric sensors can be prohibitive for monitoring a large number of 

locations during processing. 

SW, on the other hand, offers a simpler yet effective alternative to dielectric cure 

monitoring. The DC signal obtained from SW provides a reliable representation 

of the ionic conductivity without any intermediate computational steps involved. 

SW offers the advantage of cost-effective multiplexing with the current 

University of Delaware system capable of handling 4096 nodes. SW 

accomplishes multiple goals of intelligent processing and control of large parts 

and identification of defects. SW has been used on large bridge components at 

an average cost of $0.20/sensor including placement and materials costs. 

Owing to the multiple advantages inherent to the SW system, this work is based 

extensively on DC behavior to model the relevant processing parameters. 

However, every attempt has been made to compare dielectric response and to 

identify the advantages and disadvantages of each approach. 

1.4 Previous Work on Ionic Conductivity Modeling 

While use of a DC-applied voltage for tracking the flow front during liquid 

molding processes was patented by ARL in 1990 [3], little fundamental research 

has been done on this issue [3,5-q., Kikuchi et al. investigated the sensing of the 

resin flow during molding processes using a modified SW system [S]. This 

system suffered from a low signal-to-noise (S/N) ratio and there was no attempt 

6 
made to measure viscosity and degree of conversion based on the SW data. 

Schwab et al. [9] used a novel parallel plate design consisting of individual 

sensors mounted in an RTM tool and proposed a theoretical model to relate 

sensor output to material behavior. The theoretical model developed by Schwab 

et al. was the basis on which England [4] developed a model of DC conductivity, 

which could predict the sensor response as a function of macroscopic viscosity 

changes and degree of cure. 

1.4.1 Review of England’s Model [4] 

Figure 6 schematically represents the different modules adopted by England [4] 

to model the DC conductivity signal as an in-situ sensing tool to predict the 

macroscopic viscosity and degree of cure as obtained from Fourier-transform 

infrared (FTIR). As a means of quantifying the concentration of the conducting 

ions in the resin system, England used an organic salt as a dopant. About 

0.1 weight-percent of tetrabutyl ammonium acetate (TA) was used in all of this 

experimental work. The previously mentioned concentration of TA, being far 

greater than that of other contaminant ions inherent in the resin system, presents 

a useful way of controlling the concentration of conducting ions present in the 

system for modeling purposes. 

England adopted Equation 3 for ionic conductivity modeling: 

Rj(t) = 6~n(t)L/A(XiQ~2/ri) (3) 

where l+(t) is the junction resistance of the resin at time t, Ci is the ionic 

concentration in ions per cubic meter, Qi is the charge carried per ion, ri is the 

radius of the ion in meters, q(t) is the viscosity of the resin at a given time t, and 

L is the separation distance between the electrodes and A is the area of cross 

section of the electrodes “visible” to the ions. 

For resin systems doped with TA, the model inputs were n(t), L, A and Ci. The 

characterization of model inputs can be found elsewhere [4]. During cure, the 

separation distance, L, is no longer the shortest distance between the electrodes. 

The network formation impedes the motion of ions in a linear path, forcing them 

to travel increasingly tortuous paths to reach the electrodes. This increases the 

separation distance with cure. For purposes of simplicity, the tortuosity effect 

was neglected by England. 

Module I of Figure 6 deals with developing resistance (R) vs. viscosity (q) 

relationship. This is accomplished by assuming that during cure the remaining 

parameters in equation 3 do not undergo a change except for R and n. Therefore, 

one can relate these two parameters as: 

rl(t) = d-0 * Rj WRo r (4 

where no(T) is the initial viscosity at temperature, T, and R, is the initial 

resistance of the resin system at t = 0. 

7 
MODULE I MODULE II 

* 

Resistance vs. Degree of Conversion 

MODULE III 

R = 6nqL/ AZ:iCiQi’/ ri 

Through Model of Polymer 

Electrolytes 

MODULE IV 

Figure 6. Schematic representation of England’s model [4]. 

Module II deals with deriving a resistance, R, vs. degree of cure, a, relationship. 

This was accomplished by way of curve fitting experimental a vs. R data. A 

typical equation derived for cure temperature of 40 “C is given as 

v(aT&~ = 1.07-0.11oT,,l + 4.18 x 103a+oti1-6.66 x lo-%&a,. (5) 

Module III attempts to relate degree of cure and macroscopic viscosity through 

resistance, R, which acts as the common parameter linking the two. Module IV 

presents the degree of cure, a, vs. macroscopic viscosity, n, relationship as 

rlbT) = WRno(T)/V(d-WI - [RqoO/Ro] . 05) 

Degree of cure observations were carried out by England using FTIR. This 

proves to be a superior technique as compared to differential scanning 
calorimeter (DSC), since FTIR enables the estimation of individual degree of cure 

of VE and styrene monomers. A knowledge of the degree of conversion of 

monomers is used extensively in this research work to draw insight into the 

network formation during cure. 

England’s model [4]. was successful in predicting material properties like 

viscosity and degree of cure until gelation. Section 1.4.2 discusses the need for a 

continuum model-one that would allow modeling ionic conductivity beyond 

gelation until vitrification1.4.2 The Need for a Continuum Model 

The model presented by England [4] is valid until the point of gelation and fails 

to accurately model the conductivity behavior beyond gelation due to the 

assumptions implicit in the model itself. A direct dependence of ionic resistivity 

on viscosity (Module I) is questionable for VE systems based on experimental 

observation where there is an offset between the time at which the viscosity 

reaches a minimum to when the ionic conductivity reaches a maximum. Module 

II of the above model relies on an empirical relationship to model DC resistivity 

and the degree of cure. It is therefore desirable to develop a fundamental model 

for relating the two. The model also fails to take into consideration molecular 

events like change in polymer chain length and change in number-average and 

weight-average molecular weights with the degree of conversion. This 

necessitates the exploration of a “continuum model” that could accurately 

describe the viscosity and SW behavior through gelation to vitrification. 

1.5 Report Overview 

A thorough understanding of the cure kinetics, network formation and their 

relationship to ionic conductivity behavior is essential for the development of a 

continuum model to accurately describe the observed SW behavior. In this 

work, an attempt has been made to characterize the relevant parameters 

influencing the conductivity behavior of curing VE. From previous work, it is 

known that cure temperature and styrene concentration play a significant role in 

the cure kinetics and, hence, on the observed DC conductivity [4, lo]. 

Preliminary investigation also revealed a decrease in DC voltage coinciding with 

the growth of VE microgels. This indicates a possible link between the two 

events. The modeling approach would therefore have to take into account the 

following possible mechanisms that could be either individually or 

synergetically responsible for the observed DC conductivity profile: 

l Development of cross-links and network formation during cure, which 

might be responsible for restricting ionic mobility. 

9 
l The tortuosity introduced by the presence of microgels. Since ionic 

conductivity is inversely proportional to the path length, L, traveled by the 

ion, an increase in the size and number of microgels would result in higher 

tortuosities and decreased ionic conductivity as cure proceeds: 

A series of systematic experimental results were conducted in this study to 

identify the most important mechanisms governing ionic conductivity. For 

simplicity, ionic conduction through the microgels are neglected, i.e., the 

microgels are assumed to be of negligible conductivity compared to the resin 

surrounding it. Also, the previously mentioned effects are considered only on an 

individual basis and the synergetic effects are not considered. Based on the 

experimental work, two different models, one based on the percolation theory 

and the other based on the free volume theory, were proposed. The percolation 

theory takes into account the effect of microgels on ionic conductivity, while the 

free volume-based model takes into account the network development during 

cure. A comprehensive analysis of the two models revealed that the free 

volume-based model is superior. Figure 7 gives a schematic representation of 

the different steps involved in the development of the continuum models. Cure 

kinetics measurements and DC sensing of cure were used to investigate the 

dependence of degree of cure on isothermal cure temperature and initial 

concentration of the styrene monomers in the reacting resin mixture. 

In the case of the free volume model, the degree of conversion obtained is related 

to the development of glass transition temperature, T, using the Venditti’s 

relationship as follows [ll, 121: 

W,) = ((I-. WV-,) +K,WWJ MU - 4 +G) 4 , 

where T, is the glass transition temperature, a is the total degree of cure, C,, is 

the model parameter, tid Tgm is the ultimate T, 

The glass transition temperature is then used as the input parameter for 

determining ionic conductivity o and viscosity TJ using the free volume theory 

as: 

log(m/mg) = G(T -Tg)/ ((Cz + C3T,) + (‘I- -Tg)) (8) 

and 

lO&T/~Tg) = cl(T - Tg)/((G + C3Tg) + (T - TJ) . (9) 

By making use of the glass transition temperature, T, as the common link 

between ionic conductivity, viscosity and the degree of cure, it becomes possible 

to in-situ “sense” the material behavior Iike viscosity and degree of cure using 

DC sensing. In this approach, microgels do not directly influence ionic 

conductivity. 

10 
t 

Degree of Conversion (a) vs Effect of Cure Temperature and 

Initial Coacentration of Styrene 

a = f(T, CST) 

Free Volume Model ~ ~ Percolation Model 

Glass Transition Temperature ( Ta ) vs Degree of Volumetric Contribution of Microgels 

(VM~.~~~~I) vs Degree of Cure (a) 

ln(TB) = (( I-a)ln(T,)+(C,,) alu(T,“) Y((1 -a)+(W 

Figure 7. Schematic of continuum model. 

-In the case of the percolation-based model, the degree of conversion is related to 

the volumetric contribution of microgels as shown in Appendix B. The ionic 

conductivity development plotted against the volumetric contribution of 

microgels is compared to the classical percolation-based conductivity profiles. 

The viscosity modeling is accomplished through the modified Einstein equation: 

l)r =1-K, (10) 

where K is a constant in the range of 2.35 and 2.60, C is the volume concentration 

of spherical particles (i.e., microgels), and & is the apparent fluidity. Therefore, 

by using the volumetric contribution of the microgels as the common factor, the 

percolation model relates ionic conductivity to both viscosity and degree of 

conversion during cure. 

The main experimental techniques and materials used in this work are discussed 

in section 2. The experimental procedures and the data analysis techniques are 

also presented in this section. This section also draws a relationship between the 

different experimental techniques and their importance in the schema of 

continuum model. Table 1 presents the different resin systems and the various 

compositions of the reaction mixture used in this research work. 

The cure kinetics of the resin systems studied are presented in section 3. FTIR 

spectroscopic techniques and DSC were employed to obtain the conversion 

kinetics of both the VE monomer and the styrene monomer in the given VE resin 

systems. This section quantifies the influence of temperature and styrene 

concentration on the curing of the VE resin system. 

11 
Table 1. List of compositions of the reacting resin mixture used in this study. 

-. . 

Experiment VE Resin VE Resin VE Resin 

411-C-5@ 441-4OOb 825~ 

Cure 0.2 weight-percent 0.2 weight-percent 0.2 weight-percent 

kinetics CoNapd CoNap CoNap 

2 weight-percent 1 weight-percent 1 weight-percent 

Trigonoxe Tngonox Trigonox 

Viscosity 0.2 weight-percent 0.2 weight-percent 

CoNap CoNap 

2 weight-percent 1 weight-percent 

Trigonox Trigonox 

Cure 0.2 weight-percent 0.2 weight-percent 

Monitoring CoNap CoNap 

2 weight-percent 1 weight-percent 

Trigonox Trigonox 

DIS 0.2 weight-percent 0.2 weight-percent 

(microgel CoNap CoNap 

ikze) _. 2 weight-percent 1 weight-percent 

Trigonox Trigonox 

Microgel 

Separation - 

~Dow Derakane 411-C-50. 

JDOW Derakane 441-400. 

cIn-house synthesized V&325. 

dCoNap = cobalt naphthenate accelerator. 

eTrigonox = AZCO Trigonox 239 initiator. 

- 

- 

- 

0.1 weight-percent 

CoNap 

0.5 weight-percent 

Trigonox 

The cure monitoring efforts using SW and dielectric techniques are presented in 

section 4. Changes in the conductivity behavior are correlated to molecular 

events. 

Section 5 addresses the presence of inhomogeneties (microgels) ti the curing 

sample. A comprehensive set of data corresponding to the characterization of 

microgels has been presented and an explanation of the role of these microgels in 

cure kinetics and, hence, in conductivity behavior, has been explored. Section 5 

also explores the feasibility of a continuum model based solely on the volume 

fraction of the microgels. This modeling approach assumes that all reaction 

contributes only to the formation of microgels, which are surrounded by 

unreacted resin mixture. An ionic conductivity model based on the percolation 

E 

12 
theory and a viscosity model based on the modified Einstein’s relationship are 

used to used to investigate the effectiveness of the assumption in describing the 

experimental observation. A large discrepancy between model predictions and 

experimental data suggested a need for a better model, one that would take into 

account the network formation outside the microgels during cure. 

A mathematical model based on the molecular events identified in this 

experimental work is presented in section 6. This free volume-based model 

satisfies the requirements of a continuum model and describes the observed 

conductivity behavior through gelation until vitiification. Based on the 

experimental results generated, the free volume-based continuum model was 

adopted successfully for ionic conductivity modeling. The free volume model 

extends the ability to sense material properties like viscosity and degree of cure 

using the observed DC conductivity. 

Section 7 presents a discussion of the work accomplished and possible areas for 

further research. 

1.6 Section Summary 

This section established the motivation and significance for a continuum model 

to predict degree of conversion and viscosity. In summary, this research work 

contributes the following information over and above the existing body of 

knowledge regarding DC-cure monitoring: 

l Identification of the conducting system; 

l Establishment of a relationship between cure-related molecular events and 

observed DC signal; 

Establishment of the role of microgels in gelation and hence on DC signal; 

Advantages and disadvantages of DC- and AC-cure sensing techniques; 

Development of a continuum model to predict ionic conductivity, viscosity, 

and degree of conversion; and 

Establishment of a fundamental theory to enable sensing of viscosity and 

degree of conversion through DC-cure monitoring such as SW. 

13 
2. Experimental Methods 

2.1 Introduction 

Seven experimental techniques were used in this work to support the 

development of the continuum model presented in Figure 7. The viscosity 

changes during the cure reaction were obtained using a Brookfield viscometer. 

The changes in DC conductivity with cure were sensed using an ARL SW 

system. Dielectric cure monitoring was carried out using a Micromet 

manufactured dielectrometer. The degree of conversion of the VE and styrene 

double bonds were monitored using FTIR spectroscopy in the infrared (IR) DSC. 

Glass transition temperature measurements were accomplished using dynamic 

mechanical analysis (DMA). Liquid chromatography using Hewlett-Packard 

manufactured chromatographs was performed to determine the effectiveness of 

microgel separation. The chemical composition of the microgels were then 

analyzed using FTIR spectroscopy. Atomic force microscopy (AFM) was 

performed on cured samples to determine the equilibrium size of the microgels. 

This section gives the details on all the experimental methods and sample 

preparation techniques. The materials used in this study are also discussed. 

2.2 Materials 

This research focuses primarily on ionic conductivity in VE resin systems. 

Section 22.1 provides a brief description of the VE resin system, while section 

2.2.2 discusses specific VE resin systems used in this research work. 

2.2.1 Background on VE Resins 

A brief description of VE resin systems is given in section 2.2.1.1 and the 

chemistry of free-radical chain growth copolymerization is discussed in section 

2.2.1.2. 

2.2.1.1 VE Resin Systems 

VE resins fall under the category of thermosetting resin systems. These resin 

systems are characterized by polyfunctional monomeric systems, which upon 

reaction form cross-links which result in a network structure that cannot be made 

to flow upon heating, The phenomenon of formation of a cross-linked network 

due to the reaction between the monomers present in the resin system is known 

as “curing.” As the conversion of the monomers increase, the number of crosslinks also increases, leading to the tightening of the resulting network. With 

conversion, a number of resin properties changes (e.g., the glass transition 

14 
temperature, T, increases with an increase in the degree of conversion). There 

are two distinct points of interest associated with the curing process: gelation and 

vitrification. Gel&ion of a resin system can be defined as the formation of 

network structure of macroscopic dimensions so as to occupy the entire volume 

of the resin system (i-e., the formation of an infinite network) [13]. This is 

associated with macroscopic viscosity of the resin system exponentially reachmg 

infinity. Vitrification occurs when the glass transition temperature equals the 

cure temperature. Physically and macroscopically, a resin system is said to have 

vitrified when the material begins to solidify to a glassy state. At the molecular 

level, vitrification puts a severe restraint on the molecular motion severely 

curtailing the advancement of the cure reaction. In free-radical polymerization 

such as in VE resin systems, T, exceeds cure temperatures at very low degrees of 

conversion. 

VE resin systems are essentially composed of VE monomers and styrene 

monomers apart from other additional chemical species such as inhibitors, 

stabilizers, etc., which are generally proprietary to the individual manufacturers. 

VE monomers are additional products of various epoxide resins and 

ethylenically unsaturated monocarboxylic acids such as acrylic or methacrylic 

acids. At this stage in the synthesis of VE resins, one ends up with the presence 

of chloride (Cl-) ions in the resin. Traditionally, these chloride ions are 

considered to be responsible for the observed dielectric and ionic conductivity 

behavior in epoxy resins. Therefore, one could safely conclude that in undoped 

VE resins, the observed DC conductivity is the result of contribution from these 

chloride ions. 

Styrene monomers are usually added to reduce the room temperature viscosity 

of the mixture. In most of the commercial resins, the concentration of the styrene 

is restricted between 30% and 55% by weight. Figure 8 shows the chemical 

structure of both the VE monomer and the styrene monomer. As shown in 

Figure 8, the VE monomer has two reactive end groups whereas the styrene 

monomer has only one reactive end group. This essentially means that of the 

two, only VE monomers can act as the cross-links and the conversion of 

VE monomers is a measure of the degree of cross-linking in the final resulting 

network, The conversion of styxene monomers results in linear chti extensions, 

Hence, the degree of conversion of the styrene monomers is a measure of the 

approximate distance between the cross-links. 

2.2.1.2 Free Radical Chain Growth Copolymertiation 

The VE resin system reacts through a free-radical co-polymerization. Mechanism 

of such a reaction is explained in detail in other literature [14]* A brief summary 

of the three main steps are: 

15 
Styrene 

Figure 8. Chemical structure of VE and styrene monomers. 

l initiation involving two reactions: formation of the initiator radical (R) and 

addition of the initiator radical to a monomer; 

l propagation of a monomer radical to another monomer molecule; and 

l termination of all growing chains due to lack of mobility of unreacted 

monomers. 

Possible initiators for a free-radical polymerization include peroxides and 

hydroperoxides, azo compounds, redox initiators, and photoinitiators [14]. In the 

current study, an organic hydroperoxide was used as the initiator. The main 

characteristics of the initiator material are that it should be fairly stable at room 

temperature, and simultaneously, to ensure practical reaction rates, it should be 

able to decompose fairly rapidly at reaction temperatures. 

Primary radicals are formed through thermal decomposition of the peroxides. 

The addition of the monomers to the growing polymer chain results in the 

propagation stage of the polmerization reaction with continued propagation of 

the radical to the new monomer site. It is a common practice to add accelerators 

or promoters such as cobalt naphthenate (CoNap) to raise the decomposition 

rate of the initiator at low temperatures such as those used in our reactions which 

typically were between 30” and 50 “C. 

Three types of VE resins were used in this study: (1) Derakane 411-C-50, (2) 

Derakane 441&O, and (3) an in-house synthesized VE825. The type of initiator 

used in the system was Trigonox 239A, purchased from AZKO. This initiator 

contained 45 weight-percent carboxylic ester, 45 weight-percent cumyl 

hydroperoxide, and 10 weight-percent cumyl acid. CoNap containing 6 weightpercent cobalt, was used as an accelerator to induce the decomposition of the 

initiator at low-curing temperatures. Styrene of 99% purity, purchased from 

Aldrich Chemicals, was used for diluting the VE system. Benzoquinone, which 

is an inhibitor for the free-radical reactions, was used to stop the reactions where 

required in case of reactions used to study microgel compositions. 

Benzoquinone was supplied by Aldrich Chemicals. 

16 
2.2.2 Resin Compositions 

Two commercial VE resins were used in this work, namely Dow Derakane 441- 

400 and Derakane 411-C-50. For experimental techniques involving the 

separation of microgels and subsequent characterization, a specialized polymer 

designated VB825, developed in-house, was used. The previously mentioned 

commercial resins were both supplied by Dow Chemical Company. From the 1H 

nuclear magnetic resonance (NMR) spectroscopy, it was determined by Dua [lo, 

151 that the value of the n-repeat group in Derakane 441400 is approximately 

1.66. The average molecular weight of the VE monomer in the resin was 

determined to be 700. The styrene content in the resin system was established to 

be 28% by weight. Using the same NMR technique, the n-repeat unit in 411-C-50 

was determined to be 2.39, the average molecular weight was established to be 

908, and the styrene content was determined as 45% by weight. 

Derakane 411-C-50 was used to study the effect of temperature on kinetics, 

rheological changes and the modeling of the conductivity behavior. This resin is 

used widely in most of the liquid molding processes due to its lower viscosity, 

which facilitates resin infusion- Also, the longer-gel&ion time characteristic of 

this resin, makes it the ideal candidate for studying the reaction kinetics and 

viscosity changes in the pregel stage. Derakane 441400 was primarily used to 

understand the effect of dilution with styrene on the cure kinetics of the VE resin 

system. As mentioned above, Derakane 44140 contains only 28 weight-percent 

of styrene and, hence, is much more suitable for studying the effects of dilution 

up to 57 weight-percent of styrene, which is the practical upper limit for most of 

the commercial VE resin systems used in the composite industry. VE825 resin 

was also used for studying the effect of dilution with styrene. VE825 offers the 

unique advantage of offering the ability to be diluted with styrene, since this 

resin system is free of styrene monomers. The monodispersed nature of the VE 

monomers in VE825 is taken advantage of in the studies involving the microgel 

separation due to the fact that the effectiveness and ease of separation of the 

microgels is augmented. 

L 

2.3 Viscosity Experiments 

Measurement of viscosity during cure is used as an effective tool to identify the 

onset of gelation. It is also used in this research as a benchmark to compare the 

sensitivity of DC monitoring to gelation. The effectiveness of the continuum 

model as an in-situ cure monitoring tool is based on its ability to accurately 

predict the experimentally observed viscosity profile during cure. 

2.3.1 Sample Preparation 

The samples were prepared by adding the desired quantities of the reaction 

mixture in the proper order, i.e., VE resin system followed by styrene (if 

17 
required), followed by CoNap. The prepared sample was then equilibrated to 

the desired temperature at which the viscosity characteristic needs to be studied, 

e.g., T = 40 “C. Once the system was equilibrated to the desired temperature, a 

calculated amount of Trigonox was mixed to the resin system to start the 

reaction. About 10 mL (stipulated by the Brookfield Viscometer manual [16]) of 

the reaction mixture was then introduced into the cylindrical jacketed container 

of the Brookfield viscometer. The reaction was allowed to proceed within the 

cylinder and the viscosity changes were measured at fixed-time intervals. 

2.32 Instrumentation 

Viscosity experiments were performed on a Brookfield Model LVDV II+ digital 

viscometer. Sample temperature was controlled with the help of a Brookfield 

small sample adapter and Brookfield water bath/circulator model TC-200. The 

basic components are shown in Figure 9. The viscometer essentialIy consists of a 

fixed outer cylinder and a spindle that rotates at a constant angular velocity. The 

spindle is connected to a torque spring which measures the frictional resistance 

generated by the resin inside the sample container. The viscosity is then 

calculated by the viscometer. In the experiments, care was taken to maintain the 

angular velocities at 20 rpm, since the accuracy of the resulting values were 

heavily compromised below 20 rpm, due to the limitations on torque 

measurements [16]. A typical viscosity profile is given in Figure 10. Point A in 

the figure corresponds to the initial viscosity of the reacting mixture. On further 

reaction, the exothermic nature of the reaction forces the temperature of the 

reacting mixture to increase thereby decreasing the viscosity between points A 

and B. With further cure, cross linking and network formation results in an 

exponential increase in the observed macroscopic viscosity resulting in gelation 

at point C. 

2.4 SW Experiments 

SW experiments form the core of this research effort as a way of providing in-situ 

DC-cure monitoring information. The continuum model strives to relate the 

observed SW signal to material properties like viscosity and degree of cure. 

A batch of VE resin system was prepared as described before in section 2.3.1. 

The prepared resin batch was allowed to equilibriate in an oil bath. Once 

equilibrated, the sample was then transferred to the Single Node Test Cell 

(SNTC)-3 type of SW cell [4]. A typical SNTC3 single node test cell is shown in 

Figure 11. A detailed explanation of the specifications of SNTC3 is given in 

Appendix C. Throughout the reaction, care was taken to maintain the reaction 

temperature at the desired set value. The change in DC conductivity with resin 

cure was recorded and stored in a computer running the SW system. A 

18 
I I 1 I 

i 

I I I I - Small Sample Adapter 

Figure 9. Schematic illustration of a BrookEield viscometer and small sample adapter. 

yO 4 8 12 16 

Time (Min) 

Figure 10. Typical viscosity profile of a curing VE resin. 

19 
ARTweave Leads 

t 

Fiffure 11. SNTC3 single node test cell. 

description of the SW apparatus and its working has been discussed in section 

1.3. A detailed overview is discussed elsewhere [4,17-201. A typical SW profile 

generated using SNTC along with relevant explanations are presented in section 

1.3. 

2.5 Dielectric Cure Monitoring 

Dielectric sensing has conventionally been used for in-situ cure monitoring. 

Therefore, in order to benchmark the performance of DC sensing as a cure 

monitoring tool, it is essential to compare and contrast the sensitivity of both 

these tools to the cure related events such as gelation and vitrification. 

The resin system was prepared as discussed in section 2.3.1 and was then 

equilibrated using an oil bath. The cure initiation was achieved by introducing 

the calculated amount of Trigonox into the mixture. The reaction was run 

isothermally at the desired set temperature maintained by the oil bath. The data 

concerning changes in the dielectric behavior were collected and stored in a 

computer running the dielectrometer. 

The dielectric experiments were all carried out using a Eumetric 1OOA 

dielectrometer, manufactured by Micromet Instruments, Inc. The Eumetric 1OOA 

interface hardware was preset at midconductivity mode and all experiments 

were performed using a 2-in tool mount sensor. The A/D ratio of the tool mount 

sensor used has been predetermined to be 40, where A is the surface area of the 

electrode and D is the separation distance between the electrodes. 

20 
ve411c5Otemp30 

0 1 2 3 4 5 

1 ine < Hours > 

cFl> HELP : csmace> UNZOOH : al t_cF7/F8> SfORE/RECRLL : shift_cESC> FXll 

Figure 12. Typical dielectric signal of a curing VE sample. 

The dielectric measurements were performed at seven different frequency modes 

to collect information on the rate of change of log loss factor and log ionic 

viscosiv with cure. A review on the dielectric technique and the relevant 

parameters is presented in Appendix A. A typical dielectric profile is shown in 

Figure 12. 

2.6 FYUR Experiments 

FTIR measurements yield degree of conversion of monomers with time, thereby 

enabling one to relate cure events like gelation and vmification to the extent of 

cure. The experimental data are also used extensively, in the modeling effort to 

analyze volumetric contribution of the microgels, in the latter stages of this 

research work. Section 6 deals with the effectiveness of a continuum model to 

predict the degree of cure profiles over a wide range of temperatures. 

2.6.1 Instrumentation and Sample Preparation 

Cure monitoring studies involving a study of the degree of conversion of VE 

double bonds and styrene double bonds were performed using a Nicolet 20 DXB 

FTIR spectrometer in the transmission mode working in the IR region of the 

spectrum. A batch of the resin system was prepared as described in section 2.3.1 

and then the calculated amount of Trigonox was introduced. A drop of the 

reacting mixture was then placed in between two NaCl transparent crystal plates 

supplied by International Crystal Labs. A 0.025~mm Teflon spacer was used to 

regulate the sample thickness between the crystal plates. The crystal plates were 

equilibrated prior to the introduction of the resin mixture and the reaction was 

21 
allowed to proceed at the desired temperature in an isothermal mode. The 

crystals containing the sample between them was then placed in a sample holder 

housed in an assembly consisting of an aluminum block containing two 100-W 

cartridge heaters. A constant temperature was maintained through regulation by 

a thermocouple and a temperature controller. Figure 13 shows a typical cell 

design used in the FTIR spectroscopy studies. 

Heater Cartridge Slots 

Cell Holder 

Teflon Snacer 

Figure 13. FTIR experimental setup. 

2.6.2 IR Spectra of VE 

FTIR spectroscopy is a characterization method that can be used to determine the 

degree of conversion of VE and styrene monomers of a curing resin system. In 

transmission mode FTIR, a beam of IR light is transmitted through the sample 

contained between the NaCl plates and the absorbance of laser light as it passes 

through the sample is measured. The amount of absorbed laser light, at 

characteristic wavelengths, is a measure of the increase or decrease of the 

concentration of those bonds that dissipate energy at those corresponding 

wavelengths [21]. 

The characteristic wavelengths of VE and styrene monomers are 945 cm-1 and 

910 cm-i, respectively. The absorbances of IR at these wavelengths result from 

the vibration and dissipation of energy by the carbon-carbon double bonds along 

the backbones of the monomers under consideration. With the proceeding of the 

cure, these double bonds break and are integrated into cross-links. This is 

reflected as the depletion in the C=C double bonds, which decreases the 

22 
f 

absorbance at the characteristic wavelengths of 945 cm-1 and 910 cm-l. 

Absorbance is normalized (to compensate the error introduced by way of 

evaporation of styrene and cure shrinkage) by a set of reference peaks. The 

reference peak for VE is set at 830 cm-1 and at 700 cm-1 for styrene. These 

reference peaks correspond to C-H bonds along the carbon backbone of the VE 

and styrene monomers [22]. 

Equations 11 and 12 were used to calculate normalized fractional conversion of 

VE and styrene double bonds from FTIR absorption data respectively: 

uvE(t) = 1 - (ABS(t)9$5cm=/ABS(t=0)~5&l)(ABS(f=0)830em~/ABS(t)830cm=), (11) 

asr(t) = 1 - (ABS(t) gioJ/ABS(t=O)~oJ)(ABS(t=0)700cm=/ABS(t)7o0cm-~), (12) 

where a is the fractional conversion of double bonds associated with each 

monomer at time t and ABS is the absorption intensity of the peaks. The 

magnitudes of the relevant absorbance peaks were measured taking into 

consideration slight shifts in peak locations and baselines. Figure 14 shows an 

FTIR spectra of VE resin at cure time t. 

Wavenumbers (cm-l) 

Figure 14. FTIR spectra of VIZ825 at the be@nning of cure at 40 “C cure temperature. 

2.7 DSC Experiments 

DSC experiments are used in this work to complement the FTIR results on the 

cure kinetics. While FTIR is a handy tool to measure the individual monomers’ 

degree of conversion, DSC provides the total degree of conversion for the 

reacting mixture. DSC measurements are used in the T,-a model developed by 

Stone [ll], required for the continuum model developed in section 4. 

Autocatalytic models have traditionally been used for modeling the cure kinetics 

of thermosets. In this study, an autocatalytic equation of the form given in 

23 
equation 13 was used to describe the cure rate of VE resin 411-C-50 as studied 

using the DSC technique: 

da/dt = (lG+Kzum)( a,,-+ _ (13) 

Stone [ll] has explored the reaction order (m + rt) for isofiermal cures of VE 411- 

C-50. Kinetic parameters for the often used second order autocatalytic model are 

given in Table 2: 

Table 2. Autocatalytic parameters for the depee of conversion as observed using DSC. 

Cure C0m. 

Temp 

($.A) 

M n Coeff. 

(“C> 

20 0.0003 + O.oool 0.01 + 0.002 1.075 + 0,015 0.925 + 0,015 0.9949 

I 30 1 0.0012 + 0.0001 1 0.1273 + 0.070 1 1.038 + 0.004 1 0.962 + 0.004 1 0.9900 1 

I 40 1 0.0035 + 0.0001 1 0.1694 + 0.002 1 1.037 f 0.009 1 0.963 f O.OEJ 1 0.9895 1 

This study used cure simulation software, PIRSA [23], that incorporated the 

previously mentioned kinelk parameters to obtajxl degree of cure for isothermal 

runs of 20”, 30”, and 40 “C. A typical profile of the curing resin mixture 

generated using PIRSA is shown in Figure 15. 

150 200 250 3DD 490 

Time (Min) 

Figure 15. Degree of conversion of VE 411-C-50 at 30 “C as obtained from PIIGA. 

24 
2.8 DMA Experiments 

DMA measurements yield information on the glass transition temperature T, of 

the cured resin mixture. A knowledge of T, is used in section 4 to relate the 

development of network structure to the observed SW behavior. 

Sample Preparation and Instrumentation. Resin mixtures prepared as described 

in section 23.1 were cured as plaques on aIum.inum sheets at the desired cure 

temperature. Rectangular samples of dimensions 0.125 in x 0.25 in x 2.5 in were 

prepared from the cured plaques for DMA analysis. The DMA experiments were 

carried out using a 983A type dynamic mechanical analyzer at fixed frequency. 

All experiments were started at 25 “C and the samples were ramped to 200 “C at 

2 OC/min to maintain thermal equilibrium. A schematic representation of the 

experimental set up is shown in Figure 16. 

DMA 983 

Coni and 

Data Acquisition 

Computer 

Figure 16. Schematic illustration of DMA setup. 

2.9 Liquid Chromatography 

Liquid chromatography was used in this research work to ascertain the 

effectiveness of the removal of unreacted VE and styrene monomers from the 

reacted high molecular weight component, namely microgels. The microgels 

were removed from the reacting mixture to characterize their chemical 

composition. Since contamination by unreacted VE and styrene monomers could 

introduce inaccuracies, it became essential to monitor the effectiveness of the 

“fractionation process” using liquid chromatography. 

25 
2.9.1 Sample Preparation 

A batch of VE825 was mixed with 28 weight-percent styrene to obtain the VE 

resin system for liquid chromatographic analysis of the microgels. The VE resin 

system was equilibrated to 40 “C prior to the addition of CoNap and Trigonox. 

The choice of low styrene content in the resin sample was based on preliminary 

work where microgel separation was unsuccessful due to the presence of excess 

unreacted styrene monomers. Very low gelation times were experienced with 

this resin system at normal concentrations of 0.2 weight-percent CoNap and 2 

weight-percent Trigonox. Consequently, lower and lower concentrations of 

CoNap and Trigonox were tried until a combination of 0.1 weight-percent 

&Nap and 0.5 weight-percent Trigonox yielded an acceptable time to gelation of 

10 min at a 40 “C isothermal cure temperature. 

Once the reaction was initiated, the reaction was allowed to proceed for 9 min at 

which time the reaction was stopped by the addition of 0.25 weight-percent 

benzoquinone. Care was taken to introduce the same volume of benzoquinone 

mixture as that of the reacting. mixture with continuous vigorous shaking. The 

terminated mixture was then dissolved in an equal volume of tetrahydrofuran 

(THF) followed by reprecipitation by the addition of methanol. This stage 

presents multiple problems in that if excess volume of methanol was added, a 

large fraction of the unreacted monomers also were precipitated; on the other 

hand, a shortage of methanol addition results in no precipitation at all. 

This procedure was repeated on the precipitate for 10 cycles. The final 

precipitate was then placed in a vacuum chamber for a period of 24 hr to remove 

any remaining traces of unreacted styrene monomer. Ten milbgrams of the final 

sample was then dissolved in ICI mL of high-performance liquid chromatography 

(HPLC)-grade THF to prepare the experimental sample for HPLC analysis. 

2.9.2 HPLC Instrumentation 

A schematic illustration of the liquid chromatography instrumentation setup is 

shown in Figure 17. A syringe setup is used for introducing 20 mL of the sample 

solution and size variations between different chemical species in the injected 

sample are sensed and output as different peaks on a voltage versus time plot, 

with larger molecular species appearing earlier along the time axis. 

2.10 Atomic Force Microscopy (AFM) 

AFM was used to verify the presence of microgels in the reacted resin mixtures. 

Similar work on high temperature resin mixtures have shown the presence of 

these spherical entities. However, since reaction kinetics are dependent on 

temperature, it becomes essential to identify the presence of microgels in low26 
785A Programmable 

PE Nelson 500 Series Interface Absorbance Detector 

,/Sample Loader 

Figure 17. Schematic illustration of WLC experimental setup. 

temperature systems. AFM results were also used to identify the range of 

microgel sizes that were used in the parametric study presented in section 5 to 

ascertain the role of microgels on ionic conduction and gelation. 

2.10.1 Background 

Tapping mode imaging is a key advance in AEM for soft, adhesive, or fragile 

samples. This technique allows high-resolution topographic imaging of sample 

surfaces that are easily damaged. In conventional contact mode AFM, the probe 

tip is simply dragged across the surface and the resulting image is a 

topographical map of the surface. The serious drawback, however, is that the 

dragging motion of the tip, combined with the adhesive forces between the tip 

and the surface, can cause substantial damage to both the sample and the probe 

tip, besides causing artifacts in the image data. Tapping mode imaging 

overcomes the limitations of the conventional scanning modes by alternately 

placing the tip in contact with the surface to provide high resolution and then 

lifting the top off the surface to avoid dragging the tip across the surface. 

Tapping mode imaging is implemented in ambient air by oscillating the 

cantilever assembly at or near the cantilever’s resonant frequency using a 

piezoelectric crystal. The piezo motion causes the cantilever to oscillate with a 

high amplitude when the tip is not in contact with the surface. The oscillating tip 

is then lowered toward the surface, until it begins to lightly touch or tap the 

surface. During scanning, the vertically oscillating tip alternately contacts the 

surface and lifts off, generally at a frequency of 50,000 to 500,000 cycles per 

second. As the oscillating cantilever begins to intermittently contact the surface, 

27 

Table 3. Tapping mode specifications. 

Drive Frequency Range 10 kHz-1MHz 

Drive Voltage Range O-20 v 

Drive Amplitude and Frequency Adjustment Software Contiolled 

Detector RMS to DC Amplitude Detector 

Cantilevers Etched Silicon Cantilevers 

60-400 kHz Resonant Frequencies 

Tip-Sample Approach Motorized Sample Approach 

Nanoscope III 

l System Controller 

Laser 

Photo- n 

High Resolution 

Oscillator 

Silicon Cantilever 

with Integral Tip 

Sample \ / L I I 

Figure 19. Block diagram for tapping mode operation. 

29 
3. Cure Kinetics of VE Resins 

3.1 Introduction 

A thorough understanding of the SW signal or that of any other cure monitoring 

technique, requires a comprehensive understanding of the molecular events 

associated with curing. This section analyzes some of the parameters that must 

be considered to develop the continuum model for ionic conductivity, As 

presented in Figure 7, cure kinetic studies are the first step in the development of 

the model. Using the experimental techniques described in section 2, it becomes 

possible to understand the effects of initial concentration of styrene and cure 

temperature on the cure processes and their relationship to ionic conductivity. 

Thermal analysis using DSC has been used extensively by other researchers in 

both isothermal and nonisothermal mode to study the cure kinetics of the resin. 

However, DSC suffers from a disadvantage of not being able to yield any 

information regarding the degree of conversion of the individual components 

(i.e., VE and s tyrene) in the reacting mixture. Since the objective of this research 

work was to obtain as much information as possible regarding the individual 

components, FTIR was employed to obtain the degree of conversions of VE and 

styrene individually. 

In this work, emphasis has been placed on understanding the effects of styrene 

concentration, temperature and molecular weight on cure kinetics. A thorough 

understanding of the previously mentioned factors is an important prerequisite 

in developing the conductivity model described in Figure 7. 

3.2 Cure Kinetics Using FTIR 

Figure 20 shows typical FTIR data of the degree of conversion of VE double 

bonds and styrene double bonds with time. The degree of conversion is 

expressed here as the percentage ratio between the number of double bonds 

consumed and the initial number of double bonds. Therefore, care should be 

taken in comparing the conversion data between different species and for 

different FTIR runs. As mentioned before, VE has two reactive double bonds 

whereas styrene has just one. When a double bond reacts, it could be the first 

double bond of a new VE monomer or it could be the second double bond of an 

already reacted and, hence, bound to the network VE, monomer. In short, the 

double bond conversion of the VE monomer is not the same as the double 

conversion obtained from FTIR. Figure 20 shows three distinct regions. 

30 
0.7 

0.6 

us 

a4 

I 

'. 0.3 

a 

0.2 

0.1 

0 8 

I 

4.1 

60 80 

Time (Min) 

Region III !Ej 

I 120 140 160 

Figure 20. Typical profiles of VE and styrene double-bond conversion. 

It should be noted however that the boundaries of these three regions are not 

definitive and they are likely to be quite diffuse. In Regions I and II, the 

conversion of the VE double bonds is greater than the conversion of the styrene 

double bonds. In Region III, VE plateaus can be seen, while styrene conversion 

continues and eventually exceeds the final VE conversion. In Region I, the 

reaction kinetics are determined by the reactivity ratios of VE and styrene. The 

higher conversion of VE suggests that the VE double bonds have a higher affinity 

to react with the free radicals as compared to the styrene double bonds [lo, 151. 

In Region II, due to gelation, the bimolecular termination rate is lowered due to 

the decrease in mobility of the growing radical species. The hindered 

bimolecular termination results in an increase in the concentration of the free 

radicals and accelerates the reaction. This effect is termed the Trommsdorf effect 

[24,25]. In Region III, the diffusional limitations play a significant role. With the 

onset of vitrification, the serious restrictions placed on the molecular mobility is 

said to be the reason for the final conversion not being able to reach 100% [24, 

251. The higher final conversion of the styrene double bond suggests that since 

styrene is a smaller molecule compared to the VE monomer, it would be better 

able to diffuse to reactive sites. 

An important feature of many free-radical, chain-growth, cross-linking 

copolymerization systems is the formation of localized, highly cross-linked, 

submicron size regions called microgels [26, 271, These microgels are in the 

range of 100-150 nm in diameter and come into existence in the sea of VE resin, 

31 
almost instantaneously (as compared to the time scale of the curing process) [28]. 

With the proceeding of cure, the number of microgels in the reacting mixture 

increases with time, as opposed to the classical nucleation theory, where 

nucleation occurs simultaneously and the nucleated sites grow in size with time. 

Consequently, microgel formation is highly heterogeneous in nature. Another 

important factor that is believed to strongly affect the cure behavior of VE resins 

is the phase separation of the macromolecules from the unreacted monomers. 

Based on theoretical thermodynamic calculations, Palmese [28] and Ziaee [29] 

suggested that there is a high probability of phase separation in VE resins due to 

enthalpic contributions. 

3.3 Effect of Styrene Concentration 

Figures 21 and 22 show the effect of styrene concentration on the fractional 

conversions of VE and styrene double bonds for Derakane 441-400. The 

reactions were performed at 28%, 37%, 47% and 57% by weight of styrene. 

Owing to better temperature control available at 40 “C, all the reactions were 

conducted isothermally at 40 “C with 1.0 weight-percent Trigonox and 

0.2 weight-percent CoNap. From the observation of Figures 21 and 22, it is clear 

that the initial conversion of VE double bonds decreases with an increase in the 

styrene concentration as is the case of styrene double-bond conversion- The 

same effect was observed by researchers working with DSC on similar systems 

[24]. The initial decrease in the VE conversion can be explained based on the fact 

that with increasing concentration of styrene, the VE concentration decreases 

leaving fewer VE double bonds to participate in the cure reaction. Dua [lo] 

argues that the seemingly strange decrease in the reaction rate with an increase 

in the styrene content is due to the fact that the reactivity ratio of the VE 

monomers is higher than that of the styrene monomer. Therefore. the VE 

monomers react faster with the primary free radicals to give VE chain radicals 

which. in turn. react with the styrene monomers. This phenomenon explains 

why an increase in the styrene conversion with increasing VE concentration is 

observed, or conversely, why the styrene conversion decreases with increasing 

styrene content in the reacting mixture. 

Lee and Lee [30] and Dua [lo] have observed the formation of polystyrene 

during the latter stages of the cure and at higher styrene concentrations (47% and 

57%). They attribute the formation of this homopolymer to the phenomenon of 

phase separation. Two phases are said to form during the course of 

copolymerization. The first phase essentially is the copolymer network swelled 

by the unreacted VE monomer and, perhaps, residual styrene monomers. The 

second phase essentially is made of unreacted styrene. It is hypothesized that 

even though copolymerization stops in the first phase due to vitrification of that 

phase, the homopolymerization continues in the styrene-rich second phase. 

32 
0.8 

28 wt% 

37 wt% 

47 wt% 

57 wt% 

Time (Min) 

Figure 21. Fractional conversion of VE double bonds in Derakane 441-400 cured at 

40 “C. 

0.2 

s---x 28wt% 

- 47Wt% 

Time (Min) 

Figure 22. Fractional conversion of styrene double bond in Derakane 441-400 cured at 

40 “C. 

Dua [lo] hypothesized that the copolymerization reaction could result in the 

formation of the microgels which are responsible for trapping a large number of 

the pendant VE double bonds due to the compaciness of the microgel structure. 

The microgels are rich in VE and are surrounded by the styrene-rich region. 

33 
From Figures 21 and 22, it becomes apparent that the final conversion of the VE 

double bonds increases with the increase in styrene concentration, whereas in the 

case of styrene double-bond conversion, there seems to be no significant change 

in the final fractional conversion with styrene concentration. Similar results have 

been reported by Dua [lo] and Brill and Palmese [21] for the same resin system. 

They argue that with an increase in the concentration of styrene, more styrene 

gets incorporated in the network leading to loosely networked structure. In 

other words, it leads to a structure with lower cross-linking density. This 

basically facilitates better mobility of the VE monomers enabling them to reach 

the reactive sites, hence, a higher final fractional conversion is achieved. The 

seemingly contradictory constant final fractional conversion of styrene is 

explained by the fact that the methacrylate groups of VE reacts faster and reach 

their maximum conversion much earlier than styrene (see Figures 21 and 22). 

This results in the onset of vitrification. The vitrified system may not allow the 

free diffusion of the styrene monomer to reactive sites thereby sealing them off, 

leading to almost the same final conversion for styrene monomers. It is argued 

that the phenomenon of phase separation becomes a significant factor in case of 

styrene concentrations beyond 47 weight-percent leading to the formation of VE 

rich and styrene rich phases. Due to the phase separation, the effect of increased 

styrene concentration is not really felt by the VE monomers that are 

copolymerizing in the other phase thereby resulting in the same final fractional 

conversion of VE monomers irrespective of styrene concentration beyond 

47 weight-percent. The previously mentioned hypotheses are verified for 

accuracy using DC cure monitoring and DMA in section 4.2. The experimental 

results show that for 37- and 47-weight-percent styrene systems, the cross-link 

density is higher than for 2S- and 57-weight-percent styrene systems. This 

indicates that an increase in the initial concentration of styrene in the reacting 

mixture does not necessarily result in a loose network, suggesting various 

degrees of homopolymerization between the resin mixtures under consideration. 

3.4 Effect of Temperature 

Figures 23 and 24 show the effect of temperature on the cure kinetics of Derakane 

411-C-50. CoNap at 0.2 weight-percent was used along with 2-weight-percent 

Trigonox to initiate the reaction. From Figures 23 and 24, it is apparent that the 

reaction rates and the final conversion for both VE and styrene monomers 

increases with an increase in the reaction temperature. This can be explained by 

the fact that the additional thermal energy enables higher diffusion of these 

monomers so that more monomers are able to reach the reactive sites at higher 

temperatures. Another observation is that the final conversion of styrene is 

higher than that of the corresponding VE monomer. As described in section 3.2, 

styrene monomers are better able to overcome the diffusional limitations 

34 
0.60 

Time (Min) 

Figure 23. Fractional conversion of VE double bonds in Derakane 411-C-50 cured at 

isothermal temperatures of 30”, 40”, and 50 “C. 

0.60 

0 50 100 150 

Time (Min) 

Fiffure 24. Fractional conversion of styrene double bonds in Derakane 411-C-50 cured at 

isothermal temperatures of 304 40’, and 50 “C. 

imposed by network formation due to their relatively smaller size; the styrene 

monomers also exhibit higher final conversion. This, combined with the fact that 

one observes change in styrene fractional conversion long after the VE fractional 

conversion levels off, suggests polystyrene formation and hence a possibility of 

phase separation. Section 4 deals with the effect of temperature on the DC signal 

and how different aspects of the cure kinetics of Derakane 411-C-50 such as 

35 
development of cross-link density, formation of homopolymerised microgels and 

molecular mobility contribute towards the development of the continuum model 

presented in sections 5 and 6. 

C?n comparison of the final fractional conversion of monomer double bonds of 

Derakane 4-41400 (diluted to 47% styrene) maintained at 40 “C to that of 

Derakane 411-C-50 at 40 “C, one observes a higher VE fractional conversion in 

the case of 441-400 as compared to 411-C-50. As discussed previously, the VE 

monomers in 441400 are of lower molecular weight as compared to those in 411- 

C-50 and hence exhibit higher mobility. However, the final fractional conversion 

of the styrene monomer in both cases is roughly the same owing to the fact that 

the styrene monomers are much smaller entities and the network structure does 

not restrict their mobility in both the cases. As will be discussed in section 4, the 

T, value for 411-C-50 is much lower than that of 441-400, partly due to the higher 

fractional conversion of VE monomers. 

3.5 Autocatalytic Kinetics Model Parameters 

Autocatalytic kinetic models are widely used for fitting the experimental cure 

kinetic data for a number of VE and unsaturated polyester resins. For low 

temperature isothermal cure kinetics, the following relationship is widely used 

[30,31]: 

da/dt = (Ki + Krc~)(a,~ - a)T-m, 

where 01 is the fractional conversion at time t, amax is the maximum degree of 

conversion at that isothermal cure temperature, Kr and Kr are the reaction rate 

constants and m is the order of the reaction. This empirical reaction kinetic 

model is unsuitable for modeling the kinetic behavior as obtained from FTIR, 

which yields a rather than da/dt; so a modified form of the equation of the form 

is widely used: 

da/dt = (Kam)(a,, - a)2--m . 

This approximation is justified since Kl values as obtained from DSC data (Table 

2) are usually negligible as compared to the KZ values. This expression can be 

integrated to yield a: 

a = {am,Ftam&l - m)]l/(r-~)}/{l+[Kta,,(l - m)]M-m)} . 06) 

The autocatalytic parameters obtained from FTIR data for 411-C-50 [4] and 441- 

400 are presented in Tables 4 and 5. 

3.6 Section Summary 

The cure kinetics of Derakane 411-C-50 and Derakane 441400 were studied 

using FTIR. Derakane 44140 was used for the effect of styrene concentration 

studies as Derakane 411-C-50 already contains approximately 48 weight-percent 

36 

P 
Table 4. Kinetic parameters correspondiq to VE 411-C-50 FTIR data. 

1 Temperature 30 I 40 50 

P 

VE Monomer 

K 0.00079071 0.0018584 0.0012285 

m 0.63813 0.66051 0.55319 

Grax(%) 58.981 59.163 60.80s 

K 

m 

a-6) 

Styrene Monomer 

0.00055487 0.0010582 

0.69773 0.68739 

66.149 71.794 

0.0015359 

0.67882 

69.308 

Table 5. Autocatalytic parameters for FTIR data of VE 441XKl cured at 40 “C. 

I K (mill-11 I 0.147 I 0.087 I 0,055 I 0.031 I 

m. ) 0.653 1 0.660 1 0.688 1 0.656 I 

amaw 1 0.669 1 0.676 1 0.708 1 0.704 I 

styrene. This section discusses the effect of styrene concentration on the network 

development during cure. Styrene-concentration effect, therefore, manifests 

itself as difference in the T, development between different resin mixtures. The 

initial concentration of styrene also determines the degree of 

homopolymerisation during cure. 

The temperature effects result in accelerating the cure kinetics of the resin 

mixture at higher cure temperature. Also, the T, development with cure is 

different for different cure temperatures [ll] . Since the modehng approach relies 

on either the volumetric contribution of the microgels (percolation approach), or 

on T, development with cure (free-volume approach), the cure kinetics-related 

experiments provide valuable information towards the development and 

verification of the continuum model. 

37 
Generally, the rate of fractional conversion of the VE monomers is higher than 

that of the styrene monomers due to their higher reactivity. The final conversion 

of styrene was, however, always higher than that of the VE double bonds due to 

the fact that the diffusional limitations affect the mobility of VE monomers more 

than the styrene monomers based on the difference in the size and molecular 

weights of the monomers. As the temperature was increased, the final 

conversions of both the monomers increased owing to higher monomer mobility. 

In the section 4, DC conductivity is measured and correlated with the kinetic 

data generated herein. 

4. Cure Monitoring of VE Resin 

4.1 Introduction 

In this section, emphasis is placed on analyzing the cure signals obtained using 

SW and the dielectrometer. The signal is correlated to the FTIR data, viscometer 

data, and DMA data to establish the molecular events occurring during cure. A 

detailed description of the SW system and dielectric monitoring has been 

presented in section 1 and elsewhere [4]. 

Section 4.2 deals with the SW behavior. This section investigates the effect of 

styrene concentration in 441-400 and the effect of cure temperature on the SW 

behavior of 411-C-50. Section 4.3 deals with dielectric cure monitoring of 441-400 

diluted to different concentrations of styrene content. This section also deals with 

effect-of-cure temperature on the dielectric response of 411-C-50. Section 4.3 

compares and contrasts the dielectric behavior with SW behavior. Section 4.4 

summarizes the results from this section. 

4.2 SW Cure Data 

This section discusses the DC cure monitoring results and their correlation to 

cure-related events discussed under section 3. Section 4.2.1 discusses the effects 

of styrene concentration, while section 4.2.2 deals with temperature effects. 

4.2.1 Efrect of Styrene 

Figure 25 deals with the SW behavior exhibited by Derakane 441-400 diluted by 

(99% pure) styrene supplied by Aldrich Chemicals to a weight-percent of 28%, 

37%, 47%, and 57% of styrene. Figure 25 reveals that the effect of styrene 

addition on the initial voltage is twofold. Firstly, the initial voltage of the system 

increases upon increasing the styrene content from 28 weight-percent to 

38 
37 weight-percent. However, upon further addition of styrene, the initial voltage 

of the resin system starts to decrease. 

This seemingly contradictory behavior is explained by the fact that the styrene 

component of the resin system doesn’t supply any of the conducting ions 

responsible for the observed conductivity behavior as shown in Figure 26. 

Therefore, an addition of styrene to the system is equivalent to diluting the 

concentration of the conducting ions supplied by the VE component of the resin 

system. This explains why an addition of styrene to the system results in a lower 

initial voltage. However, this doesn’t explain the initial increase in the voltage 

from 28 weight-percent to 37 weight-percent styrene system. Figure 27 reveals 

that the viscosity of the resulting resin system after the styrene addition 

decreases with increasing styrene concentration, This reduction in viscosity can 

be interpreted as higher molecular mobility of the monomers and the conducting 

ions, resulting in higher initial voltages, consistent with the model of England [4] 

described in section 1. 

The overall initial conductivity is therefore the result of these two competing 

effects and in case of 28 weight-percent to 37 weight-percent styrene system, the 

increase in mobility dominates the dilution effect due to the additional styrene, 

resulting in higher initial conductivity. On further addition of styrene to the 

system, the dilution effect governs over higher molecular mobility resultig in 

the reduced initial voltage observed in the experiments. Increasing ion 

concentration through doping has been investigated by England [a] by 

introducing 0.1 weight-percent of TA. Preliminary investigations conducted as a 

part of this research work involved the use of tetrabutyl ammonium iodide (TT), 

a cheaper alternative to TA, as dopants. A comparison of the TI based results 

with England’s work has been presented under Appendix D. 

From Figure 25, it is observed that the gelation of resin mixtures containing 

different concentrations of styrene gets shifted further along the time axis with 

increasing slyrene content. The gelation in Figure 25 is given by the point of 

inflection in the SW profile as discussed in section 1.3 (Figure 5). The same trend 

is observed with SW cutoff. The viscosity data shown in Figure 28 confirms the 

fact that the gelation happens earlier in case of lower styrene systems. This is 

due to the fact that an increase in VE concentration results in an increased 

reaction rate as shown in the FTIR data (Figures 21 and 22) and shorter time to 

reach the gel point. 

In order to understand the difference in the SW cutoff point (i.e., the point at 

which the SW signal drops to zero), a plot between degree of conversion and the 

styrene concentration at the instant when the SW signal becomes zero was 

constructed and is shown in Figure 29. From the graph, it can be concluded that 

the degree of conversion of both the VE and styrene monomers decrease initially 

followed by an increase with increase in the styrene content. This can be 

39 
0.6 

60 60 

Time (Min) 

Fiwe 25. SW behavior of Derakane 441440 cured at 40 “C. 

60 

Styrene Concentration (weight-percent) 

Figure 26. Initial DC signal vs. styrene concentration in Derakane 441-400. 

explained: in the case of resin systems with 37 and 47 weight-percent of styrene, 

the cross-linking density is higher thereby cutting off the. mobility of the 

conducting ions at a much lower conversion value. In case of 57 weight-percent 

styrene system, the presence of excess styrene results m the formation of a much 

looser network with long linear chains of styrene between the cross-links, 

thereby facilitating an increased mobility of the conducting ions. 

40 
-25 35 45 55 65 

Styrene Concentration (Wt%) 

Figure 27. Initial viscosity vs. styrene concentration in Derakane 441-400. 

Time (Min) 

Figure 28. Viscosity development in Derakane 441400 cured at 40 “C. 

A confirmation of the previous hypothesis comes from analyzing the DMA data 

(TJ of the corresponding systems. T, is a measure of the cross-link density of the 

resulting network. It is clear from the Tg data of Derakane 441a presented in 

Figure 30, that indeed the cross-link density in the cases of 37 and 47 weightpercent styrene is higher than that of 28 and 57 weight-percent styrene, since T, 

is an estimation of the cross-link density of the resulting network. Hence, it can 

be concluded that the addition of styrene, even though it is electrically inert, 

plays a very significant role in determining the SW behavior by way of being an 

inherent part of the polymer network and directly affecting the cure kinetics. 

41 
0.3 , 

0. 

25 35 45 55 

Styrene Concentration (Wt%) 

65 

Figure 29. Fractional double-bond conversion vs. styrene concentration in Derakane 441- 

400 at DC signal cutoff. 

4.2.2 Effect of Temperature 

Figure 31 shows the effect of temperature on the SW signal for Derakane 411-C50. A common feature observed in all of these figures is that the initial SW 

voltage.mcreases with an increase in the temperature. This is due to the fact that 

the increase in temperature results in a decrease in the resin viscosity, which, as 

explained in section 4.2.1, results in an increased initial voltage. 

Figure 31 shows that the resin systems cured at higher temperatures reaches the 

gel point sooner than the system cured at a lower temperature. However, the 

SW cutoff point occurs at a much longer time period for higher temperature 

systems. Figure 32 shows the viscometer data, which confirms that the gelation 

occurs sooner for higher temperature systems. A close inspection of Figures 23 

and 24 shows that the reaction rates in the case of the higher temperature 

systems were indeed higher thereby resulting in gelation, much quicker than the 

system cured at lower temperature. 

Table 6 shows the T, data obtained by using DMA for all three cure 

temperatures. From Table 6, it becomes apparent that the cross-link density 

increases with the cure temperature that exerts a negative effect on the molecular 

mobility. However, the additional thermal energy imparted to the molecular 

mobility at higher temperatures, enables the ionic species to negotiate through 

the network for a longer time resulting in the SW signal being observed for 

longer times in high-temperature systems. So the dominating factor that 

determines the SW cutoff is the thermal energy, which results in increased 

mobility and decreased local viscosity. 

42 
- 

56. 

54. 

c? 0 

-a 

I52. 

50 * 

25 35 45 55 65 

Styrene Concentration (wt%) 

Figure 30. Glass transition temperature vs. styrene concer&ation for Der&ane 441-400 

resin. 

-0.15- 

0 20 40 60 80 100 

Time (Min) 

Figure 31. SW sifflal vs. time for Derakane 411-C-50 at different isothermal cure 

temperatures. 

4.3 Dielectric Cure Monitdng 

This research makes use of dielectric cure sensing in order to benchmark the 

performance of DC sensing for cure monitoring purposes, This section discusses 

the advantages and disadvantages of each system, delineating ways in which one 

technique can complement the other to obtain a better insight into cure related 

processes. 

43 
20 25 

Time (Min) 

Figure 32. Viscosity development in Derakane 411-C-50 at different isothermal cure 

temperatures. 

Table 6. DMA results for Derakane 411-C-50. 

Cure Temperature 

(“Cl 

30 

50 

4.3.1 Effect of Styrene 

Figure 33 illustrates the effect of styrene concentration on the dielectric cure 

behavior of Derakane 441-400 at an isothermal cure temperature of 40 “C. As a 

general observation, the time period at which the loss factor and the ion viscosity 

levels off gets shifted further along the time axis with increased styrene 

concentration. This observed behavior qualitatively follows similar observations 

in the case of DC behavior. However, a quantitative comparison of the time scale 

at which the log-loss factor levels off to that at which SW signal ceases indicates 

that the SW signal ceases much earlier than the former. This is due to the fact 

that the DC signal is a measure of long-range motion of ions towards one of the 

electrodes. However, dielectric behavior is a measure of the possibility of shortrange molecular motion (i.e., dipolar rotation). Therefore, during cure, 

F 

44 
ve44140028st 

Figure 33. Effect of styrene on Derakane 441-400 cured at 40 “C using dielectric cure 

monitoring at (a) 28 weight-percent styrene, and (b) 47 weight-percent 

styrene concentration. 

the formation of a 3-D network impedes and, possibly prevents, long-range 

transport of ions. However, dipolar rotation continues for a longer time scale. A 

comparison between the dielectric signal with the fractional conversion of 

monomers obtained from FTIR reveals that the dielectric signal levels off much 

earlier than the FTIR signal. This is due to the fact that long after dipolar rotation 

ceases to be possible, reactions between the contiguous monomers continue to 

occur. 

Therefore, one can compartmentalize molecular mobility into three regions. The 

first region is characterized by the possibility of long-range motion. The second 

region extends until short-range dipolar rotations cease. The third region is 

characterized by the possibility of further reaction between contiguous 

monomers leading to an increase in fractional double-bond conversion. 

SW is an effective ox-&& monitoring tool owing to its sensitivity to long-rang& 

molecular motion. As discussed in section 1.3, the SW signal dies soon after 

45 
vitrification for the reasons previously discussed. This is a significant feature of 

SW for cure monitoring of processes, since the onset of vitrification is an 

important processing parameter related to part removal and cycle times. 

4.3.2 Effect of Temperature 

Figure 34 presents the dielectric response of Derakane 411-C-50 cured at different 

isothermal cure temperatures. The qualitative responses follow similar behavior 

as observed in the case of a DC signal with loss factor and ionic viscosity leveling 

off earlier for low-temperature cures. The quantitative comparison follows the 

argument discussed in section 4.3.1. 

Figure 35 presents the ionic conductivity obtained from dielectric measurements 

for the case study at 30 “C. It is seen that the drop in ionic conductivity very 

much follows time-scale trends previously discussed. However, the time at 

which ionic conduction ceases differs widely from that of the SW signal. A 

clearer comparison between the sensitivity of SW and the dielectrometer to 

molecular level events can be obtained from Figure 36 that shows the 

conductivity observed by SW alongside that derived from dielectric 

measurement at 2.5 Hz for Derakane 411-C-50 cured at an isothermal 

temperature of 30 “C. It is seen that SW data undergoes much larger changes in 

conductivity corresponding to gelation and vitrification as compared to the 

dielectrometer measured ionic conductivity, which remains roughly a straightincline line. This comparison illustrates one of the advantages of DC signal over 

AC measurements, where greater sensitivity to cure behavior is demonstrated 

early in the cure. The greater sensitivity of SW makes it ideal for integration into 

control systems. 

Tables 7 and 8 compare the maximum degree of conversions respective to when 

the DC and AC signals cease to yield further information. From Tables 7 and 8, 

it can be seen that the AC technique remains sensitive to the degree of conversion 

for a larger range of a, whereas the DC signal ceases early in the cure. It can be 

inferred that the dielectric related ionic conductivity gives information on the 

degree of conversion for a longer range of a as compared to DC-based ionic 

conductivity. So dielectric cure monitoring holds promise as an effective point 

sensor for cure monitoring in the later stages of cure. 

4.4 Section Summary 

A study of the effect of styrene concentration on the SW behavior of 441-400 

revealed that the slower rate of reaction with increased styrene content gets 

manifested as delayed gelation (inflection in the SW data) and delayed SW 

cutoff. Comparison of viscosity data confirms that the gelation time scales are 

consistent with the DC inflection point. Glass-transition temperature, T, data 

46 
ve4ilc5Otemp30 

(4 

Figure 34. Dielectric cure monitotig of Derakane 411-C-50 at isothermal temperatures of 

(a) 30”, (b) 40”, and (c) 50 “C. 

47 
Time (hr) 

Figure 35. Ionic conductivity from dielectric measurements on Derakane 411-C-50 at 

30°C is0tlwrmaI cure temperature. 

Time (Min) 

Figwe 36. Comparison of SW behavior of ionic conductivity with dielectic behavior of 

Derakane 411-C-50 at 30 “C cure temperature. 

for different styrene concentrations revealed differences in the cross-linking 

density between the resin compositions conforming to the observed differences 

in the SW cutoff point. This illustrates the fact that styrene, despite being 

electrically inert, significantly affects the SW behavior by being an inherent part 

of the network formation. 

48 
Table 7. Maximum conversion of 411-C-50 from DC and AC cure monitoring. 

umaw 

Cure DC 

Temperature Monitoring 

m 

30 0.129 

40 0.275 

%Imx 

AC 

Monitoring 

0.637 

0.63 

Table 8. Maximum conversion of 441400 from DC and AC cure monitoring. 

amax amax 

Styrene DC AC 

Concentration Monitoring Monitoring 

(weight-percent) 

28 0.152 0.524 

47 0.069 0.610 

. . 

* 

P 

Temperature effects on 411-C-50 reveals faster reaction rates leading to faster 

gelation times with increased cure temperature as confirmed by the viscometer 

data. However the SW cutoff happens at a later time for higher temperatures. A 

comparison of the T, revealed an increase in the cross-linking density with cure 

temperature. Hence one can conclude that the differences in the SW cutoff is due 

to the increased mobility induced by higher thermal energy, which overcomes 

the negative effect of cross-lkking on the molecular mobility. 

Dielectric behavior of both N-400 and 411-C-50 followed the SW behavior 

qualitatively. However, owing to differences in the parameter being measured, 

quantitative differences were observed. SW, due to its better sensitiviq to cure 

events like gelation and vitrification, is an effective tool for cure monitoring in 

the early stages of the cure. However, the dielectric signal far outlasts the DC 

signal, enabling its use for cure monitoring in the later stages of cure. A 

combination of SW, dielectric and FUR techniques could be used to follow the 

different scale of possible motions with the proceeding of cure. 

The experimental results discussed in this section, along with cure kinetics 

measurements provided in section 3 are used as the basis for developing a freevolume continuum model as shown schematically in Figure 7. In section 5, the 

role of microgels is investigated to understand their influence on the ionic 

conductivity. Cure kinetic data along with cure monitoring results are used to 

investigate the feasibility of a percolation-based continuum model. 

49 
5. Characterization of Microgels 

5.1 Introduction 

This section investigates the influence of microgels on the ionic conductivity of 

VE resins. Microgels are highly cyclized and cross-linked spherical entities, 

whose number increases with cure. As discussed in section 1.5, the increase in 

the number of microgels forces the conducting ions to travel increasingly 

tortuous paths around the microgels to reach the electrodes. This results in a 

decrease in the observed ionic conductivity with cure. The percolation-based 

continuum model investigated in this section takes into account the increasing 

volumetric contribution of the microgels with cure, as illustrated in Figure 7. 

The Flory-Stockmayer theory [13] has been in use for over 50 years to predict and 

understand the gelation mechanisms. Using combinatorial arguments, Batch and 

Macosko [24] were successful in predicting both the gel point and the weightaverage molecular weight of the branched aggregates at gel point. Flory coined 

the term “infinite network” to describe the resulting network formation at gel 

point. The network reaches a macroscopic dimension by occupying the entire 

volume of the reacting sample itself. Since, on the molecular level, the network is 

unbounded, it is referred to as an infinite network. 

Experiences with styrene-unsaturated polyester resins and vinyl-divinyl systems, 

however, seems contradictory to the previously mentioned gel point predictions 

[32,26,271. The measured gel point conversion for these systems was far greater 

than Flory-Stockmayer predictions. Dusek and Spevacek [26] and Dusek et al. 

[271 have shown that predominant cyclization is observed in the beginning 

stages of the reaction involving free radical polymerization systems. Dusek and 

colleagues described such cyclized structures with high cyclization and crosslinking density as “microgels.” Owing to heavy cyclization, the reactive end 

groups of the polymer chains are physically tucked away, disabling further 

participation of these end groups in the reaction process. The molecular 

shielding plays an important role in the free-radical polymerization reaction and 

is a possible cause for the final conversion of the reacting monomers to fall short 

of 100%. Dusek and colleagues found that the deviation from the FloryStockmayer theory increased with the increase in the concentration of 

multifunctional monomers. They showed that in a copolymerization reaction 

involving monovinyl and divinyl components, the deviation from the FloryStockmayer predictions increased with the increase in concentration of the 

divinyl component. Three factors are held responsible for the previously 

mentioned deviation: (1) cyclization, (2) reduced reactivity of the pendant vinyl 

reactive groups, and (3) rnicrogel formation. In the case of heavily cyclized 

50 

l 
structures, these three causes occur simultaneously in that cyclization leads to 

the formation of microgels which are then responsible for molecular shielding of 

the pendant double bonds leading to an apparent reduction in the reactivity of 

the pendant vinyl groups. 

5.2 Background 

At the beginning of a copolymerization reaction involving styrene and 

unsaturated polyester resins, the system contains styrene monomers, 

unsaturated polyester molecules, and inhibitors. When the reaction starts, the 

initiators decompose and form fr& radicals to trigger polymerization. At the 

very beginning of the reaction, most of the free radicals formed from the 

initiators are immediately consumed by the inhibitors. Very little polymerization 

occurs due to the inhibition effect at this stage, which is called the induction 

stage. 

After this stage, the initiators continuously decompose creating free radicals 

which link adjacent unsaturated polyesters and form primary polymer chains 

through connecting styrene monomers by both inter- and i&a-molecular 

reactions. These long chain molecules tend to form spherical structures due to 

the intra-molecular cross-linking among the pendant C=C double bonds of the 

polyester molecule leading to the formation of the microgels. Because of the high 

cross-link within the microgel, the free radicals on the polymer ends are likely to 

be buried in the microgels. This means that termination among the polymer 

radicals may not be an important factor and can be neglected. 

As the polymerization proceeds, the concentration of the microgels increases 

continuously. This leads to macrogelation in the system. This mechanism is 

illustrated by several key steps in Figure 37. Since gel conversion is very low for 

radical chain-growth polymerization reactions, it is difficult to relate gelation to 

the resin conversion or molecular weight. For the case of chain copolymerization 

involving Derakane 411-C-50 and styrene monomers, the conversion predicted 

by the Flory-Stockmayer theory [13] has been calculated by Dua [lo] to be 0.2 

volume-percent. However, the volume conversions at gelation, based on 

viscosity measurements, normally fall in the range of 10 volume-percent. This 

large discrepancy in the conversion values suggests the occurrence of similar 

cyclization phenomenon. Also, an observation of the T,-a, relationship of curing 

VE 411-C-50 obtained by Stone [ll] suggests that during cure, for a large range of 

a, the T, remains nearly the same. This is contrary to epoxy systems where the 

T, increases linearly with cure a, since microgel formation does not appreciably 

increase the T, of the curing system. 

51 
P 

Figure 37. Illustration of cross-linking polymerization (a) at beginning, (b) initiation, (c) 

reaction in progress, and (d) possible gelation schemes. 

The abnormal behavior of 411-C-50, therefore, indicates a minimal increase in the 

cross-linking density and an increase in the volume fraction of microgels. This 

study attempts to characterize these microgels for possible influence on ionic 

conductivity. 

5.3 Results 

Section 5.3.1 investigates the role of microgels on the ionic conductivity. A 

comparison of the growth of microgels with a decrease in the DC signal indicates 

a coupling between the two events. Section 5.3.2 presents the prelirrUnary results 

on the chemical characterization of microgels. A thorough understanding of the 

chemical composition of microgels would enable identification of the chemical 

composition of the unreacted resin and the network development surrounding 

the microgels. Section 5.3.3 deals with the AFM analysis of microgels to obtain 

an insight into the size and number density of the microgels. The microgel size is 

used as input for the percolation-based model presented in section 5.4. 

5.3.1 Comparison of Microgel Growth Kinetics with SW Data 

Figures 38 and 39 show the change in size of microgels as observed using 

dynamic light scattering (DLS) experiment [lo] as compared to the simultaneous 

change in the DC signal observed by the SW setup. A detailed discussion on 

52 

s I 
Time (Min) 

60 

mrns (Min) 

@I 

Figure 38. Influence of miaogels on SW behavior of 411-C-50 for (a) 30” and (b) 40 T, 

respectively. 

DLS and sample preparation are found elsewhere [22]. An interesting 

observation is that these microgels rapidly increase in size at the same time when 

one observes a drastic drop in the SW voltage. This time range coincides with 

the occurrence of macrogelation as observed from the viscometer data (Figures 

28 and 32). This essentially indicates the importance of microgel in the 

development of macroviscosity and hence SW signal. As discussed in section 1, 

ionic conductivity is significant beyond gelation. The role of microgels on ionic 

conductivity is investigated in section 6. 

53 
0.6 

Time (Min) 

Time (Min) 

Figure 39. DLS data showing influence of microgels on SW response of 441-400 at (a) 

28% and (b) 57% styrene. 

5.3.2 Separation of Microgels 

Figures 40-42 show the HPLC responses for pure styrene, pure VE and 

fractionated sample of microgels, respectively. The VE peak and styrene peak 

occur around 875 s and 1,100 s, respectively, along the time axis. After multiple 

cycles of dissolving followed by precipitation of microgels in order to remove the 

unreacted monomers, the fractionated high molecular weight microgel and the 

effective removal of the VE and styrene monomers can be observed in Figure 42. 

54 
0.8~10~ 

z 

E3 

'5 

s 

a 

I 

o.4x105 

300 600 900 1200 

Time (Set) 

Figure 40. HPLC response (in pV) of pure styrene. 

Time (Set) 

Figure 41. HPLC response (in pV) of pure unreacted VEX25 with 28 weight-percent 

s tyrene. 

Figure 43 shows the FTIR spectra of curing VE825 (331 at an isothermal 

temperature of 40 “C. When it is compared with Figure 44 showing the FTIR 

spectra of the fractionated microgel, one observes an anomalous decrease in the 

peak height at 700 cm-l as compared to the one at 910 cm-l, which remains a topic 

for future work. The peak at 910 cm-1 appears slightly shifted and is observed to 

occur at 900 cm-l. A comparison of the reference peaks of VE at 

830 cm-1 and styrene at 700 cm- 1 indicates a predominance of VE in the 

fractionated microgel as compared to the reacting mixture, This confirms the 

55 
4orJoo 

72 

.ar v) 

2l 

% 

20000 

0 300 600 

Time (Set) 

900 1200 

Figure 42. HPLC response (in pV) of fractionated microgels. 

1.0 

A 

b 

S 

0.5 

800 600‘ 

Wavenumbers (cm-l ) 

Figure 43. FTIR spectra of VEX25 (a) at the beginning of cure and (b) at 9 min at 40 “C 

cure temperature. 

hypothesis that microgels are highly cyclized and densely cross-linked 

structures, since only VE monomers can act as cross-linkages. The separation of 

the microgels and the FTIR spectra of these fractionated microgels were not a 

reliably repeatable phenomenon. Of the multiple successful attempts at microgel 

separation, the FTIR spectra qualitatively agrees with the above mentioned 

sample results. However, quantitatively, they showed a high degree of 

56 
. 

A 

b 

s 

Wavenumbers (cm-l) 

Figure 44. FTIR spectra of Fractionated microgels formed in the first 9 min of isothermal 

cure of VE825 at 40 “C. 

variation. One can conclude from these results that the microgels do not 

contribute directly to ionic conduction but represents dead zones that increase 

tortuosity for ionic transport. 

5.3.3 AFM Analysis of Microgels 

To investigate the potential contribution of the microgels to tortuosity, 

information on microgel size is essential. This is achieved using AFM. Figures 

45 and 46 show AFM pictures of microgels as observed on the fractured surfaces 

of cured Derakane 411-C-50 (isothermal cure temperatures of 40” and 50 “C, 

respectively). A comparison of the AFM pictures suggest an increase in the 

number density and size of the microgels with cure temperature. Effort needs to 

be directed towards the observation of such a trend. It should be borne in mind 

that similar to the case mentioned in section 5.3.2, from Figures 45 and 46, it is 

seen that the average size of microgels vary between 150 nm (at 40 “C) and 

200 nm (at 50 “C) in diameter. Similar AFM pictures of microgels corresponding 

to a cure temperature of 70 “C have been obtained by BriII and Pahnese [21]. 

These AFM pictures show microgels of roughly 150 nm in diameter. The 

microgel size as observed by DLS show an exponential increase from 20 run to 

90 nm at gelation. This most likely indicates that the microgels grow rapidly to 

their equilibrium size of around 150 nm. This postulation is in keeping with the 

nature of free-radical chain-growth copolymerization [20]. 

5.4 Percolation Model 

Based on the ‘experimental work previously described, it can be surmised that 

microgels, due to their nonconductive nature, are considered as dead zones and 

conduction through microgels need not be modeled explicitly. The formation of 

57 

59 

This section investigates the effectiveness of such an assumption in describing 

the ionic conductivity and the viscosity development during cure. A review of 

the percolation theory is presented in Appendix E. 

5.4.1 Modeling Approach 

Traditionally, the conductivity behavior using the percolation theory has been 

modeled based on assuming a network of resistances [344OJ. In one 

experimental work, Last and Thouless [41] peppered a conducting sheet of 

colloidal graphite paper of a finite resistance with holes (the resistance of holes is 

infinity, analogous to our microgels), according to coordinates obtained using a 

random number generator. A graphical illustration of the observed conductivity 

behavior as a fraction of the concentration of holes is shown in Figure 47. It is 

seen that the observed conductivity tapers off to zero when the fractional 

concentration of holes reaches 0.4. This experiment was modeled by Yuge and 

Onizuka [40] using a two-dimensional (2-D) resistor network consisting of two 

kinds of special unit resistor with different conductances, Kl and K2. The 

resistors are placed at random as shown in Figure 48. Yuge and Onizuka [40] 

designed and studied such a 200 x 200 site random-resistor network. A 

simulation of Last and Thouless’ experiment [41] by making Kl as unity (as in 

graphite) and K2 as zero (as in holes) yielded the critical fraction of Kl to be 

0.591, and K.2 to be 0.409. The value of 0.409 obtained compared to a critical 

fraction of 0.4 obtained by Last and Thouless illustrates the success of resistor 

network simulations in describing conductivity through continuous medium. 

The success of resistor network simulations, has since been applied to 3-D 

systems [34-363. Figure 49 shows a 3-D network simulation by Kirkpatrick [35]. 

For K2 of very low conductivity, a critical volume fraction of conducting material 

near 0.3 was obtained. Figure 50 illustrates how the microgel formation during 

cure can be related to a 3-D resistor network similar to the work of Last and 

Thouless. At time t=O, the resin system is unreacted and therefore equivalent to 

a resistor network of only say Kl with a conductivity value of unity. At time Ml 

into the cure, the reacting system is a mixture of reacted microgels and unreacted 

resin surrounding the microgels (similar to holes in graphite sheet in 2-D). These 

microgels are added at random to the reacting system. At this stage, the resin 

system can be simulated using a 3-D resistor network containing, Kl and K2 at 

random, with increasing fraction of K2 (corresponding to microgels) in the 

network. Since microgels are assumed to be of negligible conductivity, the 

resistor K2 is assigned negligible conductivity. With time, the volumetric 

contribution of the microgels in the reacting system increases which is simulated 

by progressively increasing the fraction of K2 at random in the resistor network. 

At a critical volume fraction, the conductivity of the reacting resin system reaches 

zero (SW cutoff). This theoretical critical volume fraction is given by Figure 49 to 

be 0.31 of Kl (corresponding to the volume fraction of unreacted resin) or 0.69 of 

K2 (corresponding to the volume fraction of reacted microgels). 
Figure 47. 2-D percolation behavior of a continuous conducting medium [41]. 

unit resistor with KY 

vlit resistor with K2 

Figure 48. 2-D percolation behavior modeling using resistor network [40]. 

Figure 49. 3-D percolation modeling using non-zero resistor values [35]. 

60 
+ Unreacted resin, Kl 

+ 

Microgel, K2 

Figure 50. Development of resistor network model for curing VE resin at (a) time t=O, (b) 

time t=tl, and (c) time t=SW cutoff. The left side illustrates different stages of 

cure and the right side illustrates equivalent resistor network. 

5.4.2 Percolation-Based Continuum Model 

5.4.2.1 Conductivity Model 

The volume fraction of microgels were calculated using the degree of conversion 

results from FTIR. Calculations and assumptions regarding the volume fraction 

estimation are given in Appendix B. Figures 51 and 52 show the corresponding 

results for 411-C-50 and 441-400, respectively. 

Figures 51 and 52 indicate that even for widely varying composition and cure 

conditions, the volume fraction corresponding to the abrupt decrease in the SW 

signal falls within the same range of the microgel volume fraction (20%). This 

significant grouping of the signal suggests that the development of phenomena 

that are responsible for controlling the DC signal all develop the same way in 

systems under consideration and are determined predominantly by the volume 

fraction of microgels as suggested by the percolation theory. Another similarity 

between the SW response and the percolation model is the tail formation at the 

end of the response signal, as opposed to an abrupt drop to zero. This 

phenomenon is explained by Last and Thouless [41], based on the fact that with 

decreasing volume fraction of the conducting material, the ions will have to 

travel more and more tortuous paths, ultimately making the path length 

61 
A 50 c 

L-’ 0 4oc 

0 30 c 

-0.5 ’ 

0 0.2 0.4 0.6 0.6 

Microgel Volume Fraction 

Figure 51. Normalized DC signal vs. microgel volume fraction of Derakane 411-D-50 at 

different isothermal cure temperatures. 

1.6 

1.2 

& B a 

> 

-c 

w 0.8 

= 

E 

z 

0.4 

0 

0 0.05 0.10 0.15 0.20 0.25 

Microgel Volume Fraction 

Figure 52. Normalized DC signal vs. microgel volume fraction of Derakane 441-400 at 

different styrene concentrations. 

prohibitively long. This is seen as the drop in ionic conductivity with increase in 

microgel concentrationA comparison between Figures 51 and 52 with 53 indicates a quantitative 

discrepancy even though qualitatively the response signals are similar. The SW 

conductivity drops to zero near a volume fraction of 0.20 of microgels in the case 

of 411-C-50 and at around 0.10 for 441-400. This is very different from an 

62 
expected value of 0.69 from the 3-D resistor simulation presented in Figure 49. 

This discrepancy between the actual behavior and the percolation model implies 

that the assumption of curing resin systems to be composed only of randomly 

distributed microgels surrounded by unreacted resin is an incomplete 

description of reality. The formation of cross-links outside the microgels, though 

negligible in volume fraction due to their highly distributed nature, introduces 

higher tortuosities in the ionic path length. As explained by Last and Thouless 

[41], the cessation of ionic conductivity happens due to the fact that the path 

length that an ion has to traverse to reach the corresponding electrode reaches 

prohibitively large values. The presence of these infinite networks in VE induces 

a similar effect on the ionic path length resulting in the cessation of conductivity 

long before the expected volume fraction of 0.69. 

Another complication one faces in modeling the resin behavior is the exothermic 

nature of the cure itself. The exotherm influences the ionic mobility and local 

viscosity, thereby making the identification of the isothermal cure effects a 

difficult exercise. The region of volume percent over which one observes the 

conductivity, increases with temperature even though the initial drastic 

reduction in the conductivity occurs around the same volume percent for all 

three temperatures. This observation, as explatied in previous discussions, is 

due to the higher mobility induced by way of increased cure temperatures. 

5.4.2.2 Viscosity Model 

In keeping with the above assumption of a curing VE system to be composed of 

only microgels (reacted component) and sea of VE resin (unreacted component), 

an attempt was made to explain the development of macroscopic viscosity with 

cure. It was originally intended to relate the three relevant material properties 

like viscosity, ionic conductivity and degree of cure to one another using the 

volumetric contribution of the microgels as illustrated in Figure 7. Section 5.4.2.1 

highlighted the discrepancy between the model assumption and reality. 

However, it is desirable to investigate the efficiency of such a model in 

describing the viscosity development. 

Literature presents a number of models to describe the development of viscosity 

for a wide range of volume fractions [42,43]. A modified Einstein equation was 

used in this study: 

or=1 -KC, (17) 

where K is a constant in the range of 2.35 and 2.60, and C is the volume 

concentration of spherical particles (microgels). The apparent relative fluidity, &, 

is given by: 

63 
where the subscript f represents the pure suspending fluid (unreacted resin) and 

the subscript s represents the suspension (suspension of microgels in unreacted 

resin). 

Oliver and Ward [4-4] have shown that at concentrations below 30%, a large 

range of particulate suspensions are well represented by this correlation. Since 

our systems rarely exhibit a volume percentage higher than 30%, the 

aforementioned relation would be a sufficient description. Figure 53 shows the 

development of fluidity with cure as estimated by the model alongside actual 

viscometer data. As explained ti section 5.4.2.1, the discrepancy between the 

model and experimental data is due to the assumption that cure reaction results 

only in microgel formation. In reality, however, curing leads to both microgel 

and infinite network formation. It is the presence of this infinite network that 

forces the macroscopic viscosity to asymptotically increase to infinity much 

earlier than dictated by the modified Einstein’s relationship. Results are 

consistent with percolation. Both these results imply that the network formation 

outside microgels play a important role in determining ionic conductivity of the 

reacting resin system. 

Experimental Vs Thaoretical Fluidity 

Figure 53. Experimental vs. theoretical fluidity of Derakane 411-C-50 at isothermal cure 

temperature of 30 “C. 

5.5 summary 

Based on DLS data [lo], FTIR analysis and AFM imaging a valuable insight into 

the growth kinetics, chemical makeup and equilibrium size estimation were 

made possible. A comparison of the DLS data with SW behavior revealed that 

an increase in the volumetric contribution of microgels forces the conductjng 

ions to travel increasingly tortuous paths. This results in the observed decrease 

in DC signal with cure. A possible extension of the influence of microgels to 

modeling the ionic conductivity behavior requires a thorough understanding of 

64 
the role of microgels in the formation of network structure. This is, however, an 

issue of contention. From percolation theory, Dua [lo] argued that linking of 

microgels alone to form gelation would require a higher volume fraction of 

conversion of nearly 20% and above whereas the actual conversion falls in the 

range of 10%. An infinite network formation based on the Flory-Stockmayer 

model [13] suggests too low a fractional conversion at gel point. Therefore a 

hybrid model including both of the previously mentioned phenomena is 

proposed by Dua [lo]. Dua argues that the final gelation scheme could be a 

combination of network structures as illustrated in Figure 37, whereby the 

microgels have a reasonable statistical chance of being incorporated into the 

overall network, if they possess at least 18 surface-reactive double bonds. 

Section 5.4 explored the possibtity of modeling ionic conductivity and viscosity 

development during cure based solely on the influence of microgels. A large 

discrepancy between the model prediction and the experimental data implied the 

significant role of network formation on the ionic conductivity behavior and 

viscosity development. Section 6 presents a free volume-based continuum model 

which takes into account the role of network formation during cure. The free 

volume model utilizes the development of T, with cure to describe the resulting 

network structure. Since rnicrogel formation does not result in an appreciable 

increase in the T, the Tg-rz profile of the curing resin system is a representation of 

the influence of both the infinite network and the microgels. 

6. Mathematical Model of the Ionic Conductivity Behavior 

6.1 Introduction 

A brief outline of different efforts directed towards modeling ionic conductivity 

to yield predictive capabilities with respect to the processing parameters such as 

viscosity and degree of cure can be found in section 1.4. Schwab et al. [9] 

modeled the observed resistance of the resin as a function of the macroviscosity 

to yield the relation: 

F+(t) = 6nqL/AZi(CiQ?/ri) , (18) 

where &(t) is the resistance of the resin at time t; L and A are the conduction path 

length and the area of the effective electric field, respectively; and IJ, G, QL and Ri 

are the viscosity, concentration of ions, charge of ions and radius of ions, 

respectively. 

65 
This relation is derived based on balance between the electromotive force and the 

viscous drag force as dictated by the Stoke’s-Einstein relationship. A detailed 

derivation can be found elsewhere [4] with an analysis of diffusion relation for 

pregel and postgel stages presented in Appendix F. 

Equation 18 enjoys success in modeling the macroscopic viscosity until gelation. 

However, the construction of the model around the macroscopic viscosity limits 

its use beyond gelation. As evident from the SW signal response, one still 

observes DC conductivity beyond gelation and it is desirable to model this 

phenomenon making use of a “continuum” model, with predictive capabilities 

through gelation to vitrification- Equation 18 also yields no information 

regarding the development of the degree of cure even though DC conductivity, 

viscosity and degree of conversion are related to each other. This work attempts 

to fill this gap. The biggest drawback of equation 18 as used for modeling the VE 

behavior is the implied relation of the resistivity being directly proportional to 

viscosity. This relation holds good only in systems exhibiting time correlation 

between viscosity minimum and ionic conductivity maximum [45]. However, in 

some systems such as Epon 828, Epon 834, VE 411-C-50, etc., there is an offset 

between the time when the viscosity reaches minirnum and when the ionic 

conductivity reaches a maximum as evident from comparison of SW data with 

the viscosity data. Usually, the minimum in viscosity precedes the rrraximum in 

ionic conductivity. This unusual behavior of 411-C-50 renders itself unsuitable 

for modeling using the previous approach. Section 6.2 details a free volumebased approach that successfully models ionic conductivity and viscosity 

development during cure. 

6.2 Free Volume Model 

This section details the adaptation of classical free volume theory for describing 

ionic conductivity and viscosity development during cure. Sections 6.2.1 and 

6.22 present the relevant background and theory regarding the free volume 

theory. Section 62.3 deals with the conductivity modeling of VE 411-C-50; 

section 6.2.4 deals with viscosity modeling. 

6.2.1 Background 

In polymer systems, viscosity and ion conductivity are macroscopic properties 

that characterize chain segment mobility and ion mobility, respectively. While 

viscosity is a measure of the response of polymer chain segments to an applied 

stress field, ionic conductivity is the response of ions subjected to an electric field. 

Although an inverse relationship has been shown to exist between viscosity and 

ionic conductivity prior to gelation these have not been extended beyond 

gelation to model the ionic conductivity. 

66 
. 

A fundamental understanding of the relationship between rheological, structural 

and DC conductivity properties throughout the entire polymerization of a 

thermoset would be extremely valuable for online cure monitoring and control. 

In general, it is difficult to characterize in-situ rheological and structural 

properties during cure. However with the development of SW, one can observe 

the changes in the ionic conductivity of the resin system in real time both in the 

pregel and postgel regions. This suggests that it would be beneficial if 

rheological or structural information including the degree of cure information 

could be interpreted from these DC signals. 

Free volume models have been widely used for characterizing and correlating 

the viscosity and the ionic conductivity for pregelled systems [46,471. The basic 

principle behind these models is that sufficient free volume must be available for 

the diffusion of a molecular unit through a polymer matrix. This polymer unit 

may be a solvent, an ion, or a small chain segment of the polymer itself. The 

current study attempts to develop a continuum model specific for the VE resins 

system under consideration to describe viscosity and degree of cure using DC 

signal for both pregel and postgel regions of the thermoset polymerization. 

6.2.2 Theory 

Free volume theory proposes that the controlling mechanism for molecular 

transport in polymeric systems (for T<Tg + 100 “C) is the availability of sufficient 

free volume for the mobility of the given molecular species [46]. When there is a 

relatively large amount of free volume, the chains may move unhindered. 

However, as the cure proceeds, the free volume decreases and the chain becomes 

crowded by the neighbors, leaving very little room for the chains to move 

without colliding with its neighboring chains. This limits the abihty of the 

-polymer to rapidly respond to a perturbation by moving to a new equilibrium 

state. 

A commonly used definition of the free volume is the volume due to thermal 

expansion, Vf = V - VO where Vf is the free volume, V is the total volume and VO 

is the volume at 0 K. Another commonly used definition comes from the 

argument that the volume of the polymer is the sum of the volume occupied by 

the chains of the polymer itself and the volume between the polymer chains, i.e., 

the interstitial volume. 

The fractional free volume f defined as Vf/V is given by the expression 

f=f,+uf(T-T,), (19) 

where fp is the fractional free volume at the glass transition temperature, (xf is the 

thermal expansion coefficient of free volume, and T, is the glass transition 

temperature, defined as the temperature at which the material changes from the 

glassy state to a rubbery state. 

67 
The first free volume theory application to polymer near the glass transition 

temperature is attributed to Flory [13] while studying the viscosity and specific 

volume of polystyrene over a range of temperatures. He noted that the 

traditional Arrhenius theory wasn’t sufficient to explain the viscosity behavior 

thereby leading to the conclusion that the temperature dependence of the 

viscosity was governed largely by the available free volume in contrast to the 

activation energy approach. 

The most widely used free volume relationship was proposed by Williams, 

Landel, and Ferry (WLF) as an empirical equation to describe the relaxation time 

during dielectric studies at a given temperature relative to the glass transition 

temperature and is given as [48]: 

Log aT = Lo&T/TTg) = G(T - T&/G + (T - TJ) , cm 

where aT is the shift factor, TT is the relaxation time at the isothermal cure 

temperature T K, TTg iS the relaxation time at the glass transition temperature, 

and Cl and CZ are empirically determined parameters. 

The WLF relationship has been widely used for modeling the temperature 

dependent viscosity behavior of various polymers and polymer blends near the 

Tg [49, 501. The WLF relationship also enjoys success in the modeling of 

dielectric responses and ionic conductivity of various epoxy amine systems [46, 

471. 

Although the WLF equation was proposed as an empirical expression, theoretical 

support for equation 20 has been derived by Cohen and Turnbull [51], Bueche 

[52] and Adam and Gibbs [53]. These approaches were based on molecular 

events, statistical mechanical and molecular kinetic theories, yielding 

relationships equivalent to the WLF model. Senturia and Sheppard [54] has 

proposed with theoretical support, an extension to the WLF relationship: 

Log aT = Log(TT/zTg) = CI(T - TJ/((C2 + C3TJ + (T - T,)). (21) 

The shift factor & is the ratio of the material property Iike conductivity, viscosity 

or dielectric relaxation time at cure temperature to that at the glass-transition 

temperature. All temperature values are in K. In this work, the shift factor is 

taken to be the ratio of conductivities (for conductivity modeling) or viscosities 

(for viscosity modeling). 

6.2.3 Conductivity Model 

The use of WLF relationship to model the polymer behavior comprises of three 

’ steps that are three modeling efforts in themselves. First, one must develop a 

cure kinetic relationship relating degree of cure with time and the isothermal 

cure temperature. For 411-C-50 system, the relationship between the degree of 

conversion as estimated by FTIR is different from as estimated using DSC 

(equations 13 and 16). In this section, only the degree of conversion obtained 

68 
from FTIR is used for modeling, Modeling details based on a DSC-estimated 

degree of cure are presented in Appendix G. Equation 22 describes the degreeof-cure relationships for FTIR. The model parameters are given in Table 5. 

a = {urn&turn& - m)]l/(l-m)}/(l + [Ktu,,(l - rn)Jl/@m)} (22) 

where cx is the degree of conversion of either VE or styrene monomers. 

The second step in the free volume modeling is the development of the T, vs. 

degree-of-cure relationship. Linear relationships of the form T, = Ts + Ka have 

usually been used in the literature for the T~CL model. However, in this study, 

the T,-a. model developed by Stone [ll] is used. For many therrnosetting 

systems, such as epoxy and polyimide systems, the Tp-a curve for various 

isothermal temperatures have all been found to collapse on to one curve [55- 581, 

showing a one-to-one relationship between T, and CL. However, in the case of 

411-C-50, a one-to-one relationship wasn’t obtained. This is because the WE resin 

system exhibits competing reactions and the influence of these competing 

reactions also vary with temperature [ll]. Thus, a single model cannot be used 

to describe the T, as a function of conversion; however, the estimated Ta-a 

parameters for fitting the Venditti’s relationship (equation 23) to the 

experimental data for different isothermal cure temperatures were used: 

WT,) = W#-G) + (C,J WT,“) MU - 4 + G) a> . (23) 

Stone [ll] had proposed a set of T,-a parameters applicable for the isothermal 

cure temperatures of 30’ and 40 “C (Table 9). These parameters, however, were 

obtained for relating T, to a determined using DSC. Since this experimental 

work aims to utilize FTIR for cure kinetics, a different set of parameters specific 

to FTIR-based (3t were estimated. Equation 16, in conjunction with the kinetic 

parameters for styrene presented in Table 5, is used to calculate conversion as a 

function of time. The new set of T,-u parameters are presented in Table 10. The 

total degree of cure a was obtained from am and czst using the relationship [4]: 

~TOtd = 0.2am + 0.8ast. (24) 

Table 9. T,-a model parameters for 411-C-50 corresponding to DSC. 

1 Temperature 1 O<U<Uvit I &+t<U<l I 

w> (CpJl (Tg& CL?)1 G& UP)2 t-m2 

293 150 248.15 294.15 0.15 289.15 398.15 

303 100 248.15 308.15 0.15 303.15 398.15 

313 35 248.15 330.15 0.15 319.15 398.15 

69 
Table 10. T,-u parameters for Vend&i’s relationship for 411-C-50 corresponding to FTIR. 

Temperature O<U<cSit 

(W G>l (M CL% 

303 39.314 248.15 309.95 

313 53.103 248.15 331.09 

The third step is the estimation of “constants” in the WLF equation for ionic 

conductivity and viscosity. These constants, though, usually are invariant from 

one cure temperature to the other [53]. Similar to the case of T, the coefficients 

are slightly different from each other for the cure temperatures under study. The 

WLF equation used for the modeling of ionic conductivity is given by relation 25 

and the estimated WLF constants are given in Table 11. 

log(CondT/CondTJ = G(T-T,)/((G+GT,)+(T-T,)) , 

and 

log(CondT,) = C4. (25) 

The ionic conductivity data in equation 25, were obtained using SW, while the T, 

data were generated using equation 24 with u as the model input, The ionic 

conductivity and the T, data were time correlated to yield conductivity vs. T@ A 

commercial curve-fitting software was used to fit equation 25 to the previously 

mentioned data, from which the WLF constants were estimated. The WLF 

parameters determined previously are presented in Table 11 for ionic 

conductivity at 303 and 313 K. 

Table 11. WLF Parameters for conductivity model. 

Temperature 

(K) 

303 

313 

Cl c2 G G 

0.98553 6.3703 -0.012869 -7.2115 

0.27303 4.7636 -0.0085545 -6.4166 

Figures 54 and 55 illustrate the free volume model fit to the experimental data. 

Excellent agreement is achieved for 30 “C, while some deviation is noted for 

40 “C. This is due to the slight temperature increase due to the exotherm which 

increases the conductivity. Shutoff is predicted accurately for both temperatures. 

70 
mime (Min) 

Figure 54. SW behavior prediction using free volume theory at 30 “C. (Degree of 

conversion obtained using FTIR.) 

3.0x10.' 

0 5 IO 15 20 

Time (Min) 

Figure 55. SW behavior prediction using free volume theory at 40 “C. (Degree of 

conversion obtained using FTIR.) 

6.2.4 Viscosity Model 

Equation 26 gives the WLF relationship used for describing the viscosity 

behavior. A similar procedure explained in section 6.2.3 was adopted for 

obtaining the WLF constants. Table 12 gives the estimated values of the WLF 

constants. A value of 15 was chosen for the log (qTg) Vah? [%I. 

71 
l”&d-td ” W- - Tg)/((C2 + C3Tg) + (T - Tg)) I (26) 

and 

log(qrp) = C4 = 15. 

Table 12. WLF parameters for viscosity modeling. 

Temperature 

("Cl 

30 

40 

Cl c2 c3 c4 

-13.507 7.2620 -0.020030 15 

-13.372 7.3472 -0.020304 15 

Figures 56 and 57 illustrate the comparison of the free volume model to the 

experimental data. Excellent agreement.is achieved at both temperatures, 

0' I 

0 5 10 15 20 25 

Time @din) 

Figure 54. Viscosity prediction using free volume theory at 30 “C. (Degree of conversion 

obtained usirq STIR.) 

The estimation of the WLF constants for both ionic conductivity and viscosity 

models, presents an elegant way of “sensing” viscosity and degree of cure using 

the SW signal as the model input. Figure 58 illustrates the model input and 

model predictions, i.e., viscosity and degree of cure. From Figure 58, it is seen 

that the model input (SW signal) is used to generate the corresponding Tg data. 

This, in turn, is used to yield predictions of viscosity and degree of cure. 

72 
16 

Time (Min) 

Figure 57. Viscosity prediction using free volume theory at 40 “C. (Degree of conversion 

obtained using FTK) 

, ‘3 / 

log(Coad~/Cond~& = CI(T-Tj/((C,+c,TJ+(T-T3) 

Figure 58. Schematic of viscosity and cure sensing using SMARTweave sipal as the 

model input. 

In essence, the glass transition temperature T, is used as the common link to 

relate the three material parameters: (1) ionic conductivity, (2) viscosity, and (3) 

degree of cure. Figure 59 presents the development of T, with cure time as 

predicted by the conductivity model using SW signal as the input. 

73 
320, 

o---a Tg vs Time at 40C 

e--a Tg vs Time at 30C 

240 I 

0 10 20 30 40 

Time (Min) 

Figure 59. T, (K) development with cure time as predicted by the free volume model. 

As shown in Figure 58, this forms the intermediate step prior to the prediction of 

viscosity and degree of cure by using the WLF relationship and Venditti’s 

relationship, respectively. While Figures 56 and 57 illustrated the predictive 

capability of the free volume model in estimating the macroscopic viscosity using 

the DC SW signal as the model input, Figures 60 and 61 present the degree of 

cure as predicted by the free volume model. 

Time (Min) 

Figure 60. Degree of cure prediction from SW data at 30 “C using free volume theory. 

74 
Time (Min) 

Figure 61. Degree of cure prediction from SW data at 40 “C using free volume theory. 

Figures 62 and 63 present a parametric study performed using the previously 

described free volume model corresponding to an isothermal cure temperature 

of 40 “C. The parametric study was aimed at identifying the effect of 

experimental deviation of the ionic conductivity from the WLF model predicted 

by equation 25. A deviation of 1% and 5% were artificially introduced into the 

theoretical ionic conductivity predicted by the free volume model, and the 

subsequent effect on the model predictions of viscosity and the degree of cure 

was quantified. Figure 62 presents the variation in degree-of-cure prediction 

while Figure 63 presents the variation predicted for viscosity development 

during cure. From these figures, it is observed that the degree of cure and 

viscosity predictions deviate further from the actual values as bigger deviations 

are introduced to the model input, i.e., ionic conductivity. Figure 63 shows that 

the viscosity profiles corresponding to the variations in ionic conductivity, still 

show accurate predictions of gel lime with in *2 min. Figure 62 shows large 

variations in degree-of-cure prediction in the early stages of cure. However, the 

degree of conversion values merge at vitrification. This is significant in resin 

infusion molding processes, where an accurate prediction of vitrification is key to 

demolding. 

6.3 Predictive Capability of the Free Volume Model 

Section 6.2 highlighted the ability of the free volume theory to predict the degree 

of cure, a, and viscosity, q, from the observed DC conductivity at 30” and 40 “C. 

However, these predictive capabilities depend on the specific model parameters 

obtained for the corresponding cure temperatures. In order to evaluate the 

predictive capability of this model, one set of universal parameters that 

75 
Figure 62. 

+-+I % Error 

-No Error c +-i 96 Error 

c-596 Error 

.OD, . . . z .. . f . . . . . 6 . I,,......... lo II . . . 1: . 16 . f 

Time (Min) 

Effect of deviation of ionic conductivity on degree of cure prediction from the 

free volume model at 40 “C for 411-C-50. 

1600 

++l% Error 

0 5 10 15 20 

Time (Min) 

Figure 63. Effect of deviation of ionic conductivity on viscosity prediction from the free 

vchme model at 40 “C for 411-C-50. 

successfully describe the ionic conductivity and viscosity development within 

the temperature range of interest is used. These universal parameters were 

obtained as mathematical averages of the WLF constants corresponding to 

30” and 40 “C in Tables 11 and 12. Section 6.3.1 discusses the effectiveness of 

these WLF parameters in describing the ionic conductivity behavior within the 

temperature range (3040 “C> of interest. Section 6.3.2 presents the predictive 

capability of the WLF relationship in describing the viscosity development 

during cure. 

76 
6.3.1 Conductivity Model 

As explained in section 6.2.3, the WLF relation given by equation 25 was used for 

ionic conductivity prediction: 

log(CondT/CondTp) = G(T - TJ/((G+ C3Tg) + (T - TJ) , 

and 

10g(COndTg)=6. (25) 

The WLF parameters G-6 were obtained as the average of 30” and 40 “C given 

in Table 13. The averages are: 

l Cl = 0.629 

l CT= 5.567 

l c3 = -0.011 

l C+ = -6.814 

Figure 64 shows ionic conductivity behavior predicted at 30 “C and 40 “C by the 

free volume model. The predicted curves closely follow the time-related 

behavior of the experimental data. The theoretical ionic conductivity reflects the 

temperature effects on SW signal, by exhibiting slower rate of change at lower 

temperatures as discussed in section 4. An observation of Figure 64 is that the 

theoretical curves bound the experimental data on either side. For a lower 

temperature cure, the theoretical ionic conductivity is higher than the 

experimental data, while, in the case of 40 “C, the predicted values are lower than 

the experimental values. This suggests that, within the temperature range of 30” 

to 40 “C, the maximum deviation of the theoretical prediction from the 

experimental measurements wiII not exceed that shown in Figure 64. For 

temperatures between 30” and 40 “C, the theoretical predictions will be closer to 

the experimentally measured ionic conductivity. In all cases, the cutoff time for 

the SW signal is accurately predicted and serves as a good measure of 

vitrification. 

6.3.2 Viscosity Model 

Figure 65 shows the viscosity profile at 30” and 40 “C as predicted by the free 

volume model. The corresponding average WLF parameters are: 

l Cl = -13,426 

l c2 = 7.3749 

l C3 = -0.020657 

l cq=lS 

77 
ume Model 30C 

ume Model 40C 

Time (Min) 

Fipe 64. Free volume modeling of ionic conductivity using average WLF parameters. 

0 5 10 15 20 25 

Time (Min) 

Figure 65. Free volume modeling of viscosity using average WLF parameters. 

The predicted viscosity profiles closely follow the experimental values, 

highlighting the effectiveness of the average WLF constants in yielding accurate 

predictive capability to the free volume model. The predicted curves reflect 

differences in gel time and slower reaction rates at lower temperature as 

discussed in section 4. 

78 
l 

6.4 Section Summary 

This section discussed the applicability of free volume theory in modeling ionic 

conductivity and viscosity development during cure. The free volume modeling 

involved a three-step process, requiring cure kinetic model relating degree of 

cure and time, a T,-a model relating the development of T, during cure with the 

degree of conversion, and the use of WLF equation relating ionic conductivity 

and viscosity to the glass transition temperature, T, A modified form of the 

WLF equation was adopted for this research work. The conductivity model 

described in section 6.2.3 develops the free volume-based conductivity model at 

cure temperatures of 30” and 40 “C. WLF parameters specific to these processing 

temperatures were estimated. Section 6.2.4 develops the free volume modeling 

of viscosity. The free volume model serves as the continuum model, descrlblng 

the material properties through gelation until vitrification. Figure 58 presents a 

schematic of the use of a free volume model in sensing the degree of cure and 

viscosity using the ionic conductivity observed by SW. This section also 

explored the feasibility of using a universal set of WLF constants for describing 

the ionic conductivity behavior and viscosity behavior within the temperature 

range (30-40 “C) of interest. The predicted ionic conductivity behavior and 

viscosity profiles closely followed experimental observations discussed in section 

4. 

The free volume model, similar to England’s model, utilizes equations (27) and 

(28) for estimating ionic conductivity from the SW signal: 

Rj(t) = (lO/Vm(t))Rs - Rs, (2T) 

Q = L/(I$(t)A). (28) 

England [4] has shown the variation of the observed SW signal with changes in 

either the separation distance between the electrodes or the area of the 

electrodes. For relating the SW signal to the material properties like viscosity 

and the degree of cure, it is necessary to convert the observed SW signal to ionic 

conductivity, since ionic conductivity is an intrinsic material property and is 

independent of the way is measured, In this work, the observed SW voltage was 

converted to the resistance by equation 27. The resistance is related to the ionic 

conductivity by equation 28. An aspect ratio of 172.45 was estimated for the 

SNTC3 single node test cells used in this research work, The conductivity hence 

obtained is related to the degree of conversion and viscosity through the WLF 

relationship. 

The free volume model presented in this section satisfies the requirements of a 

continuum model. In short, the present model extends the capability of DC 

sensing as an effective cure monitoring tool, combining the ability to sense 

viscosity to gelation and degree of cure through gelation to vitrification. 

79 
7. Conclusions and Future Work 

7.1 Introduction 

SW is a flow front visualization and detection system that hacks the DC ionic 

conductivity of the polymer under consideration. This research is part of the 

ongoing effort to investigate how the DC signal could be utilized to measure insitu the viscosity and degree of cure of the reacting resin. Previous work on 

conductivity modeling [4], though successful to gelation, failed to take advantage 

of the full capability of the SW system that reads the DC signal till vitrification. 

Above all, the current model attempts to correlate the intrinsic ionic conductivity 

changes to the resin’s intrinsic parameters like viscosity and degree of 

conversion. The goals of this particular study which were successfully 

accomplished are: 

l Develop a theoretical understanding of the ionic conductivity of the 

reacting resin system with an understanding of the relevant molecular 

events. 

l Develop a continuum model describing SW data to vitrification with 

predictive capabilities with respect to degree of conversion and viscosity. 

l Develop a methodology for characterizing other resin systems. 

An attempt was made to extensively characterize the various molecular events 

possibly associated with the DC conductivity to develop the understanding of 

this phenomenon. The sensitivity of SW over the more widely used dielectric 

cure monitoring has been explored and possible reasons for the better capability 

of SW signal in representing the changes in resin properties were discussed. A 

free volume-based model was eventually adopted to describe the resin 

characteristics from the SW signal. 

Section 7.2 provides a brief summary of sections 3-6, while section 7.3 outlines 

the free volume methodology for modeling any resin system based on DC 

sensing. Lastly, section 7.4 provides further insight into the possible research 

fronts one can adopt as a follow-on to this research effort. 

7.2 Conclusions 

Section 3 investigates the cure kinetics of two commercially used VE resins, 

namely 411-C-50 and 441-400, with emphasis on understanding the effect of 

temperature and styrene concentration. Autocatalytic modeling and the relevant 

kinetic parameters were obtained. FTIR measurements of the individual 

80 
conversions of VE and styrene were used for subsequent modeling in sections 5 

and 6. 

Section 4 dealt with the cure monitoring efforts on the previously mentioned 

resin systems using both SW and dielectrometer setups. The changes in the 

observed SW signal were linked with the molecular events such as 

macrogelation, network formation and cross-linking density. A comprehensive 

analysis of the dielectric behavior and the sensitivity of this cure monitoring 

technique to the previously mentioned molecular events have been explored. 

From the experimental results, it is seen that DC sensing is far more sensitive to 

cure-related changes in the early stages of cure, while AC sensing measures cure 

for a larger range of degree of cure. 

Section 5 dealt with the analysis of heterogeneities in a VE resin system in the 

form of microgels. The relevance of rnicrogels to the observed DC behavior was 

explored along with comprehensive efforts to separate the microgels from the 

reacting mixture for FTIR analysis. This section also presented visual evidence of 

the presence of these microgels in the form of AFM micrographs. Section 5 also 

explored the feasibility of a continuum model based solely on microgels. The 

discrepancy between the model predictions and the experimental results 

suggested a need for a better model, one that would take into account the 

development of network formation during cure. 

Section 6 discussed the use of a classical free volume approach to model the 

conductivity behavior offering degree of cure and viscosity prediction capability 

based on the observed SW signal. This model takes into account the 

development of T, with cure for relating ionic conductivity to degree of cure and 

viscosity. Since the development of T, with cure reflects the extent of reaction 

going into network formation, the difficulty faced in section 5 is circumvented. 

7.3 Summary of Free Volume Methodology 

This research work presents a unique methodology of cure monitoring using DC 

sensors. The free volume model developed in section 6 presents a successful 

adaptation of the classical free volume theory to sense material properties till 

vitrification The free volume-based continuum model, however, is even 

applicable to resin systems other than 411-C-50., A brief summary of the 

methodology that needs to be adopted for modeling other resin systems is 

presented. 

The use of the WLF relationship to model the polymer behavior comprises three 

steps, which are three modeling efforts in themselves. First, one must develop a 

cure kinetic relationship relating degree of cure with time. Depending on the 

resin system, one can use either DSC or FTIR to obtain this information. 

81 
The second step comprises the development of T, vs. the degree of cure 

relationship. This was accomplished using Venditti’s equation (equation 23) in 

this research work. Typically linear or empirical relationships are utilized for the 

T,-a model. 

The third step is the adaptation of the modified WLF relationship (equations 25 

and 26) for relating ionic conductivity and viscosity to the glass transition 

temperature T, The WLF parameters are obtained by fitting the corresponding 

WLF equations onto the experimental data. In systems such as epoxies, a set of 

temperature independent model parameters are known to exist, Figure 25 shows 

schematically how the continuum model already developed can be used for 

sensing the degree of conversion and viscosity during cure by making use of the 

measured SW signal as model input. 

7.4 Recommendations for Further Research 

7.4.1 Fundamental Understanding of Tga Relationship 

The modeling effort presented in this research work highlighted the difference in 

the behavior of T, vs. a at different cure temperatures. This necessitates the 

prediction of WLF parameters for discrete cure temperatures. However, a 

fundamental understanding of the T, vs. a behavior in VE resins, would enable 

the development of a single Tga model. Such a development in the 

understanding of T, behavior could be used for WLF modeling of ionic 

conductivity with a set of universal parameters, that would describe ionic 

conductivity behavior at any desirable cure temperature. 

7.4.2 Positron Annihilation Studies 

Effort should be directed to observe the actual development of the free volume 

through the use of positron annihilation studies [60]. A direct measurement of 

the free volume development with cure would eliminate the need for curvefitting options to obtain the free volume parameters. Also this would eliminate 

the need to use the Tp-a relationship developed by Stone [ll], which, as 

explained before, introduces variations in the observed WLF constants. Efforts 

should also be directed toward the use of radiotracers to identify the ionic 

pathways leading to the observed ionic conductivity. 

82 
8. References 

. 

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Gradients in Thermosetting Composites,” Ph.D. Dissertation, University of 

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20, 1990. 

3. Walsh, S. M. ‘%-Situ Sensor Method and Device.” U.S. Patent No. 5,210,499, 

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4. England, K. M. “Direct Current Sensing of Viscosity and Degree of Cure of 

Vinyl Ester Resins.” Master’s Thesis, University of Delaware, Newark, DE, 

1997. 

5. Fink, B. K., S. M. Walsh, D. C. DeSchepper, J- W. Gillespie, Jr., R. L. 

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8. Kikuchi, A., E. Higuerey, ‘md J. Coulter. “An Experimental Investigation of 

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Materials and Technology, vol. 117, pp. S&93,1995. 

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vol. 17, pp. 312-318,19X. 

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for Composite Materials, Newark, DE, 1998. 

83 
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24. Batch, G. L., and C. W. Macosko. “Kinetic Model for Crosslinking Free 

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25. Ems, J. B., and J. K. GilIham. “Time-Temperature-Transformation (TTT) Cure 

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Polymer Science, vol. 28, pp. 2567-2591,1993. 

26. Dusek, K., and J. Spevacek. “Cyclization in Vinyl-divinyl Copolymerization.” 

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no. 9, pp. 742-749,1994. 

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for the Autocatalytic Curing of Styrene Based Thermoset Resins.” Journal of 

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45, pp. 574-588,1973. 

37. Lobb, C. J., and D. J. Frank. “A Large-cell Renormalization Group Calculation 

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38. Straley, J. P. “Critical Exponents for the Conductivity of Random Resistor 

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pp. L763-L765,1978. 

41. Last, B. J., and D. J. Thouless. “Percolation Theory and Electrical 

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vol. 171, p. 396,1953. 

45. Hadad, D. K. Epoxy Resins Chemistry and Technology. 2nd Edition, edited by C. 

A. May. New York, NY: Marcel Dekker, 1988. 

46. Simpson, J. O., and S. A. Bid&up. “Correlation Between Chain Segment and 

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87 
INTENTIONALLY LEFT BLANK. 

88 
Appmdix A. Dielectric Cure Monitoring 

. 

A.1 Basis of Dielectric Behavior 

When a viscoelastic polymeric material containing permanent dipoles are placed 

in an alternating electric field the reorientation of dipoles upon the reversal of the 

electric field is not instantaneous. Consequently, when an alternating timedependant voltage is applied to a parallel plate condenser, the corresponding 

time-dependent current will lag behind the applied voltage by a phase angle 6. 

Applying the phenomenological theory of linear dielectric relaxation behavior,‘? 

it can be shown that the complex dielectric constant is given by 

E- = Eu + (6, - &“)/(I + iss) VW 

or 

E*=E’- iE”, (A-2) 

where E’ = permittivity (real or storage component of the dielectric constant), 

and E” = loss factor (imaginary or loss component of the dielectric constant). 

By using the parallel plate approximation, 3 the capacitance of can be related to 

the permittivity and the loss factor to obtain: 

Dissipation = E”/E’. (A-3) 

The permittivity and loss factor can then be used to determine the material’s 

average dipole relaxation time and the specific conductivity. The loss factor has 

two components, one associated with ionic conduction and the other associated 

with dipolar rotation: 

E” = G/(os,) + E”(dipolar) , CA.41 

where o = specific conductivity, o = angular frequency, so = permittivity of free 

space, and 6” (dipolar) = &polar contribution to the loss factor. 

The specific conductivity is usually assumed to be a direct function of the loss 

component of the dielectric constant, when the loss factor exceeds 50: 

cs = (E”)(O)(&O). (A.51 

’ Mccrum, N. G., B. E. Read, and G. Williams. Anelastic and Dielectric E$cts in Polymeric Solids. 

New York, NY: Wiley, 1967. 

2 Ferry, J. D. Viscoelastic Properties of Po@ners. Second Edition, New York, NY: Wiley, 1980. 

3 May, C. A. Interrelations Between Processing Structure and Properties of Polymeric Materials. 

Amsterdam: Elsevier, 1984. 

89 
This is the region where the dipolar contribution to the loss factor for this system 

usually is less than 5% of the total observed signal. The dipolar relaxation time z 

is given by the reciprocal of angular frequency corresponding to when the 

dipolar contribution to the loss factor reaches the maximum. 

f = 1/Gnas, (A.61 

where z = dipole relaxation time and Omizv = angular frequency corresponding to 

when the dipolar contribution to the loss factor reaches the maximum. 

A.2 Dielectric Measurements for On-line Cure Monitoring 

The major limitation of dielectric techniques for in-situ monitoring of cure is the 

lack of both fundamental and phenomenological correlations between the 

dielectric signal and the processing parameters. Apart from the theoretical 

challenge, such information would be of considerable importance to the 

manufacturers of composites. 

It must be noted that the dielectric behavior of a substance depends essentially 

on its structure and on the true electric field acting on it in the presence of an 

external macroscopic electric field. The available expressions for nonpolar 

materials when only electronic or atomic polarizations are observed can be well 

represented by the dielectric properties for gas and liquid states. On the other 

hand, the development of expressions relating the molecular structure and the 

dielectric constant for simple polar substances in the liquid state, such as water, 

is a difficult matter as a consequence of the effect of the local electric field, 

usually different from the macroscopic one. The prediction of the dielectric 

properties in the solid state is still more complex, not only as a consequence of 

the differences in the local and macroscopic electric field, but also because the 

dipoles are hindered in the motion. Reactive mixtures such as unsaturated 

polyester resin systems with many pendant polar groups and stearic hinderances 

are much more complicated to model. As a result, the dielectric behavior have 

been correlated only qualitatively to fundamental processing parameters4< 5 

A-2.1 Ionic Resistivity 

The determination of ionic resistiviq with the currently available sensor 

instruments, is based upon the assumption that the free migrating ions are 

initially present in the resin owing to the contamination and other impurities 

such as cl-, which are unavoidable owing to the very nature of the synthesis of 

epoxies and, hence, vinyl-ester (VE) resins. Ionic resistiviv depends on the ionic 

4 Kranbuehl, D. E., S. E. Delos, and P. K. Jue. “Dielectric Properties of the Polymerization of an 

Aromatic Polyimide.” F’oolym~r, vol. 27, pp. ll-18,1986. 

5 Day, D. R. “Dielectric Determination of Cure State During Non-Isothermal Cure.” IWyrrw 

Engineering and Science, vol. 29, pp. 334-3381989. 

90 
charge, q, number of ions, n, and on the mobility factor, m, sensitive to the 

structural changes of the matrix. 

During cure, the ionic conductivity decreases owing to the reduction in the 

mobility of the ions as a result of cross linking and other related molecular 

events. The type and the concentration of the ions, as well as the effect that these 

two parameters exert on the dielectric measurements are not worthwhile 

quantifying considering the large variety of resin systems, and the inevitable 

vicissitudes of the batch-to-batch characteristics. The isolation of ionic 

contribution to the dielectric signal occurs at different frequencies corresponding 

to different stages of the resin cure and it is more of an educated guess than an 

accurate representation .of the actual contribution within the resin system. This 

also necessitates experiments performed at a series of frequencies until the right 

range is chanced upon. 

A.22 Dielectric Constant and Dielectric Loss 

Most of the research dealing with the dielectric constant and the dielectric loss 

has been devoted to the derivation of a fundamental expression for loss factor, 

which can then be used for correlating to describe the observed experimental 

results. Many difficulties arise from such an approach because in polymeric 

systems, the local internal electric field is not known. Its accurate determination 

is difficult, as the number of dipoles to the electric field varies as a function of the 

size of the segment to which the dipole is attached and the surroundings that 

hinder the dipole rotation to a different degree. This impedes any work directed 

towards relating the observed loss factor to the degree of reaction directly. 

Recently, Maffezzoli et al6 were able to identify a frequency range in which the 

dielectric behavior was dominated by the disappearance of epoxy groups, 

allowing for a direct correlation between the dielectric signal and the degree of 

cure. 

6 Maffezzoli, A., A. Trivisano, M Oplaicki, J. Mijovic, and J. M. Kenny. “Correlation Between 

Dielectric and Chemorheological Properties During Cure of Epoxy-Based Composites.” JownnZ of 

Muterials Science, vol. 29, pp. 800~808,1994. 

91 
hdTENTIONALLY LEFT BLANK. 

92 
Appendix B. Calculation of the Volume Fraction of Microgels 

The following calculation of the volume fraction. of microgels assumes the 

following: 

l All the reaction as observed by the Fourier-transform infrared (FTIR) goes 

into the formation of microgels. 

l All microgels are of uniform spherical size of say diameter = 15Onm. 

l Density of monomers in the unreacted resin and that in the microgel 

remains the same. 

l All vinyl-ester (VE) monomers are double-end reacted. 

(1) Density of VE resin system = DResh 

(2) Density of styrene (ST) monomer = DX 

(3) Density of VE monomer = l&r 

(4) Volume of VE resin system= V~e~in 

Volume of VE monomers = 0.52* V,R DR&Dw =VVE 

Volume of ST monomers = 0.48” VRM* DR,~/Ds~ = VST 

At time t.- 

(B-1) 

(B-2) 

l Degree of conversion of VE = WE 

l Degree of conversion of ST = air 

Volume of VE in microgels = VVE * WE =VVE Microgel (‘13.3) 

Volume of ST in microgels = VS~* asr = VSTM~+ (B.4) 

Volume of microgel = 4*x* Rkicrogel/3 = VM~+ (B-5) 

Number of microgels = VW~J (VVE Microgel + VS~ Microgel ) ow 

93 
94 
Appendix C. Determination of L/A Ratio of Single Node Test 

Cell (SNTC)3 

A typical SNTCS-type cell is shown in Figure C-l. Owing to the very nature of 

the placement of the electrodes, i.e., orthogonal placement, it presents a special 

problem in obtaining the conductivity data from the observed SMARTweave 

(SW) voltage. A typical single-node circuit diagram is given in Figure C-2. 

Applymg basic Kirchoff’s laws, one ends up with an expression for the 

Resistance of the resin as: 

Rj = (lO*Rseme/Vmeasurd) -Sense, Cl> 

where Rjis the resistance of the resin, I& eMe is the sense resistance of value 10MQ 

and Vrneasured is the measured SMARTWeave (SW) voltage. 

/-Resin Level 

ARTweave Leads 

Fiq.rre C-l. SNTC-3 single node test cell. 

From the resistance one can obtain the conductivity D as: 

o=L/(RjA), (C-2) 

where L is the separation distance between the elecnodes and A is the effective 

electrode surface area. 

In case of parallel plate setup, this is essentially a straightforward problem. 

However, for the orthogonal set-up in single node test cell (SNTC)-3, the L/A 

ratio needs to be estimated indirectly. 

95 
Switch 

I-Y 

Power 

10.0 

Supply 

v 1 

I 

Junction Resistor (RJ) 

(Resistance of the Resin) 

Sense Resistor (R,) 

Figure C-2. Circuit diagram of a single node cell. 

There are many different ways of determining the characteristic conductivity of a 

material. American Society for Testing and Materials (ASTM) standard D257-781 

offers a variety of solutions for determining the DC conductivity of a material. 

One such method has been adopted for our purposes of DC conductivity 

measurements. The basic setup consists of two concentric cylinders sealed at one 

end made of aluminum. Figure C-3 shows the basic components and dimensions 

of the fabricated DC conductivity cell used in this study. 

Dl = 20.55 mm 

02 = 25.27 mm 

Ohm Meter Leads 

I Aluminum Tubing 

t 

L = 23.85 mm 

Teflon Seal 

Figure C-3. Experimental cell for conductivity studies. 

The outer and inner cylinders were machined out of aluminum and the seal was 

fabricated out of Teflon owing to its inertness. 

Resistance values obtained using this setup can be converted into resistivity 

values by using the following equation: 

p = 2dR/(h(Dz/D1)). (C.3) 

’ American Society for Testing and Materials. “Test Method for Determining D-C Resistance or 

Conductance of Insulating Materials.” ASTM D257-78,1986. 

96 
The resistivity obtained can then be equated to the resistivity calculated using the 

resistance measured using SNTC-3 cell as follows: 

psNTc-3 = Rj&wrc-3/ LMTC-3. (C.4) 

This exercise was performed for different resin types at different temperatures. 

An average value of 172.45 was obtained for (L/A)sNTc-3. 

f 

97 
98 
Appendix D. Doping Results 

D.1 Introduction 

Vinyl-ester (VE) resins are inherently high resistance resins, i.e., they possess 

high resitivity. The source of ions in VE resins are primarily from tie 

manufacturing step involving synthesis from epoxies, which are known to have 

chloride ions (Cl-) as contaminants. Research work by England [4] has shown an 

increase in the ionic conductivity of VE with the addition of both cobalt 

naphthenate (CoNap) and Trigonox. This is due to the fact that CoNap and 

Trigonox dissociate on addition to VE resins. 

The concentration of chloride ions are highly variable from one batch of VE resin 

to another. Also the SMARTweave (SW) signal obtained exhibited a low signal 

to noise (S/N) ratio. To improve the quality of observed direct current (DC) 

signal and to quantify the concentration of ions in the resin system, doping was 

adopted by England. Doping was achieved by introducing 0.1 weight-percent of 

an organic salt into the neat VE resin. England identified two such organic salts 

that favorably increase the observed DC signal on addition to the resin mixture: 

tetiabutyl ammonium acetate (TA) and tetra butyl ammonium iodide (TI). In his 

research work, England adopted the use of TA for doping. A cost analysis, 

however, indicated that replactig TA ($3.50/g), with TI ($0.25/g) is desirable 

from an economic point of view. 

D,2 Cure Monitoning 

Figure D-l shows a comparison of an SW signal obtained using TI as a dopant 

against TA-doped 411-C-50 VE resin and undoped 411-C-50 resin mixture at an 

isothermal cure temperature of 40 “C. Figure D-Z presents the SW response of 

undoped resin on a different scale for better comparison. From Figure D-l, it is 

seen that the addition of dopants increases the SW signal by as much as a factor 

of 15. This translates into a better S/N ratio as observed from a comparison with 

Figure D-2 corresponding to undoped resin, where one sees a significant 

presence of noise. 

As evident from Figure D-l, though the addition of dopants to the resin mixture 

increases the ionic conductivity, the SW profile of the curing resin remains 

largely unaltered. A comparison of Figures D-l and D-2 reveals that the TAdoped resin mixture shows faster gelation (inflection point) and faster cutoff of 

the DC signal. However TI doped resin, follows more closely the behavior of 

undoped resin, highlighting another advantage to the use of TI over TA. 

99 
20 40 60 

Time (Min) 

Figure D-l. Comparison of SW response of TI-doped 411-C-50 against TA- doped and 

undoped 411-C-50 at an isothermal cure temperature of 40 “C. 

0 IO 20 30 40 50 

Time (Min) 

Figure D-2. SW response of undoped 411-C-50 at an isothermal cure temperature of 

40 “C. 

D.3 Cure Kinetics 

One of the desirable qualities of dopants is that the addition of dopants to resin 

mixtures should not affect the rate of cure reaction. To investigate the effect of TI 

on the cure kinetics of the VE resin, infrared (IR) spectroscopy was performed on 

curing VE samples at an isothermal temperature of 40 “C. Figure D-3 

0.3 / 

Q--+ Undoped 411 -C-50 

100 
0.8, 

0.6 

M Alpha styrene dopad 

- Alpha VE doped 

M Alpha styrene undoped 

u Alpha VE undoped 

1 

50 100 150 200 

Time (Min) 

Figure D-3. Degree of conversion comparison ,between doped and undoped resin at 

40 “C isothermal cure temperature. 

presents the degree of conversions of VE and styrene monomers for both doped 

and undoped 411-C-50 resin mixtures. Figure D-3 reveals that the addition of TI 

to the curing resin mixture results in slower rates of monomer conversion and a 

lower maximum degree of conversion. Similar effect has been reported by 

England1 for TA-doped resin mixtures. This suggests that the addition of 

dopants could potentially affect the network development during cure. Since 

one of the objectives of this research work is to gain an understanding of the 

network development during cure, dopants were not used for the remainder of 

-this project. 

’ England, K. M “Direct Current Sensing of Viscosity and Degree of Cure of Vinyl Ester 

Resins.” Master’s Thesis, University of Delaware, Newark, DE, 1997. 

101 
f 

102 
Appendix E. Percolation Model 

E.l Introduction 

Percolation theory is a mathematical theory which deals with disordered systems 

and give good application. to the description of electrical conduction in 

disordered materials, such as conductor-insulator mixture. The conductivity of a 

composite material with spherical particles, of different electrical behavior (say 

insulator) can be predicted by a percolation model. Literature presents a number 

of efforts directed towards observing such a system.‘FA4 

In this study, an effort is made to describe the SMARTweave (SW) data based on 

the percolation model. The system under consideration is vinyl-ester (VE) resin 

undergoing cure, and the SW data corresponds to the drop in the observed 

conductivity with the proceeding of cure. This essentially presents a classical 

percolation problem in which regions (roughly spherical) of differing electrical 

behavior appear in a continuous medium in a random manner. In the system 

under consideration, the curing leads only to the, formation of microgels, of a 

roughly spherical nature, which are assumed to have zero contribution towards 

the observed conductivity. With time, the number and hence the volume 

percentage of these dead zones (microgels) increase and this manifests itself as a 

decrease in the observed conductivity. Figure E-l represents various stages of 

cure. 

E-2 Theory 

A percolation model was proposed first by Broadbent and Hamrnersley5 in 1957. 

Hamrnersley developed the theory further by successive papers on this 

approach. A detailed introduction and review of the applicability of percolation 

1 Abeles, B., H. L. Pinch, and J. I. Gittleman. “Percolation Conductivity in W-Al203 Granular 

Metal Films.” Physical Review Letters, vol. 35, pp. 247-250,1975. 

2 Deutscher, G., M. Rappaport, and 2. Ovadyanh. “Random Percolation in Metal-Ge Mixtures.” 

Solid State Communication, vol. 28, pp- 593-595,1978. 

3 Gurlaud. J. “The Fracture Strength of Sintered Tungsten Carbide-Cobalt Alloys in Relation to 

Composition and Particle Spacing.” Trunsactions of Metuflurgicul Society ofAlME, vol. 227, pp, 1146- 

1150,1963. 

4 Gurland, J. “An Estimate of Contact and Continuity of Dispersions in Opaque Samples.” 

Transactions of Metallurgical Society of AlME, vol. 236, pp. 642&6,1996. 

5 Broadbent, S. R., and J. M. Hammersley. “Percolation Processes I. Crystals and Mazes.” 

Proceedings of Cambridge Philosophical Society, vol. 53, pp. 629~641,1957. 

103 

sites are connected by a sequence of sites and bonds. Though there may be many 

paths between a given pair of sites, the sites are said to be connected if there 

exists at least one path between them. This is known as “pair connectedness,” 

and its probability plays a significant role in many applications. The presence of 

the path, for example, allows the flow of charges between the two sites which are 

connected by the path. A set of occupied sites connected to one another through 

bonds is called a “cluster.” When the probability of occupied sites P, or that of 

occupied bonds Pb increases so do the cluster size. At a critical value of Pb or P, 

the cluster size becomes infinite, At this stage, the system is said to be in a 

percolating stage. A detailed description and applicability are discussed 

elsewhere.” 

Table B-1 gives the various lattices and the corresponding critical pb (Pcb) and P, 

03 

Table E-l. Percolation thresholds. 

E.3 Percolation and Conduction 

Electrical conductivity in disordered systems akin to that present in our resin 

system has been studied extensively.24fg Gurland4 studied the system composed 

of Bakelite and silver, The system exhibited a strong and abrupt transition in its 

conducting behavior at a volume-percent of 304 (silver). In 1975, Abeles et al.1 

s Malliaris, A., and D. T. Turner. “Influence of Particle Size on the Electrical Resistivity of 

Compacted Mixture of Polymeric and Metallic Powders.” JOKOLUZ ofApplied Physics, ~0142, pp. 614- 

618,19?l. 

’ Hammersley, J. M-, and K. W. Morton. “Poor Man’s Monte Carlo.” Journal ofRoyal Stntisticnl 

Society. B, vol. 16, pp. 23-38,1954. 

105 
studied a composite of W-Al203 exhibiting a sharp transition between a 

conducting material to being an insulator below a critical volume fraction of W of 

0.47. A study of a nickel-polyvinylchloride (PVC) mixture by Mallaris and 

Turners deals with percolating situation, very similar to that observed in VE resin 

systems. The study successfully applied percolation principles to describe the 

observed conductivity, as well as catalogued a detailed study on the influence of 

particle size on the observed electrical resistivity of the mixture. 

E.4 Evidence of Percolation in VE system 

A key feature that sets apart a percolating system is the abrupt transition of, say, 

electrical behavior with change in the volume contribution of one of the 

constituents. This seems to be true in the case of the VE resin system, too, as 

illustrated by experimental results presented in Figures E-Z and E-3. These 

figures illustrate the convergence of the curves in the region of acute 

conductivity transition to a narrow range of volume fraction (of microgels). 

Based on the success of percolation model in describing systems similar to the 

VE systems and primarily due to the fact that the conductivity of VE follows the 

expected trends of a percolation model, one can reasonably expect to model the 

VE system based on percolation. 

A 50 c 

L 

0 40 c 

0 NC 

I - 

0 

0.2 0.4 0.6 0.8 

Microgel Volume Fraction 

Figure E-2. Normalized DC signal vs. microgel volume fraction of Derakane 411-C-50 at 

different isothermal cure temperatures. 

106 
h 5OC 

i 

0 4OC 

0 30C 

-I 

0.2 0.4 0.6 0.8 

Microgel Volume Fraction 

Figure E-3. Normalized DC signal vs. microgel volume fraction of Derzikane 411-C-50 at 

different isothermal cure temperatures. 

107 

Appendix F. Analyzing Diffusion in the Pregel and Postgel 

Stage 

F.1 Regel Stage 

Diffusion is a direct result of the Brownian motion of particles (molecular or ionic 

species) in the system. The diffusion processes tend to have all the species 

uniformly distributed in the system. In the presence of an electric field, there 

exists another transport process as a way of migration of ionic species towards 

one of the two electiodes. 

Einstein’s relationship between the mobility of ions and the ionic diffusion 

coefficient is given as follows in Bock%’ 

k= QiDi/kT , (‘F-1) 

where b is the mobility of the ions, Di is the diffusion coefficient of ions, Qi is the 

charge carried by each ion, and KS is Boltzmann’s constant. If only one type of 

ion is considered, the ionic conductivity is given by 

Cf=Qi@Ji, F.2) 

where cr is the ionic conductivity and N is the number of ions per unit volume. 

Thus for the isothermal cure without any generation of ions, the ionic 

conductivity is proportional to the diffusion coefficient of ions. 

According to the Stokes-Einstein relation, 

Di = KB T/~R~R, (F.3) 

where DL is the diffusion coefficient of ion, q is the viscosity, and R is the radius 

of the particle. Combining equations F.l-F.3, one can see that the ionic 

conductivity is inversely proportional to the macroscopic viscosity. However in 

case of vinyl-ester (VE) resin systems studied in this work does not exactly fall 

under this relationship. But due to the universality of the application of 

diffusion modeling and owing to limited success of ionic conductivity modeling 

based on the above relationships applied to VE 411-C-50, it is worthwhile to 

proceed with diffusion modeling based on the above relationship. 

More importantly, equation F.4 establishes a direct relationship between the size 

of a particle and its diffusion coefficient. Therefore, the diffusion coefficient of 

1 Bockris, J+ 0. M, and A. K. N. Reddy. Moah Electrachzisty. New York, NY: Plenum, 1970. 

109 
ions and the diffusion coefficient of the monomer may be correlated through 

their sizes as below: 

D, = D& = K~(T/ Kl , (F.4) 

where D, is the diffusion coefficient of monomer, Kl is given by Qi2Ni/&T, and 

K2 is the ratio of the size of ions to that of the monomer. 

The diffusion coefficient of a particle is by definition 

D, = <S2>/6t, (F.5) 

where GP> is the mean square displacement that the molecule as a whole 

undergoes over a time period, t. By evaluating the total mean-square 

displacement of all the monomer units in the system during the same time 

period, the overall diffusion coefficient, or the average diffusion coefficient of 

monomer unit, is given by: 

D = D,Xi , (F.6) 

where X, is the number-average degree of polymerization. Consequently, before 

gelation, the overall diffusion coefficient can be estimated using the following 

diffusion model by substituting equation F.4 into equation F.6: 

D = &a X,-r/K1 . (F.7) 

F.2 Postgel Stage 

Since a scaling relationship between the diffusion of the gel and the diffusion of 

the gel and the diffusion of free chains is not known to exist, a different model 

based on dipolar relaxation tie has been proposed, The ionic conductivity is 

directly related to the mobility of the ionic species, while the dipole relaxation 

time is a direct indicator of the mobility of the molecular species. 

The model that describes the free volume dependence of diffusivity is given by 

Kumins:2 

D = Daxp(-bnv’/vf), (F-f9 

where vf is the average free volume and v* is the average close-packed-sphere 

volume or the critical free volume needed for a segmental jump to take place. 

For the dipole relaxation time, the free volume model is given by 

r = rOexp(-brv/vf) , F-9 

2 Kurnins, C. A. and T. K. Kwei. Di@usion in Polymers. Edited by J. Crank, and G. 5. Park, New 

York, NYI Academic Press, 1968. 
where I7 is the dipole relaxation time, r, is a constant, b is a constant that 

includes the critical free volume for dipole relaxation, and v (=v* + vf) is the 

average free volume per chain segment. 

Combining the equations F-8 and F.9, one ends with 

rP= I?& (F.10) 

where n (=bo/ br) is a constant independent of conversion and temperature and 

K.3 is a constant. 

Rewriting equation F.10 yields 

LogD= -n Log r + Log LG. (F.11) 

Since equation F.ll holds for even in case of pregel stage, substitution of 

expression of pregel D in equation F.ll yields: 

LO$ (a X,-l) =-nLogP+LogG, (F-12) 

where I&’ (=I& &/ K2) depends only on the temperature. From relation F.12, one 

can obtain the power law index that can then be subsequently used for diffusion 

modeling in the postgel stage. 

Thus, the overall diffusion coefficient may be determined using equation F.7 in 

the pregel stage and equation F.10 in the postgel stage. In principle, however, 

equation F-10 can be used both in the pregel and postgel stage. However, owing 

to tie difficulty in isolating the ionic contribution from the dipolar contribution 

in the pregel stage, equation F.7 presents itself as a more reliable model for 

diffusion behavior. 

111 
INTE~I~NALLY LEn BLANK. 

112 
Appendix G. Differential Scanning Calorimeter (DSC)-Based 

Free Volume Modeling 

G.1 Introduction 

Section 6 examined free volume modeling of ionic conductivity and viscosity 

development during cure, based on Tga relationship. The degree of cure a was 

obtained using Fourier-transform infrared (FTIR) for the same. This appendix 

provides information on the development of free volume model, for degree of 

conversion estimated using DSC. For VE 411-C-50, the degree of conversion as 

obtained using DSC is different from FTIR data. This -makes it necessary for 

explicit estimation of the Williams, Landel, and Ferry (WLF) parameters required 

for describing conductivity and viscosity. 

G.2 Cure Kinetic Model 

The cure kinetic expression corresponding to degree of conversion determined 

by DSC is given by: 

da/dt = (Kl+ KKP)( urnax- CL)” , G.1) 

The autocatalytic parameters for equation 13 are presented in Table G-l. 

Table G-l. Tgu model parameters. 

(2.3 Tgar Model 

Linear relationships of the form T, = T$ f Ka have usually been used in the 

literature for the Ts-a model. However in this study, the Tgcr model developed 

by Stone’ would be used. 

1 Stone, M. A. “Thermo-chemical and Thermemechanical Response of Reacting Polymers.” 

CCM Report No. 97-13, University of Delaware, Center for Composite Materials, Newark, DE, 

1997. 

113 
Equation G.2 presents the Vend&i’s relationship between T, and IX 

WJ = ((1 - 4N&J + Gr> cWT,“) >/CC1 - 4 + C,r) a> . 

The model parameters corresponding to the degree of conversion obtained using 

DSC are presented in Table El.1 

(2.4 Conductivity Model 

The WLF equation used for the modeling of ionic conductivity is given by 

equation G.3 and the estimated WLF constants are given in Table G-2. 

log(CondT/CondT,) = Cl(T - Tg)/((C2+ GTg) +(T - Tg)) , (C.3) 

and 

log(Condr,) = Ca . 

Table G-2. WLF parameters for conductivity model. 

Temperature 

(K) 

303 

313 

Cl c2 c3 c.4 

1.1696 9.5453 _ -0.026298 -7.3974 

0.24118 8.5876 -0.020983 -6.3851 

Figures G-l and G-2 illustrate the free volume model comparison with the 

experimental data. 

42.5 Viscosity Model 

Equation G.4 gives the WLF relationship used for describing the viscosity 

behavior, Table G-3 gives the estimated values of the WLF constants. A value of 

15 was chosen for log (TjTg) value. 2 Figures G-3 and G-4 illustrate the comparison 

of the free volume model to the experimental data. 

~O~(IJT/IJT~) = Cl(T - Tg)/ ((C2 + C3Tg) + (T - Tg)) , ’ G-4 

and 

log@& = c4 = 15. 

2 Maffezzoli, A., A. Trivisano, M. Oplaicki, J. Mijovic, and J. M. Kenny. “Correlation Between 

Dielectric and Chemorheological Properties During Cure of Epoxy-Based Composites.” Joma of 

Materials S&me, vol. 29, pp. &IO-808,1994. 

114 
0 ID 20 30 40 

Time (Min) 

Figure G-l. SMARTweave (SW) behavior prediction using free volume theory at 30 “C. 

axd 

6x10-' 

0 5 10 15 20 

lime (Min) 

Figure G-2. SW behavior prediction using free volume theory at 40 “C. 

The estimation of the WLF constants for both ionic conductivity and viscosity 

models, presents an elegant way of “sensing viscosity and degree of cure using 

SW signal as the model input. Figure G-5 illustrates the model input and model 

predictions, i.e., viscosity and degree of cure. From Figure G-5, it is seen that the 

model input (SW signal) is used to generate the corresponding T, data. This in 

turn is used to yield predictions of viscosity and degree of cure. Figures G-6 and 

G-7 illustrate fie predictive capability of the free volume model in estimating the 

macroscopic viscosity using DC SW signal as the model input, while Figures G-8 

and G-9 presents the degree of cure as predicted by the free volume model. 

115 
Table G-3. WLF parameters for viscosity modeling. 

Temperature 

6) 

303 

313 

Cl c2 c3 c-4 

-13.505 7.2285 -0.020029 15 

-13.347 7.5213 -0.021285 15 

20 25 

Time (Min) 

Figure G-3. Viscosity prediction using free volume theory at 30 “C. 

5 

0 4 6 12 16 

Time (Min) 

Figure GA Viscosity prediction using free volume theory at 40 “C. 

116 
Figure G-5. Schematic of viscosity and cure sensing using SW signal as the model input. 

0.12 

- Free Volume Model 

Degree of Conversion from DSC 

0.08 

0.04 

0 

0 

Time( Min) 

Figure G-6, Degree of cure prediction from SW data using free volume theory at 30 “C. 

117 
- Free Volume Model 

s-4 Degree of Conversion from PSC 

z 

J 

0 5 10 15 20 

Time(Min) 

Figure G-7. Degree of cure prediction from SW data using free volume theory at 40 “C. 

T 

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137 
138 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 07WO188 

Bruce K. Fink, Mahendra B. Dorairaj.* and John W. Gillespie, Jr.* 

PERFORMING ORGANlZATION NAME(S) AND ADDRESS 

3. Army Research Laboratory 

AT-IN: AMSRL-WhI-MB 

Aberdeen Proving Ground, MD 21005-5069 

8. PERFORMING ORGANIZATION 

REPORT NUMBER 

11. SUPPLEMENTARV NOTES 

*University of Delaware, Center for Composite Materials, Newark, DE 19716 

12a. DISTRIBUTlON/AVAILABILllYSTATEMENT 

Approved for public release; distribution is unlimited. 

12b. DISTRIBUIlON CODE 

13. A0STRACT(Maxlmum 2w word?+ 

High-performance thermosetting composites typically consist of a high-modulus fibrous material embedded in a 

thermosetting polymer man-ix. The behavior of the resulting composite depends on the properties of the 

reinforcement, the interphase, and the matrix. Vinyl-ester (VE) resins are relatively low-cost matrix resins used in 

liquid molding of large structures such as contiguous vehicle hulls. In liquid-molding processes, quality-control 

sensors can ensure resin impregnation of the preform and cure of the resin after infiltration. For these purposes 

SMARTweave (SW), based on direct current (DC) sensing, is used as an in-situ flow-front detection and cure. 

monitoring system. SW measures change in the ionic conductivity with cure, which can then lx related to the material 

properties like viscosity and degree of cure. This enables in-situ measurement of degree of cure and viscosit] 

development during cure from SW measurements. This report builds on previous modeling work that assumed B 

direct dependence of DC resistance on the resin viscosity, limiting the use of such models beyond gelatlon. Tbis reporl 

presents a continuum model based on free volume theory to describe ionic conductivity through gelation tc 

vitrification. 

14. SUBJECT TERMS 

composite material, vinyl ester, SMARTweave, cure kinetics 

15. NUMBER OF PAGES 

145 

16. PRICE CODE 

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UNCLASSIFIED UXCLAS SIFIED UNCLASSED UL 

USN 75A,%nr.X&%~Vln Standard Fern? 298 IRw- 2-891 

139 299-102 
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140 
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