the rheological properties optimization of fumed silica dispersions using statistical experimental...

Polymer Testing17 (1998) 225–235 1998 Elsevier Science Ltd. All rights reserved

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EXPERIMENT DESIGN

The Rheological Properties Optimization of FumedSilica Dispersions Using Statistical Experimental Design

and Taguchi Method

Sangwoo Kim,a Jyongsik Janga* & Ohyoung Kimb

aDepartment of Chemical Technology, Seoul National University, San 56-1, ShinlimdongKwanakgu, Seoul, South Korea

bDepartment of Polymer Science and Engineering, Dankook University 8, Hannamdong,Yongsanku, Seoul, South Korea

(Received 21 July 1997; accepted 14 September 1997)

ABSTRACT

The rheological properties of fumed silica filled Bis-GMA dispersions were analyzedusing statistical experimental design and Taguchi method. Viscosity and shear thin-ning property were considered as the rheological properties. Silica content, silaneconcentration, diluent concentration, shear rate, and temperature were chosen assignificant factors. Statistical experimental design using analysis of variance andorthogonal array was applied to optimize the viscosity of the dispersions, and Tagu-chi’s parameter design was simultaneously performed to analyze the shear thinningproperty of the dispersions. Shear rate, silica content, andg-MPS concentrationshowed major effects on the viscosity, and silica contents andg-MPS concentrationalso had principal effects on shear thinning property of the fumed silica dispersions.Diluent concentration was determined as the only insignificant factor concerning theviscosity, while the temperature was the sole factor not to influence the shear thinningproperty of the dispersion. Optimum viscosity condition and less shear thinning con-dition were also determined using statistical experimental design and Taguchimethod. 1998 Elsevier Science Ltd. All rights reserved

*To whom correspondence should be addressed

225

226 Sangwoo Kim et al.

1 INTRODUCTION

Inorganic filler filled 2,29-Bis[4-(methacyloxy-2-hydroxy-propoxy)-phenyl]-propane (Bis-GMA) composites have been widely used as dental materials.Bis-GMA composites used to be highly filled with rigid inorganic fillers toimprove the mechanical properties.1–3 However, such high filler content drasti-cally increases the viscosity of dispersions and makes it difficult to performthe manufacturing process (e.g. mixing). Especially in the case of filling withfumed silica, which has a large surface area and submicron size, this phenom-enon is prominent. Therefore, it is important to understand the rheologicalphenomena (e.g. viscosity) of Bis-GMA dispersions heavily filled with fumedsilica in order to optimize the manufacturing process. However, rheologicalinformation concerning this system has been very limited.4–6

Rheological properties of fumed silica dispersions are affected by variousfactors such as the composition of dispersions, filler surface treatment, tem-perature, shear rate, and so on. In our study, the influence of these factors onthe viscosity of fumed silica dispersions was analyzed using a rheometricsmechanical spectrometer (RMS) and a syringe type rheometer. The mixingprocess and actual usage environment were simulated by shearing the disper-sions. The interrelationships between the above factors are complex, and theanalysis of this system to optimize the factors is a time and labour-consumingwork. Hence, the analyses using conventional experimental methods are inef-ficient.

The efficient analyses of the complex system using statistical experimentaldesign and the Taguchi method have been performed recently.7,8 The statisticalexperimental design can determine the effect of the factors on characteristicproperties and the optimum conditions of the factors. It uses the tables oforthogonal arrays and analysis of variance (ANOVA) as the tools of analysis.ANOVA can estimate the effect of a factor on the characteristic properties,and an experiment can be performed with the minimum replication using thetable of orthogonal array. Conventional statistical experimental design candetermine the optimum condition on the basis of the measured values of thecharacteristic properties, while Taguchi’s experimental design (also known asa robust parameter design) does this on the basis of the variability of character-istic properties. In other words, the Taguchi method can determine the experi-mental condition having the least variability as the optimum condition.9,10

The variability of a property is due to ‘noise factor’, which is a factordifficult to control. On the contrary, the factor easy to control is called ‘controlfactor’. The variability can be expressed by signal to noise (SN) ratio. TheSN ratios are defined differently according to the type of characteristic. In thecase that smaller characteristics are better, the SN ratio is defined as:

227Rheological properties optimization of fumed silica dispersions

FSN[db] = − 10logF1n On

i = 1

y2i GG

whereyi is the characteristic property,n is the replication number of theexperiment. The unit of SN ratio is decibel (db), which is frequently used incommunication engineering. The experimental condition having the maximumSN ratio is considered as the optimum condition, as the variability of charac-teristics is in inverse proportion to the SN ratio. Consequently, the Taguchimethod can determine the condition of least variability by the SN ratios.

In this study, statistical experimental design and Taguchi’s parameter designwere carried out simultaneously. The first can be considered as the raw dataanalysis, for it focuses on the measured value itself, and the latter as the SNdata analysis. By raw data analysis, the effects of several factors on the vis-cosity of dispersions were analyzed. Silica content, silane concentration, dilu-ent concentration, shear rate and temperature were chosen as significant fac-tors. In the case of SN data analysis, shear rate was chosen as a noise factor.Accordingly, the dependency of viscosity on shear rate, i.e. the shear thinningproperty, was investigated by SN data analysis. It is important in controllingthe manufacturing process of Bis-GMA/silica composites to analyze thedependency of viscosity on shear rate. The influence of the other factors,except shear rate, on the shear thinning property was also analyzed by SNdata analyses. Therefore, the first purpose of this study is to evaluate the effectof several factors on the viscosity of fumed silica filled Bis-GMA dispersionsand to optimize the factors using statistical experimental design. The secondobjective of this study is to analyze the influence of the factors on the shearthinning property of the dispersions by Taguchi’s parameter design,

2 EXPERIMENTAL

2.1 Materials

Bis-GMA was used as a matrix resin and triethylene glycol dimethacrylate(TEGDMA) as a diluent. Bis-GMA and TEGDMA were supplied by Shin-Nakamura Chemical Company (Wakayama, Japan). Molecular structures ofthe resin and diluent are illustrated in Fig. 1. The fumed silica used wasAerosil OX-50 supplied by Degussa company (Frankfurt, Germany) with pri-mary particle size of 0.04mm and surface area of 50 m2/g. The silane couplingagent used for the filler surface treatment wasg-methacryloxy propyl trime-thoxy silane (g-MPS) supplied by Korea Dow Coring company (Seoul,Korea).


Fig. 1. Molecular structures of matrix resin and diluent.

2.2 Sample preparation

The silica surface was treated with prehydrolyzedg-MPS. g-MPS washydrolyzed for 1 hr in an aqueous solution of 70 wt% ethanol/30 wt% de-ionized water. The silane treated silica was dried for 20 days at room tempera-ture. Fumed silica filled Bis-GMA dispersions were made by mixing the silanetreated fumed silica and the mixture of Bis-GMA and TEGDMA

2.3 Orthogonal array and experimental factors

The orthogonal array of L8 type was used, and is represented in Table 1. Land subscript 8 means respectively Latin square and the repetition number ofthe experiment. Instead of 3-level factors, 2-level ones were adopted, becauseviscosity showed no maximum and minimum points over the entire regionsof all significant factors.10 Seven 2-level factors can be positioned in a L8orthogonal array table. Two columns of the orthogonal array were assignedas error terms to increase the accuracy of the analyses. The numbers 1 and 2in Table 1 respectively indicate the first and second levels of a factor. Thecontrol and noise factors and their levels used in this experimental design arelisted in Table 2. The levels were determined according to the usage levelsof commercial Bis-GMA/silica composites.12,13 The maximum and minimumlimits of the factors used in commercial Bis-GMA/silica composites were


TABLE 1Orthogonal array table of L8 and measured values of shear viscosity

Factors A B C D E Error Error Shear viscosity*(Pa s x102)

Row no. Noise factor(Shear rate)

Exp. no. 1 2 3 4 5 6 7 1 s−1 100 s−1

1 1 1 1 1 1 1 1 548.90 1.282 1 1 1 2 2 2 2 363.29 0.303 1 2 2 1 1 2 2 149.52 0.914 1 2 2 2 2 1 1 4.13 0.085 2 1 2 1 2 1 2 462.61 1.656 2 1 2 2 1 2 1 214.33 0.167 2 2 1 1 2 2 1 0.51 0.038 2 2 1 2 1 1 2 0.30 0.01

*Mean value of 3 repeated measurements.

TABLE 2Factors and levels used in this experiment

Levels

Control factors 1 2

A: g-MPS concentration (wt%) 1 20B: Silica content (wt%) 60 40C: TEGDMA concentration (wt%) 60 40D: Temperature (°C) 30 100E: Shear rate (s−1) 1 100

Noise factor

Shear rate (s−1) 1 10 100

adopted as the first and second levels. In case of raw data analysis, shear rate(E) acted as a control factor, while it was a noise factor in the case of SNdata analysis. ANOVA-TM software was used as a tool of analysis.


2.4 Measurements

The viscosity of the dispersions was measured using RMS (RMS-800, Rheo-metrics corporation). Data were obtained in the parallel plate mode. Steadytype mode was applied to measure the viscosity. The typical range of shearrate of mixing and extrusion is from 10° to 102 s−1.14 Viscosity in this rangeof shear rate was mainly investigated. In the case of steady mode, however,reliable viscosity data at high shear rate (above 10 s−1) could not be obtaineddue to splitting between the sample and plate. Therefore, viscosity at 102 S−1

shear rate was measured using a syringe type rheometer, which consists ofsyringe and universal testing machine (UTM, Inston 4201). The syringe con-taining the dispersion was compressed with the UTM. Load and crossheadspeed can be easily converted into viscosity and shear rate using followingequations.

P = Khdxdt

(1)

g =4Qpr3 =

4R2

r3

dxdt

(2)

whereP = load pressure (Pa)K = constanth = viscosity (Pa•s)dx /dt = crosshead speedg = shear rateQ = volume flow rater = radius of syringe tipR = radius of syringe barrel

K is a constant related to the syringe dimension.P was measured at differentcrosshead speeds andh was calculated by eqn (1). Crosshead speeds can beconverted into shear rates using eqn (2). More detailed theory is presentedelsewhere.15

3 RESULTS AND DISCUSSION

The results of viscosity measurements are listed in Table 1. The ANOVAresults of raw data are represented in Table 3. The ‘significance’ of the control


TABLE 3ANOVA table of raw data

Factors Pool Variance F rho%

A N 28.10 5.53 8.75B N 66.23 12.05 23.91C Y 8.79 – –D N 45.30 8.92 15.59E N 94.61 18.64 35.20

error – 43.05 – 16.55

factors on viscosity can be estimated by the result of the ANOVA process.The significance means the extent of a control factor’s effect on viscosity,and can be determined using the F values of the F-distribution. The F valueswere used to determine whether a control factor can be pooled to an errorterm or not. The confidence level of this experiment was 95%. The resultsshow thatg-MPS concentration (A), fumed silica content (B), temperature(D), and shear rate (E) have significant effect on viscosity, but TEGDMAconcentration (C) has no significance and was pooled to the error term. Rho%in Table 3 indicates the actual percentage of a control factor’s effect on vis-cosity. According to the rho%, shear rate has the largest significance, andsilica content also shows a relatively large significance.g-MPS concentrationhas relatively low influence on viscosity. The difference of viscosity betweeng-MPS treated and untreated dispersions is prominent. However, the differ-ence is reduced wheng-MPS treated ones were compared with each other.This is whyg-MPS concentration shows lower influence than expected. It isalso unexpected that TEGDMA concentration has no significance on viscosity.This result may be due to the range of TEGDMA concentration being limitedso as not to reduce the mechanical properties and depth of cure of Bis-GMA/silica composites. To summarize the above results, viscosity of fumedsilica dispersions can be efficiently controlled by the shear rate (or mixingrate) and filler content.

Table 4 shows the ANOVA result of SN data. As mentioned previously,the ANOVA process of SN data analyzes the effect of each factors on theshear thinning property of the fumed silica dispersions. Silica content (A) hasthe largest significance on the SN data, andg-MPS concentration (B) is next.That is, silica content shows the greatest influence on the shear thinning pro-perty of the dispersions. TEGDMA concentration (C) has significance in theSN data, while it has none in the raw data. However, temperature (D) givesthe opposite result. This means that TEGDMA concentration affects only theshear thinning property of the fumed silica dispersions, but that temperature


TABLE 4ANOVA table of SN data

Factors Pool Variance F rho%

A N 427.25 16.78 18.12B N 1419.64 55.77 62.88C N 268.33 10.45 10.96D Y 85.13 – –

error – 25.45 – 8.04

only has influence on the viscosity of the dispersions. To summarise, theANOVA results of raw and SN data, shear rate, silica content, andg-MPSconcentration are the factors having the major effect on the viscosity and shearthinning property of the fumed silica dispersions, with TEGDMA concen-tration and temperature having relatively minor effects.

The optimum conditions can be determined through the response table ofthe ANOVA-TM software. The level average graph of the raw data is illus-trated in Fig. 2. The level average means the mean viscosity of a level. Inthis experiment, two levels are enough to analyze the factors, because viscosityof the dispersions shows no maximum points over the whole regions of allfactors. The first and the second levels in Fig. 2 were adopted respectively asthe minimum and maximum limit values used in commercial Bis-GMA/silica

Fig. 2. Level average graph of raw data.


composites. Therefore, all regions of the factors were fully considered. As theviscosity is a ‘the smaller the better’ case, the combination of the levels havingthe lowest level averages is the optimum condition. The optimum conditionof raw data is A2, B2, D2, and E2 (A2 indicates the second level of factorA). Viscosity is the lowest at the optimum condition of raw data means. Inthe case of SN data, when the levels have the lowest level averages, viscosityis the most robust to the noise factor. In other words, shear rate shows theleast influence on viscosity at that condition. Figure 3 shows the level averagegraph of SN data. The level combination with the lowest level averages ofSN data indicates the condition of least shear thinning property, and viceversa. In this analysis, least shear thinning condition was determined as anexample. As shown in Fig. 3, that condition is A2, B2, and C1. This conditionis similar to the optimum condition of raw data, i.e. the lowest viscosity con-dition. It indicates that viscosity is robust to shear rate as it decreases. Opti-mum viscosity condition and least shear thinning condition are summarizedin Table 5.

It is desirable that the optimum condition is determined considering othermechanical properties at the same time. If other mechanical properties aretaken into account, the optimum condition of the internal or compositionalfactors (silica content,g-MPS concentration, and TEGDMA concentration)has to be reconsidered. Higher silica content and lower TEGDMA concen-tration are needed to promote the mechanical properties of Bis-GMA/silicacomposites, e.g. hardness, compressive strength, and fracture toughness.1–3

Fig. 3. Level average graph of SN data.


TABLE 5The optimal condition of viscosity and the condition of less shear thinning property

Levels

Factors Raw data SN data

Silane concentration (wt%) 20 20Silica content (wt%) 40 40

TEGDMA concentration – 60(wt%)

Temperature (°C) 100 –Shear rate (s−1) 100 –

However, viscosity of the fumed silica dispersions is inclined to be high atthat condition. Tensile strength of Bis-GMA/silica composites is mainly affec-ted by g-MPS concentration, and it has the maximum value near 5 wt%g-MPS concentration.16 Viscosity of the fumed silica dispersions is also rela-tively high at this concentration. Therefore, the optimum conditions of othermechanical properties are different from that of viscosity. Shear rate and tem-perature, especially shear rate, efficiently control the viscosity, as shown bythe above results. They can be called external factors. Fortunately, they donot change the mechanical properties of Bis-GMA/silica composites withinthe regions used in this experiment.11 Therefore, viscosity of fumed silicadispersions can be effectively controlled by the external factors, especiallyshear rate, without the loss of mechanical properties. Consequently, it is betterto reduce the viscosity of fumed silica dispersions by external factors insteadof internal factors.

4 CONCLUSIONS

Rheological properties of fumed silica filled Bis-GMA dispersions were inves-tigated using statistical experiment design and the Taguchi method. Variousfactors affecting the viscosity and shear thinning property of the dispersionswere analyzed and optimized. The followings are concluded from the aboveresults.

(1) Shear rate, silica content, andg-MPS concentration are the factors hav-ing major effects on the viscosity and shear thinning property of thefumed silica dispersions.

(2) TEGDMA concentration and temperature had relatively minor effectson viscosity and shear thinning property.


(3) Optimum viscosity condition was 20 wt%g-MPS concentration, 40wt% silica content, 100°C temperature, and 100 s−1 shear rate. Leastshear thinning condition was 20 wt%g-MPS concentration, 40 wt%silica content, and 60 wt% TEGDMA concentration.

(4) It is desirable to control the viscosity of fumed silica dispersions byexternal factors instead of internal factors.

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