Ind. Eng. Chem. Res. 1998, 37, 1335-1340
1335
Rheological Properties of Poly(dimethylsiloxane) Mamdouh T. Ghannam† and M. Nabil Esmail*,‡ Department of Chemical Engineering, University of Saskatchewan, 110 Science Place, Saskatoon, Canada S7N 5C9, and Department of Mechanical Engineering, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Canada H3G 1M8
Poly(dimethylsiloxane) solutions are widely used in coating mixtures of many industrial coating processes. The flow of these solutions in and around the coating devices is strongly dependent on their rheological properties. This work presents a comprehensive experimental study of these properties. The tests were carried out for two poly(dimethylsiloxane), PDMS, solutions with vastly different viscosities, 1000 and 30 000 mPa‚s. The measurements were taken on the RheoStress RS100 rheometer of Haake, over the range of temperatures 10-50 °C. The solutions were tested for steady shear values, thixotropic behavior, transient shear stress response, yield stress values, creep-recovery response, and dynamic response. Introduction The silicon fluids poly(dimethylsiloxane)s are widely used in many industrial applications due to their numerous advantages. In particular, they are transparent liquids that have remarkable mechanical, chemical, and thermal stabilities. Among other features, poly(dimethylsiloxane) (PDMS) solutions have low surface tension coefficients, around 20 dyn/cm, and high zero-shear viscosity values of up to 30 000 mPa‚s. They are polymers melted at ambient temperature. Consequently they can be used cold. They have been commonly used in the production of fiber-optic cables. They are commonplace in many industrial coating mixtures in paper-coating processes. In general, PDMS has been used in coatings, seals, gaskets, adhesives, and medicine (Moore et al., 1984). Poly(dimethylsiloxane) is a silicon polymer, originally developed for use as a dielectric coolant and as a solution in solar energy installations. Its resistance to degradation is the result of the high energy (106 kcal/mol) and the relatively large amount of ionic character of the siloxane bond. PDMS maintains thermal stability and its mechanical, chemical, and electric properties between -70 and 250 °C. In the absence of oxygen, PDMS degrades at temperatures greater than 350 °C to give cyclic products. Oxidative degradation generally occurs at lower temperatures. So, PDMS is highly resistant to oxidation and to biodegradation by microorganisms. Companik et al. (1994) studied the effect of chain length and ion size on the viscosity and ion conductivity of poly(dimethylsiloxane) systems. They applied free volume, Arrhenius type viscosity, and ion conductivity models. Graebling et al. (1989) studied the viscoelastic properties of poly(dimethylsiloxane)-poly(oxyethylene) blends. They characterized the polymer blends by high values of the storage modulus at low frequencies and by long relaxation times. They related the rheological behavior to a few physically significant parameters such * To whom correspondence should be addressed. Telephone: (514) 848 3060. Fax: (514) 848 4509. E-mail: esmail@ encs.concordia.ca. † University of Saskatchewan. ‡ Concordia University.
as the zero-shear viscosity of phases, the dispersed particle size, and the interfacial tension between phases. Allcock et al. (1981) described the importance of PDMS applications in medicine, which is due to its resistance to blood fluids. Knowledge of the rheological properties of PDMS solutions is essential for the proper operation of all the industrial and other applications that involve this material. Although some studies have been published on some of the aspects of these properties, there is a need for more comprehensive studies. In this work we present such a study. It includes the depiction of the rheological fingerprints of two PDMS solutions with the zero-shear viscosities 1000 and 30 000 mPa‚s. For the sake of brevity we call these solutions PDMS1 and PDMS30, respectively. Also included in the study are the transient shear stress responses, the measurements of yield stresses, the thixotropy, and the creep-recovery tests.
Description of Measurements All tests were conducted on the Haake rheometer RheoStress RS100, which is computer-controlled. The apparatus has three modes of operation. Samplers can be tested under controlled rate (CR) mode, controlled stress (CS) mode, or oscillation (OSC) mode. One of the advantages of this rheometer is its almost frictionless transmission of the applied stress. This is primarily due to its air bearing, which centers its drive shaft. The resulting deformation in the sample is detected by a digital encoder. Particularly small yield values, strains, or shear rates can be precisely measured. Software packages are used to control test routines and data analyses. All tests were conducted using a cone and plate. The cone diameter is 35 mm. Its angle is 4°. The gap at the tip of the cone is 0.137 mm. The liquids used in the experiments were poly(dimethylsiloxane) 200 from Aldrich Chemical Company Inc., Milwaukee, WI. Solutions of two different viscosities, 1000 mPa‚s (PDMS1) and 30 000 mPa‚s (PDMS30), were used.
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1336 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998
Figure 1. Viscosity of PDMS1 and PDMS30 versus shear rate.
Figure 2. Viscosity of PDMS1 as a function of temperature.
Results and Discussion Steady Shear Flow Study. In many industrial applications PDMS solutions are subjected to steady shear. Their flows are dependent on their viscous behavior under different shear rates. Samples of PDMS1 and PDMS30 were tested under conditions of steady shear flow. Figure 1 shows the rheological fingerprints of PDMS1 and PDMS30 at the temperature 20 °C. It is obvious that PDMS1 experiences Newtonian behavior over the entire range of shear rates. Its viscosity was 1000 mPa‚s. However tests show that PDMS30 changed its behavior over two ranges of shear rates. At lower shear rates the shear stress of PDMS30 is proportional to the shear rate. Its viscosity was around 30 000 mPa‚s, the so-called zero-shear rate viscosity η0. At shear rates of about 100 s-1, the PDMS30 viscosity starts to decrease with higher shear rates. El Kissi et al. (1992) reported similar behavior for PDMS solutions. They reported a dramatic decrease in the viscosity of PDMS from about 104 to 20 Pa‚s, over the shear rate range 0.01-1000 s-1 with a critical shear around 0.9 s-1. The decrease observed in our experiments is larger. Although the molecular origin of the unusual properties is still unclear, a number of suggestions have been put forward. One involves low intermolecular interactions. Others focus on differences between the nonpolar Si-O backbone of PDMS and the very high rotational and oscillatory freedom of its methyl side groups. The slope of the rheological fingerprint of a pseudoplastic fluid is determined by an empirical power-law description. The transition from the initial Newtonian range to the pseudoplastic range depends largely on the molecular weight distribution of the liquid. At very high shear rates the viscosity may again become independent of shear rates, approaching the infinite-shear rate viscosity η∞. For concentrated solutions and melts η∞ is not usually measurable, since polymer degradation becomes a serious problem before sufficiently high shear rates can be obtained. The behavior of PDMS30 under steady shear flow in the range above 100 s-1 is shear thinning or pseudoplastic behavior. Almost all macromolecular fluids show this type of rheological properties. The decreasing viscosity with increasing shear rates is utilized for these macromolecular fluids in many high-speed industrial operations, particularly in liquid-coating technology.
Figure 3. Viscosity of PDMS30 as a function of temperature.
The influence of temperature on the rheological fingerprints of PDMS1 and PDMS30 is shown in Figures 2 and 3. The results are shown for the temperature range 10-50 °C. The viscosity-shear rate curves evidently show the same qualitative behavior at different temperatures. PDMS1 solutions exhibit Newtonian behavior over the entire range of shear rates for all temperatures. Their viscosities decrease by almost 45% (from 1200 to 660 mPa‚s) when the temperature is raised from 10 to 50 °C. This behavior can be represented by the Arrhenius relationship
η ) ae-b/T
(1)
Generally the greater the viscosity, the stronger is the temperature dependence. Regression analysis was carried out to fit the experimental data in the case of PDMS1 with the Arrhenius equation. The result was found to be
η ) 7.43e1452/T However, PDMS30 shows two distinct ranges of Newtonian and non-Newtonian flow behaviors separated by a critical shear rate around 100 s-1. Over the initial range of Newtonian flow, the viscosity of PDMS30 decreases with temperature from 10 to 40 °C and
Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1337 Table 1. Carreau-Yasuda Model T, °C
η0
η∞
λ
n
c
10 20 30 40 50
37 000 30 000 25 000 16 000 18 000
0 0 0 0 0
0.0029 0.0029 0.0029 0.0028 0.0029
0.5 0.5 0.5 0.5 0.5
2 2 2 2 2
slightly increases at 50 °C. As a result, regression analysis using the Arrhenius formula yields the relationship
η ) 41.21e1919/T Over the tested non-Newtonian range of shear rates 100 < γ˘ < 1000 s-1, shear thinning behavior was recorded for all temperatures. Generally the effect of shear rate is extremely severe on the flow behavior of PDMS30. For example at 10 °C the viscosity of PDMS30 decreases from 37 000 mPa‚s at 30 s-1 to almost 0.3 mPa‚s at 700 s-1. This effect represents a depression of five orders of magnitude over a shear rate range of less than 700 s-1. The Carreau-Yasuda model can be used with regression analysis to represent the behavior of PDMS30, in the range of shear rate γ˘ < 100 s-1.
(η - η∞)/(η0 - η∞) ) [1 + (λγ)c](n-1)/c
Figure 4. Transient response of PDMS30.
(2)
where η is the apparent viscosity, η0 is the zero-shear viscosity, η∞ is the second Newtonian viscosity, λ is the relaxation parameter, c is a constant related to the transition between the first Newtonian region and the power-law region, and n is a power-law constant. Table 1 shows the regression parameters of the CarreauYasuda model. However, the temperature effect has a slightly opposite effect on the flow behavior of PDMS30 in the range 100-1000 s-1, where the viscosity is represented by the power-law model. The viscosity of PDMS30 increases with an increase in temperature from 10 to 50 °C. At high shear rates (>300 s-1) the cross-link structure of PDMS30 may become more open with temperature, resulting in an increase in resistance to flow (Clough et al., 1996). This idea is the basis of polymer-thickened multigrade oils designed to maintain good lubrication at high temperatures. Transient Shear Stress Response. It is important to study the transient shear behavior for rheologically complex materials. The shear stress response of PDMS1 and PDMS30 was measured as a function of shear rate and time to examine the transient behavior of poly(dimethylsiloxane) solutions. A wide range of constant shear rate of 10-700 s-1 was applied, and the shear stress response was recorded over a period of 10 min. PDMS1 showed no transient behavior over the entire range of shear rate and time. However, PDMS30 experienced a gradual decrease of the shear stress response within the first 250 s to a constant value for each applied shear rate. The response shear stress steadily decreased with shear rate (>50 s-1). The thixotropic behavior (i.e. decreasing shear stress or viscosity with time at a fixed shear rate) was observed for PDMS30 at all shear rates of higher than 50 s-1 (Figure 4). Although a thixotropic behavior was observed for the shear rate range 500-700 s-1, there was a significant scatter in the shear stress-time data at this high shear rate. More details will be given later about the thixotropic structure of PDMS solutions.
Figure 5. Yield stress response to PDMS1 and PDMS30.
The gradual decrease in shear stress or viscosity with time is believed to be due to a limited structure breakdown at shear rates >50 s-1. Yield Stress. Materials that exhibit the yield stress phenomenon, when subjected to stress below the yield value, behave as a solid experiencing elastic deformation linearly proportional to the applied stress. When the applied stress exceeds the yield value, an unlimited deformation ensues and the material starts to flow. In this case the applied stress is proportional to the rate of deformation, with viscosity as the proportionality factor. Samples of PDMS1 and PDMS30 were subjected to yield stress tests. The controlled stress mode of the rheometer was employed by ramping the applied stress from 0.09 to 10 Pa to establish the so-called up curve. Then, the assigned stress was instantaneously ramped down from 10 to 0.09 Pa to develop the down curve. Figure 5 shows a typical flow behavior when using this technique. In CS mode, the RS100 applies shear stress by means of an extremely low inertia. Analysis was carried out using the Bingham correlation to determine the up and down yield stress for each solution. The analysis showed no yield stress for PDMS1. However the values 1.31 and 0.42 Pa were obtained for the up and down yield stresses of PDMS30.
1338 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998
Figure 6. Thixotropic behavior of PDMS1 and PDMS30.
Figure 7. Creep-recovery behavior of PDMS1.
Table 2. Thixotropic Hysteresis Areas
the higher viscosity of PDMS30 and its stronger transient response compared to those of PDMS1. Creep-Recovery. The creep and recovery test is usually used to study some of the viscoelastic features of the examined material. The deformation response in the viscoelastic material to an applied stress is a function of time. The structure network of the viscoelastic material is deformed within its mechanical limits. Continuous deformations lead to the dismantling of the network, and finally the viscoelastic material starts to flow. When the applied stress is released, the total substance deformation includes a permanently maintained viscous part and a recovery elastic part. To conduct a creep-recovery test, the linear viscoelastic range is initially defined by applying different values of constant shear stress for a certain period of time. The advantage of the linear viscoelasticity is that it is a nondestructive test of measuring the rheological behavior of a substance. High values of applied stress usually cause a nonlinear viscoelastic response. Therefore test results depend upon its conditions and system parameters. However lower values of applied stress provide a linear viscoelastic response, and the response measured by the compliance is independent of the applied stress. Consequently, in the linear viscoelastic range, the compliance J(t) values measured at different shear stresses should coincide. In the nonlinear viscoelastic range, the curve representing compliance separates significantly from the curve produced in the linear range. Initially a creep test was used to determine the linear viscoelastic range for PDMS1 and PDMS30. To study the viscoelastic behavior of poly(dimethylsiloxane), constant shear stresses of different values were applied for 300 s to establish the creep curves. Then the applied stress was instantaneously set to zero and the response was recorded over 300 s. The feature of frictionless airbearing of the RheoStress RS100 is extremely important for observation of the final recovery when the applied stress was brought to zero. Compliance data J(t) for PDMS1 and PDMS30 were recorded over 10 min at different values of applied shear stress. PDMS1 shows a viscous behavior in terms of its compliance J(t) over the applied range of shear stress 1-14 Pa with no significant influence for the applied shear stress itself. A slightly viscoelastic behavior was reported for PDMS30 in the recovery region at 1 Pa, whereas viscous behavior
test no.
hysteresis area for PDMS1, Pa/s
hysteresis area for PDMS30, Pa/s
1 2 3 4 5
1923 5886 6680 2325 2347
526 474 562 809 784 207 474 770 384 481
Thixotropy. From the previous discussion of the transient behavior, PDMS30 was expected to show thixotropic behavior. The thixotropy test was carried out for PDMS1 and PDMS30 using the controlled rate mode of the rheometer RS100. The test was executed by programming the shear rate to increase from an initial small value to a terminal value to establish the up curve. Then the shear rate was gradually decreased from the terminal value back to the initial value to develop the down curve. The down curve of a thixotropic structure is different from its up curve. The curves form a hysteresis process with an area A. The hysteresis area A has a dimension of energy per volume, that is, the energy required to destroy the thixotropic structure of the tested solution. Usually the total breakdown of the thixotropic structure may take more than one cycle of up and down curves. Therefore, a number of up and down cycles may be required before the up and down curves coincide. In another effective technique, the sample is sheared at the constant upper shear limit for some time before the shear rate is ramped back to its initial small value. Five different tests were carried out to determine the best technique to completely break down the PDMS structure. Test 1 consisted of a single cycle of an up curve from 0.15 to 700 s-1 and a down curve from 700 to 0.15 s-1, 2 min each. Test 2 consisted of three cycles of test 1. Test 3 had a three-part cycle of an up curve, 0.15-700 s-1, a constant shear at 700 s-1, and a down curve, 700-0.15 s-1. The period of each step was 1 min. Tests 4 and 5 are similar to test 3 with the time periods 2 and 3 min, respectively. Figure 6 shows the thixotropic behavior of PDMS solutions for test 3. The results of these tests are reported in Table 2. It is clear that test 3, which lasts only for 3 min, provided the highest thixotropic area for both PDMS1 and PDMS30 solutions. PDMS30 shows a higher thixotropic area than PDMS1 for all tests. That is due to
Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1339
Figure 8. Viscous modulus-frequency of PDMS1 and PDMS30.
Figure 9. G′ and G′′ versus frequency for PDMS30.
was observed with applied shear stress of values up to 400 Pa with the response independent of shear stress. The compliance response for PDMS1 was around 300 Pa-1, which is about 30 times the compliance of PDMS30. Figure 7 is a typical example for PDMS1. It shows the response of the creep-recovery test in terms of strain γ%, over a time period of 600 s at different values of applied shear stress in a linear viscoelastic range of up to 14 Pa. PDMS1 shows a viscous behavior with a response dependent on the applied shear stress. Almost a similar behavior was observed for PDMS30 but at higher applied shear stresses. Dynamic Test. In a dynamic test oscillating stresses or strains are applied to the test sample to measure the storage modulus G′ and the loss modulus G′′. The storage modulus quantifies the elastic response of the sample. The loss modulus indicates the level of viscous response experienced in the test. The substance complex modulus G* represents the total resistance versus the applied strain, and it can be calculated from
Conclusions
G* ) τ0/γ0
(3)
G* ) G′ + iG′′
(4)
A dynamic test usually starts by defining the linear viscoelastic range. This is done by automatically increasing the stress to cover a wide range. The range where G* is constant with stress is the linear viscoelastic range. This indicates that the internal bonds of the sample are still intact. Stress sweeps were carried out for PDMS1 and PDMS30 samples, and the linear viscoelastic range was found to be around 50 Pa. A frequency sweep test was carried out at the stress value 5 Pa to study the viscoelastic behavior of PDMS1 and PDMS30. Figure 8 shows the viscous modulus G′′ for PDMS1 and PDMS30 over the frequency range 1-30 rad/s. PDMS30 has a higher viscous modulus than PDMS1 over the entire range of tested frequencies. PDMS1 does not show any elastic response, G′. The conclusion is that this test confirms the results of the creep-recovery test regarding the pure viscous behavior of PDMS1. Figure 9 shows the viscous and elastic moduli for PDMS30. It is clear that PDMS30 samples revealed viscous as well as elastic components in their response. However, the viscous response was higher than the elastic over the entire range of frequencies.
The rheological properties of poly(dimethylsiloxane) have been investigated in a comprehensive study of two solutions: PDMS1 and PDMS30. These properties are extremely important input for many industrial coating processes that utilize PDMS in the coating mixture. PDMS1 samples consistently showed Newtonian behavior over the entire range of shear rates to γ˘ < 1000 s-1, at all temperatures from 10 to 50 °C. They showed no transient rheological behavior but exhibited a weak thixotropic response. In creep-recovery tests PDMS1 showed viscous behavior over the range of shear stress without experiencing any influence by τ. The Newtonian viscosity of poly(dimethylsiloxane) solutions generally decreases with temperature from 10 to 50 °C. The Arrhenius model can be used to describe this behavior. However, above a shear rate of 300 s-1 the viscosity of the pseudoplastic PDMS30 gradually increases with temperature from 10 to 50 °C. PDMS30 experiences a strong thixotropic behavior within the first 250 s with shear rates higher than 50 s-1. Values of 1.31 and 0.42 Pa were measured for the up and down yield stresses of PDMS30. PDMS30 has a thixotropic structure more than 100 times stronger than that of PDMS1. Test 3 in the thixotropic study provided the best conditions for the destruction of the PDMS thixotropic structure. Creep-recovery tests showed a pure viscous response for PDMS1 over the entire range of stress testing 1 < τ < 14. However, PDMS30 revealed an elastic response at the lower stress value τ ) 1 Pa. For higher stress values PDMS30 experienced a pure viscous response. However the viscous component of the PDMS30 response is much higher than its elastic response at τ ) 1 Pa. Nomenclature A ) thixotropic area, Pa/s a, b ) liquid constants of eq 1 c ) transition factor between the initial Newtonian and the power-law ranges k ) consistency index, mPa‚sn m ) fluid behavior index n ) power-law constant of eq 2 J ) compliance, Pa-1 G* ) complex modulus, Pa
1340 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 G′ ) storage modulus, Pa G′′ ) loss modulus, Pa T ) temperature, K w ) frequency, rad/s Greek Letters η0 ) zero shear viscosity, mPa‚s η∞ ) second Newtonian viscosity, mPa‚s η ) liquid viscosity, mPa‚s λ ) relaxation parameter γ˘ ) shear rate, s-1 γ ) strain, % γ0 ) strain amplitude, % τ ) shear stress, Pa τ0 ) stress amplitude, Pa
Literature Cited Allcock, H.; Lampe, F. Contemporary Polymer Chemistry; PrenticeHall Inc.: Englewood Cliffs, NJ, 1981.
Clough, R. L.; Billingham, N. C.; Gillen, K. T. Polymer Durability; American Chemical Society: Washington, DC, 1996. Companik, J.; Bidstrup, S. The Viscosity and Ion Conductivity of Polydimethylsiloxane Systems: 1. Chain Length and Ion Size Effects. Polymer 1994, 25 (22), 4823. El Kissi, N.; Piau, J. M.; Attane, P.; Turrel, G. Shear Rheometry of PDMS. Master Curves and Testing of Gleissle and Yamamoto Relations. Theor. Appl. Rheol. 1992, Aug. 17-21, 197. Graebling, D.; Froelich, D.; Muller, R. Viscoelastic Properties of Polydimethylsiloxane-Polyoxyethylene Blends in the Melt. Emulsion Model. J. Rheol. 1989, 33 (8), 1283. Moore, G.; Kline, D. Properties and Processing of Polymer for Engineers; Prentice-Hall Inc.: Englewood Cliffs, NJ, 1984.
Received for review May 9, 1997 Revised manuscript received January 8, 1998 Accepted January 9, 1998 IE9703346
