Development and Characterization of Magnetorheological Polymer Gels

Malcolm J. Wilson

Mail Stop 170

Chemical Engineering, University of Nevada, Reno

Reno, NV 89557

Tel: 775-784-4224

E-mail: mjw@nevada.unr.edu

Alan Fuchs*

Mail Stop 170

Chemical Engineering, University of Nevada, Reno

Reno, NV 89557

Tel: 775-327-2227

E-mail: afuchs@unr.edu

Faramarz Gordaninejad

Mail Stop 312

Chemical Engineering, University of Nevada, Reno

Reno, NV 89557

Tel: 775-784-6990

E-mail: faramarz@unr.edu

*Corresponding author

Keywords: Polyurethane, Silicone, Gels, Rheology, Kinetics
Abstract

Magentorheological materials have been used in many applications in recent years. To develop new materials, polyurethane and silicone polymer gels are investigated. Rheology is controlled for each system by controlling the concentration of reactants and diluents. The resulting polymers have solid, gel, or liquid states depending on the crosslinking and dilution. The gels are characterized through kinetic analysis. Differential Scanning Calorimetry (DSC) is used with kinetic methods to find the kinetic properties for diluted and undiluted polyurethane systems. Heat of reaction, order of reaction, pre-exponential constant, and activation energy is obtained from the experimental DSC data.

Introduction

Magnetorheological polymer gels (MRPGs) are a new generation of materials used for vibration control, damping and clutch applications as well as other energy absorption applications. These composite polymeric fluids permit control of viscosity, provide high yield stress and exhibit low particle settling behavior [1].

Magnetorheological fluids (MRFs) are commercially available magnetic fluids that are currently used for a variety of applications. These include use in automotive parts: engine mounts, shock absorbers, and seat dampers [2-6]. Other applications cover a range from exercise equipment to aspherical optical lens polishing. In the area of vibration control and damping, earthquake resistant structures are built that utilize these fluids using semi-active control [2,3,5-7].

MRFs excel in these applications because their rheological properties are controlled over several orders of magnitude. Without an applied magnetic field, the typical MRF acts like a Newtonian fluid [3,8]. When a field is applied, a dipole moment is induced in the particles in the MRF. This causes the particles to align “head-to-tail” and form chains of particles parallel to the magnetic field [3]. The MRF becomes a weak viscoelastic solid when the chain or column structures form. As the magnetic field increases, the material exhibits a rapid and nearly reversible increase in yield stress. Because of the change in material properties under the influence of a magnetic field, the MRF properties are controlled and therefore provide a new means of controlling electromechanical devices. [3,6,9]

While MRF may be similar to ferrofluids, they also have important differences. They are composed of three components like ferrofluids; thus, they have a carrier fluid, magnetic particles, and additives [10]. However, the particles used in ferrofluids are superparamagnetic iron oxide nanoparticles (~5-10 nm) [2,10]. As a result, they do not exhibit a shear yield stress like MRF while under an applied magnetic field [2,5]. This is due to a reduced tendency to form chains under a magnetic field. Rather, the field acts as a body force on the entire material. Thus, while viscosity changes can be observed, they are small [5,11]. In addition to being used in seals, the ferrofluids have applications in stepper motors and sensors [10].

For an MRF, magnetic particles, such as iron, can be suspended in a fluid. Under a magnetic field, these particles form chains [2,12,13] that significantly increase the yield stress of the material. The carrier fluid acts as the medium for other components. Suspended in the medium are the magnetic particles that form chains when a magnetic field is applied. Finally, additives are used to provide stability to the mixture, corrosion control, lubrication, anti-oxidants, pH shifters, dyes and pigments, salts, and deacidifiers [2,8,12,14].

Typically, the medium is a silicone oil or hydrocarbon fluid [2,8]. This is because it exhibits many of the properties that are desirable in MRF. Ideally, the fluid should be thermally stable, have a high boiling point. The carrier fluid should be noncorrosive and nonreactive with the magnetic particles and other components, and it should be nontoxic. The fluid should contribute to the stability of the mixture, but at the same time enable the redispersibility of the magnetic particles. The temperature dependence of the medium’s viscosity is also very important, and is in fact the dominating factor in the operating range of the MRF. Finally, the fluid should not cause sealing problems in the device in which it will be used [3,12].

The dispersed phase usually is a soft magnetic material such as iron particles of 1-10um size [2]. Several important factors must be considered in the choice of the dispersed phase. The volume fraction of the magnetic materials is usually 0.3 to 0.5 volume fraction of carbonyl iron. This leads to a reasonable yield stress but does not have the potentially undesirable higher off-state viscosity of a higher volume fraction [12]. The particle size has a great influence on the rheology of the on and off states of the fluid. For larger particles (5-7 um) the yield stress is greater than for smaller particles (~2 um). Particles larger than 10 um have increased settling and thus form less stable MRF. Several problems occur when the particles are too small. They are more influenced by the carrier fluid than the larger particles. They are also more sensitive to temperature [12]. Also, the possibility of agglomeration increases. Nano-MR Fluids are described in the literature [12,15]. BASF researchers created stable (by using polyelectrolyte adsorption) nano-MR fluids using ferrites (<100nm). However, the yield stress is only ~6 kPa and it is temperature sensitive [12].

The manufacture of iron and iron-based alloys is achieved using several methods: decomposition of iron pentacarbonyl, sol-gel ultrasonic decomposition of organometallic precursors, plasma torch synthesis, electroexplosion of metal wires, chemical reduction and precipitation, and laser ablation. Preferably, soft magnetic materials like iron are used for their high saturation magnetization. Fe-Co alloys have the highest saturation magnetization (~2.4 T), but cost and unavailability make them undesirable unless the higher material strength is needed. Ferrimagnetic materials such as manganese-zinc ferrite and nickel-zinc ferrite (~2um in size) have a lower saturation magnetization and thus they have a lower maximum yield stress. [12]

MRF additives are necessary to prevent agglomeration and settling. As the particles settle and the distance between them decreases, the small level of remnant magnetization could play a role in agglomeration. Some of the materials used as additives are nanostructured silica, fibrous carbon, and various polymers. Nanoscale silica forms a coating on magnetic particles as a thixotropic network [12].

Several approaches for development of MRFs are documented in the patent literature. Patent #5,985,168 describes the use of a bridging polymer to modify the surface of the iron particles. This approach leads to improved stability and redispersibility. In this patent only 3 polymers are described: polyvinylpyrollidone, polyethyleneamine and poly(4-vinlypyridine) [16].

Organic polymers are also used to coat the surface of iron particles that are described in Patent #5,989,447. This patent describes many families of polymers that are used and exhibit reduced abrasiveness and produce high stability with regard to settling [17].

Polymeric thixotropes are also described in Patent #5,645,752 [18]. The mechanism for stability in this invention is due to hydrogen bonding. A large number of polymeric materials are included in this patent for increased viscosity. They are used to exhibit minimum particle settling over a broad temperature range.

Polymerization of MRPGs either takes place before addition of the iron particles or in the presence of the iron particles. The latter case may result in precipitation of polymeric gels on the surface of the iron particles. This may have additional affect on the stability of the materials.

Polymers gels used in this investigation are polyurethanes and silicones. The rheology of each system is shown to be controllable. MRPGs are prepared by suspending iron particles in the polymeric gel before (or during, or after) crosslinking. Rheological properties are investigated with and without magnetic field. Because MRPGs can be developed at different levels of “off-state” properties through formulation of resin and crosslinkers, the material viscosity is custom suited to a particular device and in the case of dampers a fail-safe characteristic is possible. Additionally, since polymer crosslinking may also take place on the ferromagnetic particle surface by reaction taking place in the presence of the particles, settling of the ferromagnetic particles is reduced.

To investigate kinetic properties, several methods were examined. Ortega [19] describes a Controlled Rate Thermal Analysis (CRTA). The objective is to try to control rate of heating such that reaction rate remains constant. Sbirrazzuoli, Girault, and Elegant [20] describe several isoconversional (where properties are assessed at a set conversion) and peak maximum evolution (where properties are assessed at the thermal peak) methods of analysis. These include Friedman, Ozawa, “Ozawa corrected”, and Kissinger-Akahira-Sunose for isoconversional methods and Kissinger and Malek for peak maximum evolution methods. Single heating rate and multiple heating rate methods (such as Kissinger) may also be found in Turi [21]. The former is not well suited for systems reacting over a large time-temperature range. The Ozawa-Flynn-Wall method can be used as an isoconversional or as a peak maximum evolution multiple heating rate method [20,21].

Experimental

Materials

Three different matrix materials are investigated. A polyurethane system and a silicone system are all developed.

Polyurethanes are formulated from reactions between polyols and isocyanates. Two polyols are studied: a polyglycol and a polyether polyol. The polyglycols are linear polymers of alkylene oxides. The polyglycol used is polyethylene glycol (PEG), which has an average molecular weight of 600 and a functionality of 2.0 (Polyglycol E-600, Dow Chemical). A second polyurethane system is based on a polyether polyol (Voranol 360, Dow Chemical) with equivalent wt. of 162 and functionality of 4.5. The isocyanate used is polymethylene polyphenyl isocyanate (p-MDI, Dow PAPI 27) which has a functionality of 2.7 and the equivalent weight is 134. A non-reactive plasticizer used is propanol, oxybis-, dibenzoate (PODB, Benzoflex, Velsicol Chemical Corporation) [22].

A silicone polymer system is also investigated. Vinylpolydimethylsiloxane (VPDMS) resin is difunctional with a molecular weight of ~10,400 and contains a platinum catalyst (RTV6136A polymer gel, G.E Silicones). Dimethyl methylhydrogenpolysiloxane (DMMHPS) which is the hydride crosslinker composing about 5-10% by weight of the second part of the RTV silicone with the remainder VPDMS (RTV6136B polymer gel, G.E Silicones). DMMHPS has a molecular weight of ~10,400. Manufacturer recommendation is 1:1 wt/wt of part B to part A for forming the silicone gel. Low viscosity (5 cP) silicone oil (SF96-5, G.E Silicones) is used for viscosity control [23].

Instrumentation

For thermal analysis differential scanning calorimetry (DSC) is used. The Pyris 1 DSC (Perkin Elmer) is used to measure the heat flow relative to a reference. Temperature scans ranging from 0°C to 190°C are performed. From the heat flow data gathered, the heat of reaction, conversion, and kinetic constants can be evaluated. Analysis has been performed on the polyether polyol /p-MDI polyurethane system.

Procedure

For the polyurethane system, PODB is added to the polyether polyol. The p-MDI (cooled to about 10°C) is then added. The components are then mixed thoroughly. For DSC studies, the sample is placed into the pan and is weighed immediately after mixing. Cure is complete after about six hours at room temperature.

For the silicone system, silicone oil is added to the DMMHPS. VPDMS is then added. If the system will contain iron, it is added before thorough mixing. Complete cure takes place in about twelve hours at room temperature.

Results and Discussion

Phase Diagrams

After reaction the polymers are categorized as behaving as solid, gel, or liquid. Samples exhibiting properties of an elastic solid are identified as solid state behavior in the phase diagram. The liquid is characterized by viscous and freely flowing behavior. The gel has intermediate properties between the solid and liquid states. The dashed lines in Figures 1 to 3 have a positive slope that represents how as the stoichiometric ratio is increased, the material remains liquid at higher diluent concentrations.

Phase Diagram: Polyurethane Systems

By controlling the composition of the polyurethane using the three components described in the experimental section, the polyurethanes vary from a viscous liquid to a solid-like gel to an elastic solid. For a larger isocyanate index (the isocyanate index is the molar equivalent ratio of isocyanate to polyol), a greater degree of crosslinking occurs. With this increase, the polyurethane becomes more viscous. In the case of the PEG-600 system, shown in Figure 1[22] an index less than 45-55 typically results in a liquid. For an index greater than 70, the material is solid. Gels form between these indices as shown in the figure. Figure 2 shows the phase diagram for the polyether polyol system. In this system, without plasticizer, the gel region is at an isocyanate index of ~15-25, with liquids below an isocyanate index of ~10-15. Two samples sets were run for the isocyanate indices at 0% PODB and 7.5% PODB with consistent results.

Phase Diagram: Silicone System

A silicone polymer is composed of a resin and a crosslinker and diluted by silicone oil. Altering the ratio of the resin to the crosslinker and the percentage of silicone oil forms polymer gels. As can be seen by Figure 3, at low silicone oil levels, a large ratio of crosslinker to resin (greater than 1:1) will produce a rubbery solid, while a low ratio of crosslinker to resin (less than 1:5) will produce a viscous liquid. The formation of a gel at the 1:1 ratio with no diluent is consistent with manufacturer recommendations (G.E. Silicones). At high content of silicone oil, for example greater than 70%, the material remains a viscous liquid up to nearly 1:1 ratio and forms a gel at higher ratios. The dashed lines again reflect where the phase should change with a change in crosslinker/resin ratio or diluent concentration.

Reaction Kinetics

From the DSC heat flow data, heat of reaction can be found directly through integrating under the heat flow – temperature curve. By assuming that the heat flow is proportional to the conversion, the fraction of the area at any given point is the fraction of conversion. From this, the method of initial rates can be used to find order of reaction. Kissinger’s Method is employed to find the activation energy and pre-exponential constant.

To assess the order of the reaction, a least squares linear regression is completed on data using the initial rates method. In this method, we assume the reaction is represented by

-dC_A/dt = -r_A = kC_A^aC_B^b (1)

where k is the rate constant, C_A is the concentration of isocyanate, C_B is the concentration of polyol, a is the order of reaction with respect to A, and b is the order of reaction with respect to B. Initial values are designated with “°”. Thus initially,

(-dC_A/dt)° = -r_A° = k(C_A°)^a(C_B°)^b (2)

Taking the natural log of this equation linearizes it, and by performing experiments at different initial concentrations, different initial rates are found. The data may be then regressed to find the most suitable values for the parameters a, b, and ln(k).

Once the parameters are found, the order of reaction is determined. This is then used to find E_a and A from the Kissinger Method. The Kissinger Method is used to find kinetic properties by varying the heating rate for each experiment. Activation energy is found by

E_a = mR (3)

Where R is the gas constant and m is the slope of the line found by plotting –ln(f/T_max²) versus 1/T_max. f is the heating rate, and T_max is the peak temperature of the reaction. The pre-exponential rate constant is found by

A = [fE_a/(RT_max²)]/[e^-Ea/(RTmax)n(1-a_max)^n-1] (4)

N is the order of reaction, and a_max is the conversion at the peak temperature. This constant yields units of inverse time for an Arrhenius type rate constant.

Figure 4 shows the thermogram for two runs at C_A°=1.05 mol/L at a heating rate of 5 °C/min with no PODB. It is assumed that all the heat evolved is due to the reaction and thus conversion is proportional to the area under this curve. The first run shows a peak exotherm at 86.0°C and the second run shows a peak exotherm at 84.6°C for a difference of 1.7%.

The first experimental set is performed at different initial concentrations to find the order of reaction. The concentration of isocyanate ranged from 0.25 mol/L to 3.00 mol/L. Figure 5 shows a conversion versus time graph. This slope increases as the initial concentration increases until the stoichiometric concentration is passed, then it decreases again. This suggests that the rate is best when the two components are near stoichiometric values, since the rate is lowest as the reactions takes place furthest from stoichiometric. The initial rate was found for each run by numerically differentiating the concentration with respect to time. These values and the initial concentrations, shown in Table 1, are regressed to find the parameters of a and b as described above. a is found to be 1.90 and b is found to be 2.10 for an overall order of 4.00.

To find the activation energy and the preexponential constant, the next set of experiments is performed at 1.05 mol/L isocyanate, which is stoichiometric. These were conducted at three different heating rates: 5 °C/min, 10 °C/min, and 15 °C/min. Using Kissinger’s Method, the activation energy is found to be 46.5 kJ/mol. The value of the pre-exponential constant is on average 7.69x10⁹ min^-1. Figure 7 shows the plot with slope E_a. Repeat experiments for the different rates are + 2%. The difference is in the peak temperatures, which while close (~ 1.5 K) they are not identical.

These experiments were repeated for the polyurethane above and below isocyanate index 23 and diluted with 7.5% PODB. a is found to be 1.44 and b is found to be 1.82 for an overall order of 3.26. The heat of reaction varies depending on the index. For isocyanate index 10, the heat of reaction is –127 J/g while for isocyanate index 144 it is –319 J/g. Intermediate indexes show intermediate heats of reaction. Activation energy calculated from Kissinger’s Method is 49.0 kJ/mol. The preexponential constant is calculated to be 1.16x10¹⁰ min^-1 on average which again agrees with literature values.

These values are compared to literature values in Table 2. The values reported in the literature for the heat of reaction agree with literature. Little effect is noted between the diluted and undiluted systems as the heats of reaction cover almost the same range. The values for the preexponential constant and activation energy agree with the literature in both cases. However, the effect of diluent appears to be an increase in the pre-exponential factor. Reaction order is greater as calculated from data presented herein.

Conclusions

Magnetorheological polymeric gel (MRPG) systems have been developed which allow definable rheologies. This approach has been demonstrated in this paper for two families of polymeric gels: polyurethanes and silicones. In all cases adjusting the ratio of reactants and the concentration of modifier (reacting or nonreacting) yielded widely alterable rheological behavior from a liquid to an intermediate gel to a solid as crosslinking increases and diluent decreases. Kinetic characteristics of the polyurethane system have been investigated. Kinetic constants have been measured and pre-exponential constants and activation energy values are similar to those reported in the literature.

References

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Table 1: Initial Concentrations and Reaction Rates for pMDI / Polyether Polyol Polyurethane

System without PODB and Diluted by 7.5% PODB.

No PODB			7.5% PODB
Ca°(mol/L)	Cb° (mol/L)	-dCa°/dt	Ca°(mol/L)	Cb° (mol/L)	-dCa°/dt
0.25	1.39	2.38E-05	0.23	1.28	2.28E-05
0.50	1.28	6.32E-05	0.46	1.18	5.12E-05
1.05	1.05	7.83E-05	0.97	0.97	1.11E-04
2.00	0.66	4.57E-04	1.84	0.58	1.07E-04
3.00	0.24	4.51E-05

Table 2: Kinetic Properties of pMDI / Polyether Polyol Polyurethane System.

	w/o PODB	w/ 7.5% PODB	Literature Values
Heat of Reaction (kJ/NCO equiv.)	-14.8 to -46.5	-17.0 to -42.7	-9.46 to –24.0 [24] -60.3 [25]
Overall reaction order	4.00	3.26	1st order [25] 2nd order [24,26]
Pre-exponential Constant	4.37 x10^9 min^-1 to 1.45x10^10 min^-1	8.95 x10^9 min^-1 to 1.42 x10^10 min^-1	1.18x10^3 min^–1 to 4.36x10^10 min^–1 [24] 6.28x10^9 min^–1 to 1.31x10^10 min^–1 [25]
Activation Energy (kJ/mol)	46.5	49.0	25.5 to 64.9, average44.8 for pMDI / polyether polyol system w/catalyst [24] 61.1 for TDI/PEA system w/o catalyst [25] 32 to 48 for TDI/Polyglycol linear polyurethane system w/o catalyst [26]

Figure 1: Polyurethane phase diagram for the PEG-600 system. Decreasing index and increasing diluent results in more liquid-like state. Increasing index and decreasing diluent results in more solid-like state [22].

Figure 2: Polyurethane phase diagram for the polyether polyol system. Gel formation occurs close to an isocyanate index of 25

Figure 3: Silicone phase diagram. Decreasing index and increasing diluent results in more liquid-like state. Increasing index and decreasing diluent results in more solid-like state. Most gel formation is near the 1:1 by weight ratio of the DMMHPS/VPDMS component to the VPMDS/catalyst component.

Figure 4: Thermogram of polyether polyol / pMDI system. Reaction without catalyst results in broad peak over the temperature range. Two runs shown are both for Ca°=1.05 mol/L at a heating rate of 5 °C/min with no PODB.

Figure 5: Conversion of polyurethane with 7.5% PODB for 10°C/min. Using the assumption of porportionality between conversion and fraction of heat released in reaction, conversion is found as a function of time. The values shown are for the initial reaction for different starting concentrations.

Figure 6: Kissinger method is used to find E_a by plotting points for different heating rates as a linearized function of peak temperature for E_a = mR and where slope is m and the gas constant is R. The data shown is for Ca°=1.05 mol/L and no PODB.