PAni-PMMA blends for cryomagnetic temperature sensor applications

Presentation on ICEC 18 / India

PAni-PMMA blends for cryomagnetic temperature sensor applications

AN. Bharthwaj^a, S. Angappane^a, D. Srinivasan^a*, T.S. Natarajan^a, G. Rangarajan^a and B. Wessling^b
a Low Temperature Laboratory, Indian Institute of Technology-Madras, Chennai - 600036, India.
b ORMECON CHEMIE GmbH & Co., KG (a subsidiary of Zipperling), Ferdinand-Harten-Str. 7,
D-22949 Ammersbek, Germany.
* Present address: GE India Technology Centre Pvt. Ltd., Whitefield Road, Bangalore - 560 066, India.

Blends of polyaniline (PAni) with polymethylmethacrylate (PMMA) have electrical resistivity values which are comparable to those of disordered semiconductors such as heavily doped germanium, especially at low temperatures. We report resistance versus temperature (R-T) data for these blends containing 33% and 40% PAni, in the temperature interval 0.35 K - 10 K and compare the same with that of a commercial germanium thermometer. R-T data in the presence of applied magnetic fields up to 5.5 T are also presented. The sensitivity of these blends is about 0.1 mK at temperatures below 1 K. The data are discussed with special reference to the suitability of these materials as cryomagnetic temperature sensors and as elements of a temperature controller based on fuzzy logic.

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Introduction

Most investigators use one of the semiconductor or disordered metal thermometers and employ them as calibrated secondary thermometers in low temperatures. [1] Germanium resistors are presently the commonly used temperature sensor for high accuracy thermometry below about 40 K. Because of their strong magnetoresistance and associated orientation effect, germanium sensors are of limited use in high magnetic fields. Carbon thermometers have also been popular but limited to a relatively narrow range and are not reproducible. Cernox (Ceramic oxynitride) thermometers also have high magnetoresistance below about 2 K. The drawbacks of these thermometers make it necessary to look for a temperature sensor which is useful over a wide range of temperatures and magnetic fields.

In this paper we report the use of blends of polyaniline (PAni) with polymethylmethacryalate (PMMA) as cryomagnetic temperature sensors. PAni is one of the first few conducting polymers which are stable under ambient conditions and in commercial use. [2] When properly dispersed and blended with insulating PMMA, PAni shows enhanced conductivity than pristine PAni. It was found earlier that in these blends it has crossed from insulating to metallic state. [3,4] The low temperature characteristics of these blends are discussed below in comparison to those of germanium resistance thermometers.

Experimental

Both the PAni(33%)-PMMA(67%) and PAni(40%)-PMMA(60%) blends were made by ORMECON CHEMIE GmbH & Co. The sample thickness was 1 mm, length 8 mm and breadth 4 mm. The resistance of the PAni-PMMA blends was measured between 0.35 K and 10 K using a ³He evaporation cryostat - Heliox - 3 (Oxford Instruments) by four probe technique. The temperature was measured accurately using germanium resistor (GRT) (Lakeshore Cryogenic Inc. Model No.Gr-200a-50) in the range 0.35 K - 5 K, while a calibrated carbon glass resistor (CGR) (Lakeshore Cryotronics Inc. Model No. CGR-1-1000) was used in the range between 1.8 K and 300 K. Both GRT and CGR were energised by a constant current source (Keithley instruments Model 220) and the corresponding voltage was measured using a computing voltmeter(Solatron Instruments Model 7071). The calculated resistances of CGR and GRT were converted to corresponding temperatures using Chebychev polynomial coefficients supplied by the manufacturer of the sensors. A current of 1m A was passed through the sample using an Adventest constant current source (Model TR6142). Silver epoxy was used to make sample contacts. The sample voltage was measured using a Keithley nanovoltmeter (Model 181).

The magnetoresistance of these samples was measured at fixed temperatures (between 1.8 K and 5 K) by sweeping the magnetic field up to 5.5 Tesla. A SQUID magnetometer (Quantum Design Model MPMS.) was used for this purpose. The sample was mounted on the manual utility probe of the MPMS system. The sample was placed at the centre of the superconducting magnet and perpendicular to the magnetic field. The magnetic field was calibrated using a Hall sensor (Lakeshore Cryotronics Inc. Model No. TGHA 321).

Results

The resistance versus temperature characteristics for the blends show a trend similar to that of a germanium thermometer (fig. 1) in the temperature range between 0.35 K and 10 K. The test data were fitted to a polynomial equation based on Chebychev polynomials, which has the form:

Where 0Ł i Ł 7, A_i’s are the coefficients and ZU and ZL are the upper limit and lower limit of the variable Z over the fit range. Resistance R, and temperature T, are in ohms and Kelvin respectively.

The typical values of the coefficients for the temperature range from 1.6 K to 6 K for PAni(33%)-PMMA(67%) blend are:

A0	A1	A2	A3	A4	A5	A6	A7
3.43015	1.92286	2.17877	1.3788	0.7420	0.29469	0.07716	-0.01561

Figure 1: Plot of Resistance versus Temperature for PAni(33%)-PMMA(67%), PAni(40%)-PMMA(60%)

blends and Germanium resistance thermometer.

Because of the much higher resistance at temperatures below about 1 K, the sensitivity of the blends is high (better than 0.1 mK). In the temperature range between 2 K and 50 K, the sensitivity is about 1.0 mK.

The magnetoresistance (MR) is defined as:

where R(H,T) and R(0,T) are the resistances with and without field respectively. The magnetoresistance versus field characteristic for the blends at various temperatures (fig. 2) was always positive. The monotonic trend in MR is similar to that of the germanium resistor, but the value of MR is less in the case of the blends.[1]

Typical MR values at 5.5 T for PAni(33%)-PMMA(67%) and PAni(40%)-PMMA(60%) blends are tabulated below:

	MR ratio(D R/R₀ %)
Blend
	2.0K	2.5 K	3.0 K	4.2K	5.0K
PAni(33%)-PMMA(67%)	2.3	5.5	5.1	3.1	2.7
PAni(40%)-PMMA(60%)	2.0	1.3	1.1	0.7	0.5

Figure 2: Plot of MR versus Magnetic field for (a) PAni(33%)-PMMA(67%) and (b) PAni(40%)-

PMMA(60%) blends.

A Fuzzy logic based controller

A preliminary design of a cryogenic temperature controller was attempted using a Fuzzy logic algorithm. [5] In the case of conventional PI controller, a overshoot was observed when implementing it. In order to reduce the overshoot, set-point weighting was done to the proportional term of the control law, which changes from

Here e = y_sp - y, where e is the error, y the controlled variable, y_sp the set point, u the manipulated variable, K_c the proportional gain and t _i the integral time.[5] e_{p
= b}* y_sp- y, where b is the weighting parameter for the set-point.

This parameter b was found out at every sampling instant by using fuzzy logic, by means of e (error) and D e (change in error ) as inputs. The system was modelled by a first order differential equation of the form:

where q and I were the deviation variables of temperature and current from the steady state values respectively. The process time constant t _pand the process gain K_pwere determined experimentally for a Janis Closed Cycle Refrigerator (CCS 500). They were 300.77 seconds and 0.48 respectively. The control parameters t _i and K_c, found using Pole Placement method are 53.06 seconds and 18.71 respectively . The fuzzy states for e, D e and b are included in the table below, where the fuzzy rule base is also shown.

e Ž	NEGATIVE	ZERO	POSITIVE
D e Ż		b
NEGATIVE	SMALL	LARGE	SMALL
ZERO	SMALL	LARGE	SMALL
POSITIVE	MEDIUM	LARGE	SMALL

Figure 3: Plot of Temperature versus time for a

Fuzzy and PI controller.

The results of simulation are shown in fig.3. It shows that the fuzzy logic based controller has reduced the overshoot substantially.

Conclusions

The characteristic properties of a PAni-PMMA blend thermometer are as follows:

It can be used over a wide range of temperatures from millikelvins to 50 K.

The sensitivity of this thermometer is about 0.1 mK at millikelvin temperatures and 1.0 mK in the temperature range between 2 K and 50 K.

Small magnetoresistance, i.e., less than 5% at 4.2 K.

Reproducibility is better than 0.1 mK below 4.2 and 1.0 mK from 4.2 K to 50 K

These blends are more easily processable and can be inexpensively made in any form (for example bulk, thin films or thin coating)

Hence PAni-PMMA blends are a viable alternative to germanium, carbon glass or cernox thermometers for cryomagnetic temperature sensor applications.

References

1. Sample, H.H. and Rubin, L.G. Cryogenics (1977) 597-606
2. Wessling, B., Handbook of Nanostructured Materials and Nanotechnology (1999) 5, 501-575.
3. Wessling, B., Srinivasan, D., Rangarajan, G., Mietzner, T. and Lennartz, W., Euro Phys. Jl. E (in press).
4. Angappane, S., Srinivasan, D., Rangarajan, G., Prasad, V., Subramanyam, S.V. and Wessling, B., Proceedings of International conference on Low temperature Physics (LT22) , (in press).
5. M. Chidambaram, Applied Process Control, Allied Pub., New Delhi, 1998.

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