The influence of electrode size on resistance measurement in the modified four-electrodes method Adam Jakubas ⇑ , Pawel Jablon ´ ski Czestochowa University of Technology, Faculty of Electrical Engineering, Al. Armii Krajowej 17, 42-200 Cze ˛stochowa, Poland article info Article history: Received 19 December 2016 Received in revised form 28 April 2017 Accepted 2 May 2017 Available online 11 May 2017 Keywords: Anti-electrostatic coatings Van der Pauw method Four-electrodes method Resistivity measurements abstract The determination of resistivity of thin antistatic coatings with use of a modified four-points method is considered. 2D and 3D mathematical models taking into account cylindrical current electrodes and pin like voltage electrodes were developed. We analyzed how the size of current electrodes can change the determined resistivity. The effect of coating thickness and resistivity of the coating and background was tested. The theoretical considerations showed that the size of current electrodes has a relatively small influence on the detected resistivity. This observation was confirmed by experiments. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction Electrostatic discharges (ESD) due to natural and industrial pro- cesses create various problems and hazards. One of the most dan- gerous is fire or even explosion, which can occur when an ESD of high enough energy takes place in flammable gas or dust. Another threat is connected with personnel safety, as highly energetic ESD can be dangerous for human life. In addition, the electrostatic field generated by charged objects can cause disturbances in function- ing of electronic equipment [1–3]. In most cases, these effects can be avoided by using proper – and thereby – effective ESD pro- tection [4,5]. One of the methods used in such protection is coating objects with protective layer in the form of various varnishes and paints. The coatings also protect the objects against corrosion and other environmental impacts. In accordance with standards, anti-electrostatic coatings should have the volume resistivity not greater than 10 5 X m, and the surface resistivity not greater than 10 10 X [6]. However, these values strongly depend on the method used. In the case of the original four-points method, the detailed recommendations, methodology, information on accuracy, and used equipment can be found in [7,8]. It is required that the mea- surements have to be carried out in laboratory conditions on a suit- ably prepared sample. In practice, this is a serious limitation, because it makes it impossible to perform the measurements in- situ on a real object [4]. In this paper, we consider a modified four-points method. In particular, the considered model concerns the resistivity of anti- electrostatic coatings. The core of the paper is a theoretical model taking into account the dimensions of the sample, measurement system as well as the thickness and resistivity of the coating and background layer [4,9]. In the paper, we focused on the relation between the measurement electrodes size and other parameters, including the dimensions of the electrode system, the size of the measurement area, thickness of the coating, with background layer and resistivity ratio taken into account. This is to assess the maxi- mum size of the measurement electrodes at which they can be regarded as practically negligible in size (point-like). The knowl- edge on these parameters allows us (within certain limits) ignoring the influence of the size and shape of the surface being tested, and sometimes also the type of substrate to which the coating was applied. The determined parameter limits are then verified on a real object. The method is a modification of the classical four-points method and the method of Van der Pauw (VdP). The VdP method uses four electrodes, and is one of the most frequently used tech- niques of resistivity measurement of planar and thin samples of irregular shape. According to the method, the sample should be homogeneous and isotropic, of constant thickness and without holes (i.e. simply connected). The four pin electrodes are placed on the edge of the sample throughout its whole thickness [10–13]. The VdP method is commonly used in electric measure- ments and has many applications in physics, e.g. [14–16]. In this paper, we assume the four-points model and use the method of variable separation (amongst others) to obtain the http://dx.doi.org/10.1016/j.measurement.2017.05.006 0263-2241/Ó 2017 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: adam.jakubas@gmail.com (A. Jakubas). Measurement 108 (2017) 34–40 Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement