## 1 Introduction  
Measuring the anchoring energy \(W\) of the director at the bounding plates of a nematic cell is necessary to predict its electrooptical properties under electric field. This is important from a basic physics perspective to better understand anchoring phenomena [1; 2; 3] and for applications in electro-optic devices, such as LCD displays, to improve their performance [4]. More specifically in this paper, I focus on the measurement of the polar anchoring energy in planar cells filled with a liquid crystal (LC) of positive dielectric anisotropy. This measurement is very classical, but nonetheless extremely delicate as one immediately realizes after reading the literature on this subject. Indeed, the value of \(W\) obtained with the same LC and the same substrates may differ by several orders of magnitude when measured by different groups [5]. In practice, various techniques have been proposed to measure the anchoring extrapolation length \(L=K_{1}/W\), from which \(W\) can be deduced knowing the splay elastic constant \(K_{1}\). Some of the techniques analyze the deformation of the director field in the presence of a wall [6] or in a wedge cell [7; 8; 9]. Others use light scattering [10; 11; 12]. However, the most widely used techniques are based on the action of an external field. Among them, one can cite all-optical methods using magnetic or electric field as the ones described by [PERSON] et al. [13] or [PERSON] et al. [14] and much more standard methods using an electric field and capacitance and/or optical retardation measurements. In this last category, the method proposed by [PERSON] and [PERSON] [15] at high electric field (YvS method) is certainly the most popular. This method consists of plotting \(R/R_{0}\) as a function of \(1/CV\). Here, \(V\) is the applied voltage, \(C\) is the capacitance, and \(R\) is the optical retardation between the ordinary and extraordinary rays (with the index 0 denoting that the measurement has been performed without electric field). The model predicts that in a certain range of voltage, \(V_{\rm min}<V<V_{\rm max}\), the curve must be a line whose intersection with the ordinate axis gives \(W\). The first inequality with \(V_{\rm min}\approx 6V_{c}\), where \(V_{c}\) is the Freedericksz voltage, ensures that the tilt angle \(\phi_{m}\) in the middle of the cell is equal to \(\pi/2\) to better than \(10^{-3}\) rad. The second inequality ensures that the tilt angle on the plates, \(\theta\), remains small enough sor that the actual anchoring potential is approximately given by the Rapini-Papoular formula \(W(\theta)=\frac{1}{2}W\sin^{2}\theta\)[16]. By assuming that this is the case for \(\theta<0.2\) rad, the calculation shows that \(V_{\rm max}\approx\frac{0.2}{\pi}\sqrt{\frac{\tau_{\perp}}{\varepsilon_{\parallel }}}\frac{d}{L}V_{c}\)[17]. In practice, [PERSON] et al. have shown that similar results can be obtained by just measuring the optical retardation in the same range of voltage (RV method) [5; 17]. This method is interesting because it allows a local measurement of \(L\). The problem with these two methods is that they often give very different values of \(L\) depending on the voltage interval \((V_{1},V_{2})\) chosen to perform the fit of the experimental data, even when \((V_{1},V_{2})\in(V_{\rm min},V_{\rm max})\). Even the unphysical negative value of \(W_{a}\) can be obtained [17]. According to [PERSON] et al. [17], this unexpected behavior could be due to in-plane inhomogeneities of the cell (variations of the anchoring energy, easy axis, fractures in the patterned electrodes, etc. ), thus making these methods difficult to use to determine a reliable value for \(W\). In this paper, I propose an alternative method to measure the polar (zenithal) anchoring energy \(W\) in a planar cell based on capacitance measurements at high electric field.