Underpotential deposition (UPD) of metals is analysed from the perspective of phenomeno-logical and statistical thermodynamic considerations; the parameters influencing the UPD shift have been quantitatively indicated using a general formalism. The manner in which the macroscopic properties pertaining to the depositing ions and solvent dipoles and the nature of the metallic substrate influence the UPD process are highlighted; earlier correlations of the UPD shift with the work function differences are rationalised. Anion-induced phase transitions which manifest as sharp peaks in experimental cyclic voltammograms are discussed using statistical thermodynamic models.

The galvanostatic polymerization of pyrrole is carried out on stainless steel electrodes using 𝑝-toluene sulphonic acid. The morphology of the film is studied from Scanning Electron Microscopy (SEM) measurements while the nature of the substrate is analysed using Energy Dispersive X-ray Spectroscopy (EDAX) technique. The electrochemical behaviour is studied using cyclic voltammetry, charge-discharge analysis and impedance spectroscopy. The feasibility of the electrode for supercapacitor applications is investigated. The specific capacitance is estimated as ∼ 10² Farads per gram with 10³ charge-discharge cycles. A plausible equivalent circuit for the system is proposed and the circuit parameters are obtained by non-linear regression analysis.

The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic $2 \times 2$ matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed.

The partition function for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for a finite square lattice of 16, 25, 36 and 64 sites with the help of