In this paper we develop a theory for an excess electron in simple fluids. It is based upon the path integral formulation of quantum theory which maps the behavior of the electron on to that of a classical isomorphic polymer. The influence functional, i.e., the solvent induced potential between different sites on the polymer, is estimated from the RISM integral equation. The functional is not pair decomposable and the resulting polymer problem is not trivial to solve. The evaluation of the electron partition function and correlation functions is pursued with two approximations: (i) a mean field approximation which neglects the role of polymer fluctuations on the solvent induced interactions: (ii) a polaron approximation which is a linear approximation in the sense that it neglects large fluctuations in the polymer structure itself. The theory brings to light a new approach to the computation of multiparticle correlation functions in fluids, and the theory provides what appears to be a practical scheme for attacking a number of other problems including the analysis of polymer conformations in liquid environments. While this paper focuses on the role of packing forces in these systems, the theory can be generalized to include polarization and charge interactions as well.
Groundwater is an important source for drinking water supply in hard rock terrain of Bundelkhand massif particularly in District Mahoba, Uttar Pradesh, India. An attempt has been made in this work to understand the suitability of groundwater for human consumption. The parameters like pH, electrical conductivity, total dissolved solids, alkalinity, total hardness, calcium, magnesium, sodium, potassium, bicarbonate, sulfate, chloride, fluoride, nitrate, copper, manganese, silver, zinc, iron and nickel were analysed to estimate the groundwater quality. The water quality index (WQI) has been applied to categorize the water quality viz: excellent, good, poor, etc. which is quite useful to infer the quality of water to the people and policy makers in the concerned area. The WQI in the study area ranges from 4.75 to 115.93. The overall WQI in the study area indicates that the groundwater is safe and potable except few localized pockets in Charkhari and Jaitpur Blocks. The Hill-Piper Trilinear diagram reveals that the groundwater of the study area falls under Na+-Cl−, mixed Ca2+-Mg2+-Cl− and Ca2+-$${\text{HCO}}_{3}^{ - }$$ HCO 3 - types. The granite-gneiss contains orthoclase feldspar and biotite minerals which after weathering yields bicarbonate and chloride rich groundwater. The correlation matrix has been created and analysed to observe their significant impetus on the assessment of groundwater quality. The current study suggests that the groundwater of the area under deteriorated water quality needs treatment before consumption and also to be protected from the perils of geogenic/anthropogenic contamination.
We consider a model of self-avoiding walk on a lattice with on-site repulsion and an attraction for every vertex of the walk visited on the surface to study force-induced desorption of a linear polymer chain adsorbed on an attractive surface and use the exact enumeration technique for analyzing how the critical force for desorption f c (T ) depends on the temperature. The curve f c (T )gives the boundary separating the adsorbed phase from the desorbed phase. Our results show that * Electronic address: pramod@justice.com, yashankit@yahoo.com, ysingh@bhu.ac.in When a long flexible polymer chain interacts with an impenetrable surface its conformational properties are strongly modified in comparison with its bulk properties [1, 2]. This is due to a subtle competition between the lowering of internal energy near an attractive surface and the loss of entropy due to constraints imposed by the impenetrable surface. For a strongly attractive surface, the polymer chain sticks to the surface, and for weak attraction it prefers to stay away from the surface. Thus there is a transition from the state when chain is mostly attached to the surface (adsorbed) to the state of detachment (desorbed) when the temperature is increased. The transition between theses two states is marked by a transition temperature T a with the adsorbed phase for T < T a and the desorbed phase for T > T a .A model of self avoiding-walk on a lattice with on-site repulsion and attraction energy for every vertex of the walk visited on the surface provides an adequate model for understanding the adsorption-desorption transition [3, 4, 5]. We extend this model of self-avoiding walk to study the force-induced desorption of a linear polymer chain adsorbed on an attractive surface and calculate the critical force f c (T ) for desorption as a function of temperature.Response of a polymeric chain to externally applied force can be measured experimentally by using techniques like optical or magnetic tweezers [6] and atomic force microscope [7].We consider self-avoiding walks (SAW s) that start from a point on an impenetrable surface and experience a force f in a direction perpendicular to the surface at the other end.The applied force, because of its direction, favours desorption and one expects a critical force, f c (T ), for desorption. At a given T when the applied force f is less than f c (T ) the polymer will be adsorbed while for f > f c (T ) the polymer will be desorbed. The curve f c (T ), therefore, gives the boundary that separates the desorbed phase from the adsorbed phase in the (f, T ) plane.Let z = 0 represents the surface and walks start from a point (origin) on the surface. In case of two dimensions (2-d) the surface is a line whereas in case of three dimensions (3-d) the surface is a plane. Since the surface is impenetrable, walks are restricted to half of the space (z ≥ 0) only. We enumerated all SAW s upto a certain length on a square lattice in 2-d and on a cubic lattice in 3-d. Let C N (N s , h) be the number of SAW s of N vertex (a vertex of...
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