Stretching of Anchored to the Surface a Real Polymer Chain in a Good Solvent: The Massive Field Theory Approach

Abstract

Summary Application of the massive field theory approach in a fixed space dimensions d = 3 up to one loop order for investigation of the elastic properties of a real polymer chain immersed in a good solvent and anchored by one end to the surface and with other end being under tension of the external applied force as it is usually takes place in the single ‐ molecule force spectroscopy experiments. The obtained results include calculations of the dependence of the applied force upon stretching of a real polymer chain in a good solvent on the distance from the repulsive and inert surfaces. Besides, the obtained results are in good qualitative and quantitative agreement with previous theoretical investigations, results of Density Functional Theory (DFT) and Monte Carlo (MC) simulations and have important practical applications for understanding of the elastic properties of the individual macromolecules, networks, gels and brush layers.

Investigation of a dilute polymer solution in confined geometries

“…In a series of our papers we performed investigations for different boundary conditions. Such, for example, when we discussed the processes of adsorption and desorption on the surface of a dilute solution of polymer chains [27] and stretching anchored to the surface long-flexible real polymer chain with the EVI in a good solvent for temperatures above the θ-point [33,34], we performed calculations for the case of repulsive wall and wall where the adsorption threshold takes place (so-called [24] "inert" wall). In the case of repulsive wall (i.e.…”

“…A series of papers [31][32][33][34] were devoted to the investigation of stretching anchored to the surface long-flexible linear polymer chain with the EVI in a good solvent for temperatures above the θ-point. The difference in the strain-force and the force-strain dependences, which corresponds to the f ensemble and Z ensemble, respectively, was discussed in [31].…”

“…Such in the case of ideal polymer chain anchored by one end to repulsive surface the result for the average stretching force has a form [33,34]:…”

“…Besides, the task of investigation of the stretching and force induced desorption of anchored to the surface polymer chains which have practical application in technological process of producing new type of polymeric materials was the subject of series recent papers [31][32][33][34]. Such, for example, the theory of stretching of an end-tethered ideal chain (Gaussian chain) anchored to repulsive and inert plane was proposed in [31].…”

“…It stimulated us to apply the massive field theory approach (MFT) for investigation of stretching of long -flexible real polymer chain with the EVI in a good solvent anchored by one end to repulsive or inert surface [33,34]. It should be mentioned that initially MFT approach was proposed by Parisi for infinite systems in [35] and subsequently applied to semi-infinite systems by Diehl and Shpot in [36].…”