On the Schroeder paradox for nonionogenic polymers

Abstract

Abstract⎯The well-known Schroeder paradox, i.e., the difference in the degrees of swelling of nonionogenic polymers occurring at equilibrium with liquid and vapor phases, has been discussed. A simple example has been presented, which illustrates the unavoidability of different degrees of swelling for a polymer brought into contact with vapor and liquid phases. A simple mechanism has been proposed for the excess swelling of a nonionogenic polymer immersed in a liquid phase, this mechanism being associated with the action of van der Waals and solvation forces at a polymer/solvent interface. The estimation of the contribution from the van der Waals interaction to the "excess" swelling has shown that the predicted values of the "excess" swelling agree with the data of real experiments.

The Modeling of Interfacial Contacts in Composites Using the Sitting Drop - Solid Body System as an Example

“…According to V.I. Roldugin [2], there is now a unique situation similar to that which happened at the beginning of the twentieth century, when each phenomenon was introduced with its "own" forces. However, it has been established that, at the molecular level, the forces have the same nature and are derived from electromagnetic forces acting between electrons and nuclei.…”

“…Thus, at the boundary of the interface layer with the liquid body phase, the requirement = 0, caused by mobility of liquid molecules, is met. In the area of contact between the interface layer and the solid surface, this requirement is discarded due to the fixed position of solid state molecules, and the boundary condition results to = [2]. As shown above, the value of surface tension is the projection of the surface tension which increases with the decrease of the contact angle.…”

“…Therefore, when < π/2 the body force acts from the volume liquid phase to the solid surface, "sticking" the drop to it [9]. When > π/2, the body force has an opposite direction and attempts to detach the drop from the surface [2], which lets the drop spread across the surface. However, the surface tension acting on the interface layer tension prevents spreading.…”

Effect of Temperature on the Performance of Polymer Electrolyte Membrane Water Electrolysis: Numerical Analysis of Electrolysis Voltage Considering Gas/Liquid Two-Phase Flow

“…Discovered a century ago, this is known as Schroeder's paradox 22 and has been actively discussed. [23][24][25][26][27][28][29][30] Considering Schroeder's paradox and the electrolyte membrane immersed in liquid water, the activity of water with regard to the water content in the electrolyte membrane should be a function of the operating pressure, as shown in Eq. 20.…”

Engineering Covalent Organic Frameworks with Polyethylene Glycol as Self‐Sustained Humidity‐Responsive Actuators

“…In this study, to demonstrate this proof-of-concept, a well-studied water-stable hydrazone-linked COF, COF-42, [1,7,46] was rationally selected as the model framework material to graft flexible PEG chains, which exhibited an expansion-contraction effect upon the adsorption/desorption of water molecules. [47] The utilization of the interfacial polymerization method afforded rigid-flexible coupled freestanding membranes with adjustable asymmetrical structures, which can be applied as smart actuators exhibiting reversible bending behaviors under humidity stimulation. These actuators could achieve various motions especially continuously self-oscillating motions to generate electricity.…”