Record number 
358418 
Title 
On the curvature dependence of the interfacial tension in a symmetric threecomponent interface 
Author(s) 
Leermakers, F.A.M.; Sprakel, J.H.B.; Besseling, N.A.M.; Barneveld, P.A.

Source 
Physical Chemistry Chemical Physics 9 (2007)1.  ISSN 14639076  p. 167  179. 
DOI 
https://doi.org/10.1039/b613074g 
Department(s) 
Physical Chemistry and Colloid Science 
Publication type 
Refereed Article in a scientific journal 
Publication year 
2007 
Keyword(s) 
interacting chain molecules  statisticaltheory  tolman length  adsorption  rigidity  models

Abstract 
We consider a symmetric interface between two polymers A(N) and B(N) in a common monomeric solvent S using the meanfield ScheutjensFleer selfconsistent field theory and focus on the curvature dependence of the interfacial tension. In multicomponent systems there is not one unique scenario to curve such an interface. We elaborate on this by keeping either the chemical potential of the solvent or the bulk concentration of the solvent fixed, that is we focus on the semigrand canonical ensemble case. Following Helfrich, we expand the surface tension as a Taylor series in the curvature parameters and find that there is a nonzero linear dependence of the interfacial tension on the mean curvature in both cases. This implies a finite Tolman length. In a thermodynamic analysis we prove that the nonzero Tolman length is related to the adsorption of solvent at the interface. Similar, but not the same, correlations between the solvent adsorption and the Tolman length are found in the two scenarios. This result indicates that one should be careful with symmetry arguments in a Helfrich analysis, in particular for systems that have a finite interfacial tension: one not only should consider the structural symmetry of the interface, but also consider the constraints that are enforced upon imposing the curvature. The volume fraction of solvent, the chain length N as well as the interaction parameter chi(AB) in the system can be used to take the system in the direction of the critical point. The usual critical behavior is found. Both the width of the interface and the Tolman length diverge, whereas the density difference between the two phases, adsorbed amount of solvent at the interface, interfacial tension, spontaneous curvature, mean bending modulus as well as the Gaussian bending modulus vanish upon approach of the critical point. 
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