Scaled particle theory for wormlike hard spherocylinders: calculation of phase diagrams for ternary systems consisting of two semiflexible polymers with different lengths and a solvent

Abstract

We extended the scaled particle theory of Cotter and Wacker for multicomponent systems of straight hard spherocylinders to multicomponent solutions of wormlike hard spherocylinders and calculated phase diagrams of ternary systems consisting of two homologous semiflexible polymer components with different lengths and a low molar mass good solvent. The basic parameters in this theory are the chain contour lengths (Li, Li), the hard core diameter (d), and the persistence length (q) of the polymer components. The theoretical ternary phase diagrams calculated by this scaled particle theory for wormlike hard spherocylinders were compared with experimental ternary phase diagrams obtained previously for systems of schizophyllan + water and poly(n-hexyl isocyanate) + toluene. When the hard core diameter d was chosen to have a value close to that estimated from the osmotic pressure or solvent chemical potential data for the corresponding binary solutions, good agreements between experimental and theoretical ternary phase diagrams were obtained for the isotropic-anisotropic binodal curves and the tie lines of all the systems compared. On the other hand, the present theory failed to predict anisotropic-anisotropic-isotropic three-phase coexistence as well as anisotropic-anisotropic two-phase coexistence in ternary solutions containing two samples with the Kuhn segment numbers JVi (=LJ2q) = 0.930 andJVa (=L¡J2q) = 0.0765, whereas these multiphase separations were found for aqueous solutions of schizophyllan with the same N¡ s. When N2 was decreased to smaller than 0.07 with M kept at 0.93, these phase-coexisting regions appeared in the theoretical phase diagram.

Theory of phase separation for a solution of tridisperse rod-like particles

“…Recent computer simulations have confirmed the thermodynamic stability of these crystalline phases [14,15]. Mixtures of rod-like particles with different lengths have also attracted considerable attention both theoretically [16][17][18][19][20][21] and experimentally [22][23][24][25][26]. Above a critical length ratio two nematic phases are predicted to form [16,[19][20][21].…”

“…Mixtures of rod-like particles with different lengths have also attracted considerable attention both theoretically [16][17][18][19][20][21] and experimentally [22][23][24][25][26]. Above a critical length ratio two nematic phases are predicted to form [16,[19][20][21]. This has indeed been observed experimentally [22][23][24][25][26].…”

Chain Alignment of a Rigid Ring Polymer in the Lyotropic Liquid Crystal Phase: Cyclic Amylose Tris(n-butylcarbamate) in Tetrahydrofuran and Ethyl Lactate

“…If rigid cyclic chains behave as a pseudo-rod in concentrated solutions, the phase diagram can be expressed in terms of the scaled particle theory (SPT) for the linear wormlike spherocylinder. − According to Sato and Teramoto, − the Helmholtz energy is expressed as a function of c with the three parameters, the contour length L SC , the Kuhn segment length L k,SC , and the chain diameter d SC of the spherocylinder, which models the pseudo-rod in Figure b. The detailed expression can be found in their original paper or in our recent report .…”

Light Scattering Study of Semiflexible Polymer Solutions III. Multicomponent Solutions

“…Let us consider a solution of volume V containing r wormlike spherocylinder components; the component s has the contour length Lc,s of the cylinder part, the hard-core diameter d 5 , and the persistence length q., and the solution contains ns molecules of the component s. Applying the previous result* 2 of the scaled particle theory 13 for f.l., we have…”