A fully aromatic thermotropic main-chain liquid-crystal copolyester (70 mol % p-hydroxybenzoic acid / 30 mol % 2-hydroxy-6-naphthoic acid, HBA/HNA) with persistence length lpl_p = 12.0 ± 1.0 nm dissolves in the acidic fluorinated phenol 3,5-bis(trifluoromethyl)phenol (BTFMP) at 60 °C, where its molecules interact thermodynamically almost like rigid rods. Kroemer et al. (Macromolecules 1991) found that adding the nonsolvent nn-butanol leaves the radius of gyration essentially unchanged (32–36 nm) and the second virial coefficient A2A_2 positive (7.2 → 5.5 × 10⁻³ mol cm³ g⁻²) up to 13.0 vol %, yet the polymer precipitates at 16.7 vol %; the authors could not explain this solvent-composition dependence and only tentatively suggested formation of an ordered crystalline or mesomorphic phase rather than spinodal demixing. They also found that their universal size-exclusion-chromatography (SEC) calibration fails for the highest-molar-mass fractions. No later work resolving this issue for this system is known; rod-solution theory (Onsager, Flory) supplies only qualitative expectations. The problem — determine the phase-separation mechanism and the nature of the precipitating phase — remains open.

Background

Thermotropic main-chain liquid-crystal polymers (LCPs) are wholly aromatic polyesters whose rigid, linear backbones form an orientationally ordered (nematic) melt on heating; they are processed directly from that melt into high-modulus fibers and precision moldings. The technologically dominant chemistry is the random copolyester of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) — the Vectra family — of which the study examined here used a 70/30 molar composition. Because melt properties (viscosity, texture, mechanical performance) are governed by chain stiffness and molar mass, these quantities must be measured; but the polymers are nearly insoluble in ordinary solvents, so dilute-solution characterization is possible only in aggressive special solvents. The acidic fluorinated phenol 3,5-bis(trifluoromethyl)phenol (BTFMP) is one of the few liquids that dissolve them at practical temperatures.

Dilute-solution characterization conventionally combines static light scattering, which yields the weight-average molar mass MwM_w, the radius of gyration RgR_g (a measure of molecular size), and the second virial coefficient A2A_2 (the first interaction correction to ideal-dilute behavior, positive in a good solvent); dynamic light scattering, which yields the hydrodynamic radius RhR_h; viscometry, which yields the intrinsic viscosity [η][\eta]; and size-exclusion chromatography (SEC, also called gel permeation chromatography), which separates molecules by size and needs a calibration relating elution volume to molar mass. In universal SEC calibration the elution volume is correlated with the hydrodynamic volume [η]M[\eta]M rather than with MM itself, a relation expected to hold across polymer architectures for a given column and solvent but never guaranteed a priori for a new polymer class. Chain stiffness is quantified by the persistence length lpl_p, the distance over which the chain direction remains correlated; it is extracted from RgR_g and RhR_h data with the Kratky–Porod wormlike-chain model, which interpolates between a rigid rod and a flexible coil (Benoit–Doty formula for RgR_g, Koyama treatment for RhR_h).

In this framework, Kroemer, Kuhn, Pielartzik, Siebke, Eckhardt and Schmidt (Macromolecules 1991, 24, 1950) characterized six fractions of the 70/30 HBA/HNA copolyester in BTFMP at 60 °C: MwM_w from 7,500 to 43,000 g/mol and contour lengths of 38–218 nm, i.e. only about 2–20 persistence lengths, with lpl_p = 12.0 ± 1.0 nm. The intrinsic viscosity followed the Mark–Houwink relation — the empirical power law [η]=KMa[\eta] = K M^a linking intrinsic viscosity to molar mass — with [η]=9.93×10−4Mw0.842[\eta] = 9.93 \times 10^{-4} M_w^{0.842} ([η][\eta] in dL/g), from which a universal SEC calibration was constructed. The measured A2A_2 (6.4–8.6 × 10⁻³ mol cm³ g⁻²) is close to the value ≈ 5.2 × 10⁻³ mol cm³ g⁻² predicted for rigid cylinders by A2=v2,sp2/(2πrcyl3NA)A_2 = v_{2,sp}^2/(2\pi r_{cyl}^3 N_A) (with v2,spv_{2,sp} the polymer specific volume, rcylr_{cyl} the chain cross-section radius, and NAN_A Avogadro's number), indicating that the molecules interact thermodynamically almost like rigid rods with negligible intramolecular contacts.

For an ordinary flexible coil, adding a nonsolvent to a good solvent shrinks the coil and drives A2A_2 toward zero before liquid–liquid demixing sets in — separation into polymer-rich and polymer-poor liquid phases, either by nucleation and growth below the coexistence (binodal) boundary or by the continuous, barrier-free spinodal mechanism. For rodlike solutes the classical theories of Onsager (1949) and Flory (1956) predict a different scenario: the isotropic solution separates into an ordered, liquid-crystalline (mesomorphic) phase driven by anisotropic excluded volume — a packing-entropy effect that can occur even while the effective pair interactions remain repulsive in the good-solvent sense. This expectation is well documented for model rodlike polymers such as poly(γ-benzyl L-glutamate), a synthetic polypeptide that adopts a rigid α-helical conformation in helix-promoting solvents.

The unresolved observation motivating this problem is that the HBA/HNA copolyester in BTFMP behaves in the rodlike, not the flexible-coil, manner but without a demonstrated mesomorphic mechanism: on adding nn-butanol to BTFMP at 60 °C, RgR_g stays essentially unchanged (32, 35, 36 nm at 0, 9.1, 13.0 vol % nn-butanol) and A2A_2 remains positive (7.2 → 5.5 × 10⁻³ mol cm³ g⁻²), yet the polymer becomes insoluble at 16.7 vol %. The authors could not offer a satisfactory explanation for this solvent-composition dependence and only tentatively suggested that phase separation proceeds by formation of an ordered crystalline or mesomorphic phase rather than by spinodal demixing. Compounding this, for the highest-molar-mass fractions the molar masses from light scattering and from the universal SEC calibration disagree, which the paper attributes to the limited validity of the universal calibration at high molar mass.

Problem Statement

For the fully aromatic thermotropic liquid-crystal copolyester of 70 mol % p-hydroxybenzoic acid (HBA) and 30 mol % 2-hydroxy-6-naphthoic acid (HNA) (persistence length lpl_p ≈ 12 nm in BTFMP at 60 °C), establish the thermodynamic mechanism of its phase behavior in mixtures of 3,5-bis(trifluoromethyl)phenol (BTFMP) with nn-butanol at 60 °C. Specifically: explain why the molecular dimensions remain essentially unchanged (RgR_g ≈ 32–36 nm) and A2A_2 stays positive (7.2 → 5.5 × 10⁻³ mol cm³ g⁻²) as nn-butanol increases from 0 to 13.0 vol % while the polymer nevertheless becomes insoluble at 16.7 vol %; and determine the nature of the separating phase — dilute-solution demixing (spinodal or binodal liquid–liquid separation) versus formation of an ordered crystalline or mesomorphic (liquid-crystalline) phase.

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