Ca/Na montmorillonite and natural Wyoming bentonite (MX-80) have been studied experimentally and theoretically. For a clay system in equilibrium with pure water, Monte Carlo simulations predict a large swelling when the clay counterions are monovalent, while in presence of divalent counterions a limited swelling is obtained with an aqueous layer between the clay platelets of about 10 A. This latter result is in excellent agreement with X-ray scattering data, while dialysis experiments give a significantly larger swelling for Ca montmorillonite in pure water. Obviously, there is one "intra-lamellar" and a second "extra-lamellar" swelling. Montmorillonite in contact with a salt reservoir containing both Na(+) and Ca(2+) counterions will only show a modest swelling unless the Na(+) concentration in the bulk is several orders of magnitude larger than the Ca(2+) concentration. The limited swelling of clay in presence of divalent counterions is a consequence of ion-ion correlations, which reduce the entropic repulsion as well as give rise to an attractive component in the total osmotic pressure. Ion-ion correlations also favor divalent counterions in a situation with a competition with monovalent ones. A more fundamental result of ion-ion correlations is that the osmotic pressure as a function of clay sheet separation becomes nonmonotonic, which indicates the possibility of a phase separation into a concentrated and a dilute clay phase, which would correspond to the "extra-lamellar" swelling found in dialysis experiments. This idea also finds support in the X-ray scattering spectra, where sometimes two peaks corresponding to different lamellar spacings appear.

Aqueous dispersions of pure sodium and calcium smectite clays with platelet sizes on the order of a few hundred nanometers were characterized using a combination of cryotransmission electron microscopy (cryo-TEM) and small-angle X-ray scattering (SAXS). With monovalent sodium counterions the clay is dispersed as individual platelets, as seen by cryo-TEM, that order into a nematic phase. From SAXS a onedimensional swelling of the clay in water is observed with the characteristic spacing h s = δ/ϕ c , where h s is the separation between the platelets, δ = 1 nm is the effective platelet thickness, and ϕ c is the clay volume fraction in the sample. In calcium montmorillonite, on the other hand, cryo-TEM images clearly show the presence of tactoids, where the platelets have aggregated into stacks with a periodic spacing of 2 nm. From imaging a large number of tactoids the distribution function f(N) for the number of platelets per tactoid was estimated, and the average number ⟨N⟩ ≈ 10. The characteristic 2 nm spacing as well as the small number of platelets per tactoid was also confirmed by SAXS. The present study demonstrates that cryo-TEM, with carefully prepared specimen, is a very useful technique to characterize clay dispersions, particularly in aggregated systems.

Aqueous dispersions of Ca montmorillonite contain small clusters of clay platelets, often named "tactoids". In these tactoids, the platelets are arranged parallel to each other with a constant spacing of 1 nm. We have used smallangle X-ray scattering (SAXS) to determine the average number of platelets per tactoid, ⟨N⟩. We found that this number depends on the platelet size, with larger platelets yielding larger tactoids. For a dispersion in equilibrium with a mixed electrolyte solution, the tactoid size also depends on the ratio of divalent to monovalent cations in the reservoir. Divalent counterions are strongly favored in this competition and will accumulate in the tactoids. In dispersions of pure sodium montmorillonite, that are equilibrated with a mixture of Na + and Ca 2+ cations, the Na + cations initially cause a repulsion between the platelets, but the divalent ions rapidly replace the monovalent ones and lead to the formation of tactoids, typically within less than one hour based on the divalent to monovalent ratio. This cation exchange as well as tactoid formation can be semiquantitatively predicted from Monte Carlo simulations.

Chain entanglements govern the dynamics of polymers and will therefore affect the processability and kinetics of ordering; it follows that through these parameters chain dynamics can also affect charge transport in conjugated polymers. The effect of nematic coupling on chain entanglements is probed by linear viscoelastic measurements on poly[N-9′-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2thienyl-2′,1′,3′-benzothiadiazole)] (PCDTBT) and poly-((9,9-dioctylfluorene-2,7-diyl)-alt-(4,7-di(thiophene-2-yl)-2,1,3-benzothiadiazole)-5′,5″-diyl) (PFTBT) with varying molecular weights. We first verify the existence of nematic phases in both PFTBT and PCDTBT and identify nematic−isotropic transition temperatures, T IN , between 260 and 300 °C through a combination of differential scanning calorimetry, polarized optical microscopy, temperature-dependent X-ray scattering, and rheology. In addition, both PCDTBT and PFTBT show a glass transition temperature (T g ) and T IN , whereas only PFTBT has a melting temperature T m of 260 °C. Comparing the molecular weight dependence of T IN with theoretical predictions of nematic phases in conjugated polymers yields the nematic coupling constant, α = (550 ± 80 K)/T + (2.1 ± 0.1), and the long-chain limit T IN as 350 ± 10 °C for PFTBT. The entanglement molecular weight (M e ) in the isotropic phase is extracted to be 11 ± 1 kg/mol for PFTBT and 22 ± 2 kg/mol for PCDTBT by modeling the linear viscoelastic response. Entanglements are significantly reduced through the isotropic-to-nematic transition, leading to a 10-fold increase in M e for PFTBT and a 15-fold increase for PCDTBT in the nematic phase.