Shorter Rods Research Articles

Aspherical, Nano-Structured Drug Delivery System with Tunable Release and Clearance for Pulmonary Applications.

Addressing the challenge of efficient drug delivery to the lungs, a nano-structured, microparticulate carrier system with defined and customizable dimensions has been developed. Utilizing a template-assisted approach and capillary forces, particles were rapidly loaded and stabilized. The system employs a biocompatible alginate gel as a stabilizing matrix, facilitating the breakdown of the carrier in body fluids with the subsequent release of its nano-load, while also mitigating long-term accumulation in the lung. Different gel strengths and stabilizing steps were applied, allowing us to tune the release kinetics, as evaluated by a quantitative method based on a flow-imaging system. The micro-cylinders demonstrated superior aerodynamic properties in Next Generation Impactor (NGI) experiments, such as a smaller median aerodynamic diameter (MMAD), while yielding a higher fine particle fraction (FPF) than spherical particles similar in critical dimensions. They exhibited negligible toxicity to a differentiated macrophage cell line (dTHP-1) for up to 24 h of incubation. The kinetics of the cellular uptake by dTHP-1 cells was assessed via fluorescence microscopy, revealing an uptake-rate dependence on the aspect ratio (AR = l/d); cylinders with high AR were phagocytosed more slowly than shorter rods and comparable spherical particles. This indicates that this novel drug delivery system can modulate macrophage uptake and clearance by adjusting its geometric parameters while maintaining optimal aerodynamic properties and featuring a biodegradable stabilizing matrix.

Bismuth sulfide nanorods by thermal decomposition of a complex: Effect of reaction temperature on microstructural and optical properties

Bismuth sulfide nanorods have been prepared by thermolysis of a bismuth dithiocarbamate complex, as a single-source precursor, in a mixture of solvents (oleylamine, 1-dodecanethiol, and 1-octadecene) at various temperatures. Bismuth sulfide nanorods denoted as BS(120), BS(150), BS(180), BS(200), and BS(220) have been obtained at the specified temperatures (°C). They have been characterized by X-ray diffraction analysis, scanning electron microscopy (SEM), transmission electron microscopy (TEM), UV/Vis spectrophotometry, and photoluminescence (PL) spectroscopy. The effect of temperature on the microstructural and optical properties of the obtained Bi2S3 has been studied. The results show that interactions of the N–H group of oleylamine and the S–H group of dodecanethiol with the nanoparticles are temperature-dependent. The crystallite sizes of the nanoparticles were calculated using the Scherrer equation, Williamson–Hall (W–H) analysis, and Rietveld analysis, which yielded values in the ranges 20.1–45.9, 20.9–26.6, and 23.0–29.6 nm, respectively. Analysis of the microstrain in crystals of the nanoparticles showed that while the strain therein was due to contraction of the nanoparticles obtained at 180 °C, the strains at other temperatures were due to expansion, thereby confirming the effect of temperature on the nature of the defects in Bi2S3 crystals. The lattice strains were estimated by the W–H and Rietveld analyses to be in the ranges 3.19 × 10−5–1.04 × 10−4 and 0.008–0.067, respectively. The crystallite sizes and lattice strains estimated by both W–H and Rietveld analyses were mutually consistent, showing similar trends. SEM and TEM analyses showed that the nanorods were aggregated into longer rods at 120 and 150 °C, whereas shorter rods were obtained at 180 and 220 °C, suggesting a change in preferential growth direction. The widths and lengths of the nanorods were estimated as 20.97–41.25 nm and 79.4–111.0 nm, respectively, giving aspect ratios in the range 1.92–5.52. The band-gap energies of the nanorods varied in the range 1.08–0.78 eV, which can be related to differences in tail state width as observed in the absorption spectra. Calculation of texture coefficients showed preferential growth in the (111), (020), and (321) directions.

Interfacial aggregation of Janus rods in binary polymer blends and their effect on phase separation.

Janus particles interfacially self-assemble into different structures when incorporated into multiphase systems. Dissipative particle dynamics simulations are employed herein to investigate the interplay between aggregation mechanisms and phase separation in polymer blends. Shorter rods with a standing configuration become increasingly "caged" or trapped in larger aggregates as weight fraction increases, which is reflected in the way that their diffusion is coupled to their aggregation rates. Janus rods of higher aspect ratios that are tilted at the interface aggregate side-by-side and are able to hinder phase separation kinetics. This is due to a combination of individual Janus rod conformations at the interface, their intrinsic aggregation mechanisms, aggregate fractal dimension, and aggregation rates, and can also be traced back to the scaling of the diffusion coefficient of aggregates with their size. Findings presented provide insight into the mechanisms governing two dimensionally growing colloidal aggregates at fluid interfaces, more specifically, those associated with Janus particles, and shed light on the potential of these systems in paving the way for designing new functional materials.

Influence of metal coordination and light irradiation on hierarchical self-assembly processes.

Smart light-responsive supramolecular materials have been extensively investigated in the past decade, but so far the impact of metal coordination on hierarchical supramolecular structures of light-responsive building blocks has remained nearly unexplored. Herein, we unravel the hierarchical self-assembly of a small π-conjugated azo-containing pyridyl ligand that is able to respond to UV-light and metal complexation. The ligand self-assembles in an antiparallel fashion into long twisted fibers, which are then disassembled upon photoisomerization of the azobenzene groups, resulting in shorter rigid rods with a different packing motif. Complexation of Pd(ii) ions enhances the cooperativity of the aggregation and induces a molecular rearrangement into slipped stacks with subsequent formation of long thin fibers. These are then transformed into thinner, shorter rods upon light irradiation. The observed different light-responsiveness, besides clearing up the influence of metal coordination and light irradiation in self-assembly processes, paves the way towards the design of novel supramolecular photochromic systems.

Reply to “Molecular mechanics models for the image charge”

We have considered the system investigated by Steinmann et al. by means of the image charge model originally proposed in Iori and Corni, J. Comput. Chem. 2008, 29, 1656. Qualitatively correct results are obtained, that compare favorably with the relevant analytical benchmarks. We show that the effect of the asymmetry of the rod model can be controlled, when needed, as originally suggested, that is, by shorter rods. This strategy does not increase neither the complexity of the model nor its computational cost. © 2017 Wiley Periodicals, Inc.

Using of Finite Elements Modeling Computer Simulation in Impedance Prediction and Data Evaluation

With the electrochemical impedance measurement capability becoming more and more standard in the present day electrochemical instrumentation, the technique is also being introduced in experimentation and more routinely at that. While the danger of misinterpretation based on analogs derived from equivalent circuits remains as it always has been, the occurrence of such interpretation is increasing because the impedance nonlinear least square fitting procedures are often included in the instrumental software package and allow mechanical modeling without requirement of deeper understanding the fundamentals. While this is natural consequence of the mass availability, some undesirable outcome may be for example alleviated by closer attention to the chosen sample geometry. The sample geometry and the location of the electrodes (often four, in the 4-point measurement) is crucial in collecting proper impedance data, interpretation of the impedance measurements, and correlating the results to the properties of the studied material. As an example, the included picture shows a simulation of resistance as it would be measured on a rod (left) of a varying length. The rod has a radius of 14 mm and the contact electrode (“zero resistance”) covers the entire cross sectional bottom of the rod. However, the upper electrode, placed on the axis of the rod, has a radius of only 7 mm, thus only area under the electrode is covered. The graph on the right shows the calculated measured resistance, divided by the rod length, as a function of the length of the rod. If the upper electrode covered the entire cross section, then the value of such resistance should be constant (expected, but also verified by a simulation). However, with the upper electrode smaller, the scaled resistance is higher for thinner disks (shorter rods) and then it decreases, reaching a limiting constant value for long rods. This value corresponds to the value calculated, for any distance, for rods with electrodes completely covering both ends. The simulation for this work was done using the ANSYS software package. In our experimental work the impedance measurements that we perform on doped conducting ceramics, the electrode placement is extremely crucial as the samples are thin disks and the advantage of the long rods cannot be utilized. We will demonstrate some experimental measures that we utilized to maintain uncertainly arising from the geometry issue minimal. Acknowledgement This research has been financially supported in part by the Ministry of Education, Youth and Sports of the Czech Republic under the project CEITEC 2020 (LQ1601), under NPU I program (project No. LO1210) and the COST project LD15068. Figure 1

Cellular Uptake and Movement in 2D and 3D Multicellular Breast Cancer Models of Fructose-Based Cylindrical Micelles That Is Dependent on the Rod Length.

While the shape effect of nanoparticles on cellular uptake has been frequently studied, no consistent conclusions are available currently. The controversy mainly focuses on the cellular uptake of elongated (i.e., filaments or rod-like micelles) as compared to spherical (i.e., micelles and vesicles) nanoparticles. So far, there is no clear trend that proposes the superiority of spherical or nonspherical nanoparticles with conflicting reports available in the literature. One of the reasons is that these few reports available deal with nanoparticles of different shapes, surface chemistries, stabilities, and aspects ratios. Here, we investigated the effect of the aspect ratio of cylindrical micelles on the cellular uptake by breast cancer cell lines MCF-7 and MDA-MB-231. Cylindrical micelles, also coined rod-like micelles, of various length were prepared using fructose-based block copolymers poly(1-O-methacryloyl-β-d-fructopyranose)-b-poly(methyl methacrylate). The critical water content, temperature, and stirring rate that trigger the morphological transition from spheres to rods of various aspect ratios were identified, allowing the generation of different kinetically trapping morphologies. High shear force as they are found with high stirring rates was observed to inhibit the formation of long rods. Rod-like micelles with length of 500-2000 nm were subsequently investigated toward their ability to translocate in breast cancer cells and penetrate into MCF-7 multicellular spheroid models. It was found that shorter rods were taken up at a higher rate than longer rods.

Fractionation and Characterization of High Aspect Ratio Gold Nanorods Using Asymmetric-Flow Field Flow Fractionation and Single Particle Inductively Coupled Plasma Mass Spectrometry

Gold nanorods (GNRs) are of particular interest for biomedical applications due to their unique size-dependent longitudinal surface plasmon resonance band in the visible to near-infrared. Purified GNRs are essential for the advancement of technologies based on these materials. Used in concert, asymmetric-flow field flow fractionation (A4F) and single particle inductively coupled mass spectrometry (spICP-MS) provide unique advantages for fractionating and analyzing the typically complex mixtures produced by common synthetic procedures. A4F fractions collected at specific elution times were analyzed off-line by spICP-MS. The individual particle masses were obtained by conversion of the ICP-MS pulse intensity for each detected particle event, using a defined calibration procedure. Size distributions were then derived by transforming particle mass to length assuming a fixed diameter. The resulting particle lengths correlated closely with ex situ transmission electron microscopy. In contrast to our previously reported observations on the fractionation of low-aspect ratio (AR) GNRs (AR < 4), under optimal A4F separation conditions the results for high-AR GNRs of fixed diameter (≈20 nm) suggest normal, rather than steric, mode elution (i.e., shorter rods with lower AR generally elute first). The relatively narrow populations in late eluting fractions suggest the method can be used to collect and analyze specific length fractions; it is feasible that A4F could be appropriately modified for industrial scale purification of GNRs.

Below melting point photothermal reshaping of single gold nanorods driven by surface diffusion.

Plasmonic gold nanorod instability and reshaping behavior below melting points are important for many future applications but are yet to be fully understood, with existing nanoparticle melting theories unable to explain the observations. Here, we have systematically studied the photothermal reshaping behavior of gold nanorods irradiated with femtosecond laser pulses to report that the instability is driven by curvature-induced surface diffusion rather than a threshold melting process, and that the stability dramatically decreases with increasing aspect ratio. We successfully utilized the surface diffusion model to explain the observations and found that the activation energy for surface diffusion was dependent on the aspect ratio of the rods, from 0.6 eV for aspect ratio of 5 to 1.5 eV for aspect ratio less than 3. This result indicates that the surface atoms are much easier to diffuse around in larger aspect ratio rods than in shorter rods and can induce reshaping at any given temperature. Current plasmonics and nanorod applications with the sharp geometric features used for greater field enhancement will therefore need to consider surface diffusion driven shape change even at low temperatures.

Seed‐Mediated Growth of Gold Nanorods: Limits of Length to Diameter Ratio Control

The effects of the seed reaction conditions on the two‐step seed‐mediated growth of gold nanorods and the effect of gold and reducing agent content in the growth solution were evaluated. Results indicate that the reaction conditions used to produce the seeds have a significant impact on the aspect ratio of the gold nanorods produced. Increasing the concentration of gold or the reaction temperature in the seed production step results in lower length to diameter (aspect ratio) gold rods. In addition, the amount of prepared seed added to the growth solution impacts the rod aspect ratio, with increasing amounts of seed reducing the aspect ratio. The effects of reducing agent, ascorbic acid (AA), and gold content of the growth solution on the aspect ratio of the produced rods are strongly interrelated. There exists a minimum ascorbic acid to gold concentration below which rods will not form; however, increasing the ratio above this minimum results in shorter rods being formed. Characterization of nanorod growth is performed by UV‐vis‐NIR spectrophotometry and transmission electron microscopy (TEM).

Fabrication of Silver Nanowires with Corrugated-Surface and Its SERS Performance

In order to create the effective number of surface-enhanced Raman scattering (SERS) active hot spots on the one-dimensional nanostructure surfaces for ensuring the maximum enhancement of SERS signal, smooth silver nanowires (Ag NWs) were firstly synthesized by the conventional polyol method, and then the smooth silver nanowires were subjected to chemical etching by the Fe(NO3)3 aqueous solution at room temperature to obtain corrugated silver nanowires. This corru- gated silver nanowires were systematically characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD) microscopy, Ultraviolet-visible (UV-vis) extinction spectroscopy and surface enhanced Raman spectroscopy (SERS). The SEM image of smooth silver nanowires shows that had a diameter of ca. 120 nm and lengths of about tens of micrometers, while the average thickness of corrugated nanowires was only about 100 nm. The XRD patterns for both smooth and corru- gated silver nanowires indicate that the fcc structure was preserved after chemical etching. From the measurement of UV-vis spectra we can see that after the smooth silver nanowires were subjected to chemical etching, only one broad surface plasmon peak was observed at ca. 386 nm while two significant peaks were observed at 353 and 392 nm for the smooth silver nanowires. The slight blue-shift of this peak from 392 to 386 nm could be contributed by the decrease in diameter of silver nanowires, whereas the broadening of the plasmon peak was probably a result of increased surface roughness. The SEM im- ages showed that the surface roughness of silver nanowires was dependent on the amount of Fe(NO3)3, by increasing the amount of Fe(NO3)3 added into the silver nanowires solution, the surface of silver nanowires become more and more rough. However, as the excess amount of etchant added, most silver nanowires would broke off into shorter rods, and even spherical particles. Raman analyses of crystal violet (CV) indicated that the SERS intensity changes depending on the surface rough- ness of etched silver nanowires, and the silver nanowires with corrugated surfaces exhibited higher enhancement of SERS signal than the smooth silver nanowires. In addition, the SERS detection of CV and 4-mercaptopyridine (4-Mpy) molecules exhibited high detection sensitivity and the detection concentration were as low as 10

Seed-Mediated Growth of Ultralong Gold Nanorods and Nanowires with a Wide Range of Length Tunability

This study reports a systematic approach to synthesize ultralong gold nanorods and nanowires using a seed-mediated growth approach. In the first series, the effect of growth solution pH on the lengths of nanorods prepared was investigated. Interestingly, although shorter rods (230-310 nm) were produced in a basic solution environment than in an acidic condition (330-410 nm), the nanorod yield is greatly improved with relatively few nanoplate byproducts formed. Nanorod growth proceeds quickly in a basic solution as evidenced by the fast solution color changes. By adjusting several experimental parameters with the aim to elongate the nanorod length in a tunable fashion, gold nanorods and nanowires with average lengths from 580 to 2850 nm can be synthesized by progressively increasing the HNO3 concentration in the final growth solution. Nanowire growth in a highly acidic solution is slower, and a substantially longer time is needed to reach long lengths. Further extension of the nanowire length can be achieved simply by reducing the volume of second growth solution transferred to the final growth solution. Nanorods and nanowires with lengths spanning from 700 nm to 4.5 μm were prepared in this series of experimental conditions. The longest nanowires can reach a length of up to 6 μm. The nanowires still maintain thin average diameters of 33-53 nm. The ability to make gold nanorods and nanowires over this exceptionally wide and useful length range is exciting because applications and demonstrations using ultralong gold nanorods and nanowires of most suitable lengths are now possible.

A convenient route to synthesize SBA-15 rods with tunable pore length for lysozyme adsorption

Highly ordered SBA-15 rods with tunable length and width have been synthesized by using nonionic surfactant P123 (EO20PO70EO20) as a structure-directing agent without any additives. SBA-15 rods with varying lengths (0.6–3.0μm) and widths (0.26–0.40μm) were tuned by simply adjusting the HCl concentration in the range of 0.5–2.5M. The acidity was identified to be the key factor affecting the growing manner of the rod-like particles. It was found that the length of these SBA-15 rods decreased with the increase of the HCl concentration in the synthetic mixture, while the width increased slightly. Based on our results, a possible mechanism for the effect of the HCl concentration on the growing manner of the rod-like particles was proposed. Furthermore, adsorption of lysozyme (LYS) on these SBA-15 rods was investigated and the results showed that the shorter rods with shorter pore length demonstrated very rapid LYS adsorption (<10min to reach equilibrium) and high adsorption capacity (up to 835mgg−1). This work illustrates that this route is a simple, flexible, reproducible synthesis of SBA-15 rods with tunable pore length. More importantly, it is revealed that the short pore SBA-15 rods with improved pore accessibility can greatly accelerate the adsorption rate and increase the adsorbed amount of the enzyme during the adsorption process.

Evolution of Ag 3Sn at Sn–3.0Ag–0.3Cu–0.05Cr/Cu joint interfaces during thermal aging

The intermetallic compounds (IMC) in the solder and at the interface of Sn–3.0Ag–0.5Cu (SAC)/Cu and Sn–3.0Ag–0.3Cu–0.05Cr (SACC)/Cu joints were investigated after isothermal aging at 150 °C for 0, 168 and 500 h. Different shaped Ag 3Sn phases were found near the IMC layer of the latter joint. Interestingly, fine rod-shaped and branch-like Ag 3Sn were detected near the interface after soldering and long Ag 3Sn changed into shorter rods and small particles during aging. It is investigated that the Cr addition and thermal aging have effect on the evolution of Ag 3Sn morphologies and it is controlled by interfacial diffusion. Energy minimization theory and the redistribution of elements are used to explain the morphological evolution of Ag 3Sn. Small Ag 3Sn particles were also found on the IMC layer after aging, unlike the large Ag 3Sn at that of SAC/Cu joints. In conclusion, a favorable morphology of the joint interface leads to better bonding properties for SACC/Cu joints against thermal aging than that for SAC/Cu.

From Molecular to Macroscopic Engineering: Shaping Hydrogen‐Bonded Organic Nanomaterials

The self-assembly and self-organization behavior of chromophoric acetylenic scaffolds bearing 2,6-bis(acetylamino)pyridine (1, 2) or uracyl-type (3-9) terminal groups has been investigated by photophysical and microscopic methods. Systematic absorption and luminescence studies show that 1 and 2, thanks to a combination of solvophilic/solvophobic forces and π-π stacking interactions, undergo self-organization in apolar solvents (i.e., cyclohexane) and form spherical nanoparticles, as evidenced by wide-field optical microscopy, TEM, and AFM analysis. For the longer molecular module, 2, a more uniform size distribution is found (80-200 nm) compared to 1 (20-1000 nm). Temperature scans in the range 283-353 K show that the self-organized nanoparticles are reversibly formed and destroyed, being stable at lower temperatures. Molecular modules 1 and 2 were then thoroughly mixed with the complementary triply hydrogen-bonding units 3-9. Depending on the specific geometrical structure of 3-9, different nanostructures are evidenced by microscopic investigations. Combination of modules 1 or 2 with 3, which bears only one terminal uracyl unit, leads to the formation of vesicular structures; instead, when 1 is combined with bis-uracyl derivative 4 or 5, a structural evolution from nanoparticles to nanowires is observed. The length of the wires obtained by mixing 1 and 4 or 1 and 5 can be controlled by addition of 3, which prompts transformation of the wires into shorter rods. The replacement of linear system 5 with the related angular modules 6 and 7 enables formation of helical nanostructures, unambiguously evidenced by AFM. Finally, thermally induced self-assembly was studied in parallel with modules 8 and 9, in which the uracyl recognition sites are protected with tert-butyloxycarbonyl (BOC) groups. This strategy allows further control of the self-assembly/self-organization process by temperature, since the BOC group is completely removed on heating. Microscopy studies show that the BOC-protected ditopic modules 8 self-assemble and self-organize with 1 into ordered linear nanostructures, whereas BOC-protected tritopic system 9 gives rise to extended domains of circular nano-objects in combination with 1.

Leifsonia bigeumensis sp. nov., isolated from soil on Bigeum Island, Korea

A Gram-positive, motile, mesophilic bacterium that formed yellowish-white, circular, convex, glistening colonies, strain MSL-27T, was isolated from a soil sample from Bigeum Island, Korea, and its taxonomic position was investigated by a polyphasic approach. Cells of strain MSL-27T are non-spore-forming, irregular rods, usually fragmenting into shorter rods or coccoid elements. The growth temperature and pH ranges are 20-37 degrees C and pH 6.0-12.0, with optimum growth at 28 degrees C and pH 8.0. MK-11 is the major menaquinone and dl-2,4-diaminobutyric acid is found in the cell-wall peptidoglycan. The major fatty acids are i-C16:0 (39 %), ai-C15:0 (36 %), ai-C17:0 (18 %) and i-C15:0 (2 %). The G+C content is 69.0 mol%. Phylogenetic analysis based on the 16S rRNA gene sequence revealed that strain MSL-27T should be placed in the genus Leifsonia. Levels of similarity between the 16S rRNA gene sequence of strain MSL-27T and those of the type strains of the other members of the genus Leifsonia ranged from 95.8 to 96.7 %. Based on phenotypic characteristics, biochemical properties and chemotaxonomic features, strain MSL-27T (=KCTC 19268T =DSM 19322T) represents the type strain of a novel species of Leifsonia, for which the name Leifsonia bigeumensis sp. nov. is proposed.

Detecting Water Stress in Trees Using Stem Electrical Conductivity Measurements

Using time domain reflectometry (TDR), we studied stem water content (θstem), stem electrical conductivity (σstem), and their ratio for 220 d in stressed, installation‐cured, living trees of four species. Lysimeter‐grown mango (Mangifera indica L.), banana (Musa acuminata Colla), date (Phoenix dactylifera L.), and olive (Olea europaea L.) were subjected to several types of mild (intensity and duration) water stresses simulating horticultural orchard irrigation practices. This study of living trees was triggered by our previous study accomplished in uncured, thawed, native, cut stem segments. We have confirmed in living trees our earlier findings that θstem reacts sensitively and within minutes to water stress. This response is the main driver of σstem changes, by far exceeding the salinity effect on σstem Known irrigation rates, half‐hourly tree weights from load cells, and frequent sampling of drainage solution for volume and salinity independently confirmed our findings. Relative to θstem, resistivity measurements have lower scatter because θstem–dielectric constant (ε) relationships are exponential and θstem–resistivity relationships are linear. With resistivity, there is no need to match impedances among meter, cable, and probe, implying a larger flexibility in probe geometry, longer cables, and higher accuracy with shorter rods. There is a clear economic advantage in resistivity over ε measurements. The linkage between stem resistivity and water status (designated as the linkage factor) for lysimeter plants, orchard trees, and cut stem segments demonstrates the potential in scheduling irrigation according to plant water needs with an inexpensive, direct, and simple resistivity measurement.

Effects of morphological changes in beer-spoilage lactic acid bacteria on membrane filtration in breweries

Membrane filter performance was investigated using beer-spoilage lactic acid bacteria (LAB). As a result, beer-adapted LAB strains showed considerably increased penetration rate through filters, as compared with non-adapted strains. Further statistical analyses demonstrated the significant shifts in cell size distribution towards shorter rods, when Lactobacillus brevis and L. lindneri strains were precultured in beer. These results indicate that diminished cell size is responsible for the deteriorated filter performance and, therefore, beer-adapted lactic acid bacteria are regarded as a serious threat to the production of unpasteurized beers. In addition, the selection of test strains and preculture conditions are suggested to be important for the rigorous and standardized evaluation of membrane filter performance in the brewing industry.

Zwanzig model of multi-component mixtures of biaxial particles: y 3 theory re-visited

The paper considers the thermodynamic and phase ordering properties of a multi-component Zwanzig mixture of hard rectangular biaxial parallelepipeds. An equation of state (EOS) is derived based on an estimate of the number of arrangements of the particles on a three- dimensional cubic lattice. The methodology is a generalization of the Flory–DiMarzio counting scheme, but, unlike previous work, this treatment is thermodynamically consistent. The results are independent of the order in which particles are placed on the lattice. By taking the limit of zero lattice spacing, a translationally continuous variant of the model (the off-lattice variant) is obtained. The EOS is identical to that obtained previously by a wide variety of different approaches. In the off-lattice limit, it corresponds to a third-level y-expansion and, in the case of a binary mixture of square platelets, it also corresponds to the EOS obtained from fundamental measure theory. On the lattice it is identical to the EOS obtained by retaining only complete stars in the virial expansion. The off-lattice theory is used to study binary mixtures of rods (R 1 − R 2) and binary mixtures of platelets (P 1 − P 2). The particles were uniaxial, of length (thickness) L and width D. The aspect ratios Γ i = Li /Di of the components were kept constant (Γ1 R = 15, Γ1 P = 1/15 and Γ2 R = 150, Γ2 P = 1/150), so the second virial coefficient of R 1 was identical to P 1 and similarly for R 2 and P 2. The volume ratio of particles 1 and 2, v 1/v 2, was then varied, with the constraints that viR = viP and Results on nematic–isotropic (N − I) phase coexistence at an infinite dilution of component 2, are qualitatively similar for rods and platelets. At small values of the ratio v 1/v 2, the addition of component 2 (i.e. a thin rod (e.g. a polymer) or a thin plate) results in the stabilization of the nematic phase. For larger values of v 1/v 2, however, this effect is reversed and the addition of component 2 destabilizes the nematic. For similar molecular volumes of the two components strong fractionation is observed: shorter rods and thicker platelets congregate in the isotropic phase. In general, the stabilization of the ordered phase and the fractionation between the phases are both weaker in the platelet mixtures. The calculated spinodal curves for isotropic-isotropic demixing are noticeably different between the R 1 − R 2 and the P 1 − P 2 systems. The platelet mixtures turn out to be stable with respect to de-mixing up to extremely high densities. The values of the consolute points for the R 1 − R 2 blends are remarkably similar to those obtained using the Parsons–Lee approximation for bi-disperse mixtures of freely rotating cylinders with similar aspect ratios [S. Varga. A. Galindo, G. Jackson, Mol. Phys., 101, 817 (2003)]. In a number of R 1 − R 2 mixtures, phase diagrams exhibiting both N − I equilibrium and I − I de-mixing were calculated. The latter is pre-empted by nematic ordering in all the cases studied. Calculations show the possible appearance of azeotropes in the N − I coexistence domain.

Effect of flow on solutions of rod-coil block co-polymers

An elongational flow field is imposed on a solution of block copolymers consisting of semirigid macromolecules with rigid, rodlike sequences of units in combination with random coil (flexible) units. The problem is formulated according to the lattice treatment of Matheson and Flory. In this formulation, the system consists of rigid blocks whose lengths and locations are fixed by the structure within each macromolecule. These blocks are separated by random coiled units. An excess free energy other than the equilibrium Gibbs free energy of the quiescent solution has to be considered due to the flow field that tends to align the rods. This excess free energy is calculated from the potential energy of rods when a steady-state, homogeneous and irrotational flow field is applied to the solution. The effects of composition, polymer–solvent interaction, size of the co-polymer and flow rates are investigated. Depending on the size and number of rods, some of the chains studied exhibit a biphasic region at equilibrium that shifts to lower concentrations with increasing flow. Longer chains with shorter rods that are isotropic at equilibrium, exhibit a biphasic region at finite values of flow. The degree of orientation increases sharply when the system is biphasic. For larger flows, the orientation function is very close to unity which is perfect orientation.