Effect of large degrees of polydispersity on strongly segregated block copolymers

We investigate the effect of polydispersity on the lamellar phase of a diblock copolymer melt using self-consistent field theory (SCFT). A previous SCFT calculation predicted that polydispersity increases the domain spacing consistent with experiment, but it also suggested that the effect vanishes with increasing segregation contrary to experiment. We attribute this disagreement to a problem of slow convergence of the Gaussian-quadrature technique used to integrate over the molecular-weight distribution when either the segregation or polydispersity index is large. Here the problem is overcome by a new efficient algorithm that allows high-order quadratures for relatively little computational cost. When implemented, we find that the elevated domain spacing does indeed persist into the strong-segregation regime consistent with experiment. This conclusion is also substantiated by the analytical strong-segregation theory (SST).     

Bicontinuous geometries and molecular self-assembly: comparison of local curvature and global packing variations in genus-three cubic, tetragonal and rhombohedral surfaces

Balanced infinite periodic minimal surface families that contain the cubic Gyroid (G), Diamond (D) and Primitive (P) surfaces are studied in terms of their global packing and local curvature properties. These properties are central to understanding the formation of mesophases in amphiphile and copolymer molecular systems. The surfaces investigated are the tetragonal, rhombohedral and hexagonal tD, tP, tG, rG, rPD and H surfaces. These non-cubic minimal surfaces furnish topology-preserving transformation pathways between the three cubic surfaces. We introduce `packing (or global) homogeneity', defined as the standard deviation Δd of the distribution of the channel diameter throughout the labyrinth, where the channel diameter d is determined from the medial surface skeleton centered within the labyrinthine domains. Curvature homogeneity is defined similarly as the standard deviation ΔK of the distribution of Gaussian curvature. All data are presented for distinct length normalisations: constant surface-to-volume ratio, constant average Gaussian curvature and constant average channel diameter. We provide first and second moments of the distribution of channel diameter for all members of these surfaces complementing curvature data from [A. Fogden, S. Hyde, Eur. Phys. J. B 7, 91 (1999)]. The cubic G and D surfaces are deep local minima of Δd along the surface families (with G more homogeneous than D), whereas the cubic P surface is an inflection point of Δd with adjacent, more homogeneous surface members. Both curvature and packing homogeneity favour the tetragonal route between G and D (via tG and tD surfaces) in preference to the rhombohedral route (via rG and rPD).     

Spontaneous condensation in DNA-polystyrene- b-poly(l-lysine) polyelectrolyte block copolymer mixtures

We investigated the condensation of calf thymus DNA by amphiphilic polystyrene_m-b-poly(l-lysine)_n block copolymers ( PS_m-b- PLys_n, m, n = degree of polymerization), using small-angle X-ray scattering, polarized optical microscopy and laser scanning confocal microscopy. Microscopy studies showed that the DNA condenses in the form of fibrillar precipitates, with an irregular structure, due to electrostatic interactions between PLys and DNA. This is not modified by the presence of hydrophobic PS block. Scattering experiments show that the structure of the polyplexes corresponds to a local order of DNA rods which becomes more compact upon increasing n. It can be concluded that for DNA/ PS_m-b- PLys_n polyplexes, the balance between the PLys block length and the excess charge in the system plays an essential role in the formation of a liquid crystalline phase.     

Self-assembly of rod-coil block copolymers from weakly to moderately segregated regimes

We report on the self-assembly behaviour of two homologue series of rod-coil block copolymers in which, the rod, a π -conjugated polymer, is maintained fixed in size and chemical structure, while the coil is allowed to vary both in molecular weight and chemical nature. This allows maintaining constant the liquid crystalline interactions, expressed by Maier-Saupe interactions, ω , while varying the tendency towards microphase separation, expressed by the product between the Flory-Huggins parameter and the total polymerization degree, χN . Therefore, the systems presented here allow testing directly some of the theoretical predictions for the self-assembly of rod-coil block copolymers in a weakly segregated regime. The two rod-coil block copolymer systems investigated were poly(DEH-p-phenylenevinylene-b-styrene), whose self-assembly takes place in the very weakly segregated regime, and poly(DEH-p-phenylenevinylene-b-4vinylpyridine), for which the self-assembly behaviour occurs under increased tendency towards microphase separation, hereby referred to as moderately segregated regime. Experimental results for both systems are compared with predictions based on Landau expansion theories.     

A small-angle X-ray scattering study of the isotropic and nematic phases of V2O5 suspensions

We report small-angle X-ray scattering experiments performed in both the isotropic and nematic phases of aqueous V₂O₅ suspensions. We show that the scattering in the isotropic phase can be well described in the whole accessible q-range by only considering the form factor of non-interacting ribbons. We investigate the influence of concentration and pH on the dimensions of V₂O₅ ribbons and show that these parameters do not have any significant effect, as long as the system stays well within the chemical stability domain of the ribbons. We then show that nematic single domains display an anisotropic small-angle scattering pattern, even at scattering vectors small compared to that at which a characteristic correlation peak is observed. This feature is expected for a nematic phase, but was rarely observed. We finally try to describe this scattering within the framework of theories developed for the structure factor of a nematic polymer, and we reach the conclusion that chain ends are certainly important to understand this pattern. Received 21 July 1999 and Received in final form 17 December 1999     

Shrinking of anionic polyacrylate coils induced by Ca2+, Sr2+ and Ba2+: A combined light scattering and ASAXS study

Anionic polyacrylate chains (NaPA) form precipitates if alkaline earth cations are added in stoichiometric amounts. Accordingly, precipitation thresholds were established for three different alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Close to the precipitation threshold, the NaPA chains significantly decrease in size. This shrinking process was followed by means of combined static and dynamic light scattering. Intermediates were generated by varying the ratio [MCl₂]/[NaPA] with M denoting the respective alkaline earth cation. All experiments were performed at an inert salt level of 0.01M NaCl. Similar coil-to-sphere transitions could be observed with all three alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Based on these findings, supplementary conventional and anomalous small-angle X-ray scattering experiments using selected intermediates close to the precipitation threshold of SrPA were performed. The distribution of Sr counterions around the polyacrylate chains in aqueous solution provided the desired scattering contrast. Energy-dependent scattering experiments enabled successful separation of the pure-resonant terms, which solely stem from the counterions. The Sr²⁺ scattering roughly reflects the monomer distribution of the polyacrylate chains. Different ratios of the concentrations of [ SrCl₂]/[NaPA] revealed dramatic changes in the scattering curves. The scattering curve at the lowest ratio indicated an almost coil-like behaviour, while at the higher ratios the scattering curves supported the model of highly contracted polymer chains. Most of X-ray scattering experiments on intermediate states revealed compact structural elements which were significantly smaller than the respective overall size of the NaPA particles.     

Main-chain smectic liquid-crystalline polymers as randomly disordered systems

We report a high-resolution X-ray lineshape study of main-chain smectic polymers. The results indicate that the layer ordering differs fundamentally from the algebraic decay typical for other smectic liquid-crystalline systems. The lineshapes are best described by broad squared Lorentzians indicating some form of short-range correlations. However, several higher harmonics are observed, which excludes simple liquid-like short-range order. This behaviour is tentatively attributed to a random field of defects associated with entangled hairpins in the main-chain polymer structure.     

A biaxial nematic gel phase in aqueous vanadium pentoxide suspensions

Aqueous suspensions of V₂O₅ ribbons are one of the very few examples of mineral liquid crystals. In the concentrated regime, we show that these ribbons organize in a biaxial nematic gel phase. A Couette shear cell was used to produce a well oriented sample for in situ synchrotron X-ray scattering studies. We observed two perpendicular anisotropic sections of reciprocal space, which proves the biaxial symmetry of the nematic order. The thermodynamic and flow properties of the biaxial nematic are well described by hard-core theories. We suggest the use of a shear geometry to produce and investigate single domains of other biaxial nematics, reported but still questioned in the literature. Received 26 May 1999     

Chain length dependence of anomalous swelling in multilamellar lipid vesicles

Using small-angle X-ray scattering, the repeat distance vs. temperature is measured for a homologous series of multilamellar vesicles of lecithins with varying acyl chain length in excess water condition around the lipid main transition. A systematic chain length dependence is found which is in accordance with a bending rigidity renormalization and critical unbinding of the lamellae close to the transition, as previously suggested in H?nger et al. [Phys. Rev. Lett. 72, 3911 (1994)]. Received 13 January 1999 and Received in final form 6 September 1999     

Copper and copper oxide nanoparticles in a cellulose support studied using anomalous small-angle X-ray scattering

Microcrystalline cellulose is a porous natural material which can be used both as a support for nanoparticles and as a reducer of metal ions. Cellulose supported nanoparticles can act as catalysts in many reactions. Cu, CuO, and Cu₂O particles were prepared in microcrystalline cellulose by adding a solution of copper salt to the insoluble cellulose matrix and by reducing the copper ions with several reducers. The porous nanocomposites were studied using anomalous small angle X-ray scattering (ASAXS), X-ray absorption spectroscopy, and X-ray diffraction. Reduction of Cu²⁺ with cellulose in ammonium hydrate medium yielded crystalline CuO nanoparticles and the crystallite size was about 6–20 nm irrespective of the copper concentration. The size distribution of the CuO particles was determined with ASAXS measurements and coincided with the crystallite sizes. Using sodium borohydrate or hydrazine sulfate as a reducer both metallic Cu and Cu₂O nanoparticles were obtained and the crystallite size and the oxidation state depended on the amount of reducer.     

Chain segment ordering in lamellar sublayers of block copolymers: A NMR study

The chain segment dynamics in the bulk lamellar phase of polystyrene-polydimethylsiloxane (PS-PDMS) block copolymers has been probed by NMR. The experiments were performed on a PS-PDMS diblock and on a PS-PDMS-PS triblock with twice the molecular weight. In the diblock, at room temperature, the PDMS block segments undergo uniaxial reorientations around the normal to the lamellae. In the triblock, the reorientational motions exhibit a lower degree of symmetry: deviations from a uniaxial dynamics are observed. Such a behaviour originates in the anchorage of both PDMS chain ends into the PS glassy layers. Received 27 September 2001 and Received in final form 18 January 2002     

Undulating membrane structure under mixed extensional-shear flow

We report on studies using a new X-ray extensional flow cell to examine, for the first time, the structure of undulating lamellar lyotropic liquid crystal systems under extensional flow. The extensional component of the flow profile produced within this cell causes the lamellae to orient. We find that, although the intermembrane spacing does not change at low flow rates, it suddenly decreases after a critical flow rate has been attained due to the stretching and straightening of the lamellae. The effects of the shear component of flow on this oriented system have been examined in the context of a theoretical model developed by Ramaswamy. Received 29 May 2001 and Received in final form 20 July 2001     

X-ray scattering study of the electric-field-induced layer deformations of an antiferroelectric Liquid Crystal

The effect of an external electric field on the local layer structure is investigated in the SmC^* _A, SmC^* _FI and SmC^* phases using X-ray diffraction. X-ray scattering and spontaneous polarization measurements are performed under several increasing (and decreasing) steps of AC applied voltage. The effects of the electric field differ significantly from one phase to the other. The chevron-to-bookshelf transition occurs abruptly at a high field value in the SmC^* _A phase whereas layer deformations are more progressive and occur at lower field values in the other phases. Comparison of the different behaviours suggests that the destruction of the chevron structure is mainly affected by the local molecular order. Received 16 July 2001 and Received in final form 7 December 2001     

Insertion of small anisotropic clay particles in swollen lamellar or sponge phases of nonionic surfactant

we have established experimentally the region of existence of smectic and sponge lyotropic microstructures in the presence of synthetic hydrophilic clay particles. Taking into account the adsorption isotherm, we determined the extension of the single-phase regions by visual inspection and looking at low-q behaviour of the small-angle neutron scattering. Conditions of stability such as geometric constraints associated with fluctuation quenching are discussed. Received 11 December 2000 and Received in final form 11 April 2001     

Amphiphilic diblock copolymers with adhesive properties: I. Structure and swelling with water

We study asymmetric block copolymers with the simple diblock AB architecture, in the case where the longer block A is both hydrophobic and “soft”, whereas the shorter block B is hydrophilic and “hard”. Materials with such a particular combination of physico-chemical and mechanical properties have distinctive advantages, in particular for designing water-compatible adhesive materials. The phase diagram is established, combining NMR and SAXS characterisations of the materials. The swelling with water is monitored through gravimetry and “time-resolved” SAXS. Indications of maintained adhesive properties in a wet environment are given.     

Microphase separation in weakly charged hydrophobic polyelectrolytes

Aqueous solutions of a well-defined poly(N-isopropylacrylamide-co-sodium 2-acrylamido-methylpropanesulfonate) (NIPAM/NaAMPS in a 95/5 molar ratio) have been investigated by means of small-angle neutron scattering (SANS) and rheological experiments as a function of temperature ( 25^° C T 60^° C) and polymer concentration ( 0.5wt% C 12wt%). The solutions remain optically transparent and isotropic over the whole temperature range, in contrast with the homopolyNIPAM which precipitates above its lower critical solution temperature (LCST = 32^° C). Upon addition of salt, the systems undergo a micro-macrophase separation. At temperatures above 45^° C, the SANS spectra exhibit a sharp peak at a scattering wave vector, q _max, which increases slightly with temperature. At high temperature ( T∼ 60^° C), the scattered intensity follows a power law I(q) ∼q ^-4 in the asymptotic regime, characteristic of two-density media with sharp interfaces, and q _max is found to vary with polymer concentration as q _max∼C ^0.22. Estimates of the typical sizes give values between 40 ? and 200 ?. These results provide a strong evidence of a thermally induced microphase separation, which is corroborated by the very sharp increases of the viscosity (over 2 decades) and of the stress relaxation time of the solutions, occurring in the temperature range where the scattering peak is observed. The results are discussed and compared with the theoretical models proposed for weakly charged polyelectrolytes in a poor solvent. Received 1 October 2001     

Undulated cylinders of charged diblock copolymers

We study the cylinder to sphere morphological transition of diblock copolymers in aqueous solution with a hydrophobic block and a charged block. We find a metastable undulated cylinder configuration for a range of charge and salt concentrations which, nevertheless, occurs above the threshold where spheres are thermodynamically favorable. By modeling the shape of the cylinder ends, we find that the free-energy barrier for the transition from cylinders to spheres is quite large and that this barrier falls significantly in the limit of high polymer charge and low solution salinity. This suggests that observed undulated cylinder phases are kinetically trapped structures.     

Spontaneous bending of 2D molecular bottle-brush

Using a scaling approach we consider a 2D comb copolymer brush under bending deformations. We show that the rectilinear brush is locally stable and can be characterized by a persistence length λ increasing with the molecular weight of grafting side chains as λ ∼ M³. A bending instability due to redistribution of the side chains appears in the non-linear regime where bending is strong. Arguments are presented that the brush conformations consist of alternating rectilinear and bent sections corresponding to the different free-energy minima.     

Scattering properties of gradient heteropolymers obtained by “living” free-radical copolymerization

An original, quantitative, theory of “living” radical copolymerization has been developed proceeding from the current concepts of its kinetics and mechanism. This theory enables one to calculate both the dependence of monomers' conversion on time and any statistical characteristics of the chemical structures of the copolymers formed. Expressions have been derived describing the angular dependence of the scattering amplitude of the copolymerization products. The results of quantitative calculations of these characteristics have been also presented to exemplify the potentialities of the theory. Received 13 February 2001 and Received in final form 4 February 2002