Diffusion in microstructured block copolymer solutions

This work explores the effect of heterogeneity of chemical composition on tracer diffusion, when the characteristic size of the heterogeneities approaches that of the diffusing molecule. A heterogeneous environment is created by the self-assembly of diblock copolymers in solution. The system chosen for this study is polystyrene-polyisoprene diblock copolymers in toluene, which is a common solvent for the two blocks. Above a certain critical concentration, these systems are known to microphase separate into swollen domains of polystyrene and polyisoprene. Diffusion of homopolystyrene through the microstructure is measured in this work. The characteristics of the microstructure are varied by studying block copolymers of different molecular weights and compositions. The tracer diffusion coefficients of the labelled polystyrenes are measured by forced Rayleigh scattering, while the microstructure of the matrix is inferred from small angle X-ray scattering measurements. In this paper, we report results for the diffusion of polystyrenes (molecular weights 3.2 × 10⁴ and 9.0 × 10⁴) in microstructured solutions of three copolymers. Two copolymer samples forming lamellae of alternating polystyrene and polyisoprene microphases and one sample forming polystyrene cylinders embedded in a polyisoprene matrix have been examined. The data indicate that the tracer diffusion coefficient of 3.2 × 10⁴ molecular weight polystyrene in lamellar and cylindrical solutions is comparable to that of the homopolymer in a homogeneous solution of the same concentration. In contrast, the diffusion of 9.0 × 10⁴ molecular weight polystyrene is substantially slower in the structured solutions than in unstructured solutions of the same concentration. For example, the diffusion coefficient of 9.0 × 10⁴ molecular weight polystyrene in a 47% block copolymer solution with cylindrical microstructure is lower than its value in a homogeneous solution of the same concentration by a factor of 30.     

Tracer diffusion in fluctuating block copolymer melts

We present a theoretical investigation of the tracer diffusion of diblock copolymers and homopolymers in a thermally fluctuating block copolymer melt above the order-disorder transition (ODT) temperature. Entanglement effects and differences in monomeric friction coefficients are ignored; hence, the theory should be most applicable to short copolymers with rheologically similar blocks. Overall, we find that the diffusion rates of both tracer block copolymers and homopolymers in a block copolymer melt are suppressed when compared with diffusivities in a strictly homogeneous medium with the same average composition. This mobility suppression is due to thermally excited composition fluctuations in block copolymer melts near the ODT; the latter result in transient potential barriers to diffusion. We explore the dependence of the tracer diffusion coefficient on molecular weights and compositions of both matrix and tracer, as well as temperature. A comparison of our theoretical predictions to recent experiments by T. Lodge and coworkers shows qualitative agreement. © 1996 John Wiley & Sons, Inc.     

Microphase separation transition in block copolymer melts

The microphase separation transition (MST) in block copolymer melts has been studied using synchrotron SAXS. The results indicate that the MST occurs in the range of molecular weights and Flory-Huggins interaction parameters x predicted by the theory of Leibler (Ref. 5). Studies of the MST as a function of molecular weight for constant composition can be used to determine the temperature dependence of x. The observed change of macrolattice constants with temperature is somewhat different from theoretically predicted values.     

Unusual finite size effects in the Monte Carlo simulation of microphase formation of block copolymer melts

Extensive Monte Carlo simulations are presented for the Fried-Binder model of block copolymer melts, where polymer chains are represented as self and mutually avoiding walks on a simple cubic lattice, and monomer units of different kind (A, B) repel each other if they are nearest neighbors (ε_AB > 0). Choosing a chain length N = 20, vacancy concentration Φ_v = 0,2, composition ƒ = 3/4, and a L × L × L geometry with periodic boundary conditions and 8 ≤ L ≤ 32, finite size effects on the collective structure factor S(q) and the gyration radii are investigated. It is shown that already above the microphase separation transition, namely when the correlation length ξ(T) of concentration fluctuations becomes comparable with L, a nonmonotonic variation of both S(q) and the radii with L sets in. This variation is due to the fact that the wavelength λ^*(T) of the ordering (defined from the wavenumber q^* where S(q) is maximal at λ^* = 2 π/q^*) in general is incommensurable with the box. The competition of two nontrivial lengths ξ(T), λ^* (T) with L makes the straigthforward application of finite size scaling techniques impossible, unlike the case of polymer blends. Since also the specific heat is found to have a broad rounded peak near the transition only, locating the transition accurately from Monte Carlo simulations remains an unsolved problem.     

Diffusion and reaction in polyester melts

An understanding of the physical and chemical processes involved in the melt polymerization of polyesters in the higher inherent viscosity ranges is of fundamental importance in polyester preparation. For example, the volatile condensation product must diffuse to a polymer–vapor interface before polymerization can take place. Thus, the rate of polymerization of a polyester may be dependent not only upon the chemical kinetics of the polymerization reaction but also upon the diffusion of the condensation product through the polymer melt. The objective of the work presented in this paper was to determine to what degree diffusion or reaction kinetics, or both, limit the melt polycondensation of poly(ethylene terephthalate). Degrees of polymerization in melts between 0.0285 and 0.228 cm in depth at 270°C were measured for various reaction times and were compared with the predictions of mathematical models. The polycondensation rates under these conditions depend upon both the polycondensation rate constant k₁ and the diffusivity D of ethylene glycol through the melt. Estimates of the values to these parameters are: k₁ = 0.0500 (moles/mole of repeat unit)^?1 sec^?1; D = 1.66 × 10^?4 cm²/sec.     

Surface tension of random copolymer melts

A mean-field theory is presented to describe the surface tension and interfacial profile of random A-B multiblock copolymer melts in contact with air or a solid substrate. The copolymer model accounts for variations in average composition and block sequence distribution, and reduces to a model for statistical copolymers as the block size approaches that of a monomer. Ideal copolymers lacking chemical correlations between successive segments are predicted to have a larger surface tension than “blocky” copolymers with a tendency for repeated segments of A or B. © 1992 John Wiley & Sons, Inc.     

Diffusion,rheology, and flow birefringence in block copolymer liquids near the ordering transition

Measurements of the diffusion and relaxation of block copolymer chains near the order-disorder transition (ODT) are reported. Forced Rayleigh scattering has been used to determine the diffusivities parallel and perpendicular to the lamellar planes, for poly(ethylene-propylene)-poly(ethylethylene) (PEP-PEE) melts. The anisotropy is relatively weak (i.e., less than a factor of 4), but increases steadily as temperature is decreased. Rheology and flow birefringence have been employed to examine the conformational dynamics in block copolymer solutions. For PEP-PEE in squalane, the stress-optic relation is approximately valid, but the stress-optic coefficient increases in the ordered state. The location of the ODT is consistent with the dilution approximation. For polystyrene-polyisoprene (PS-PI) diblock and triblock copolymers, the stress-optic relation fails completely. There is evidence that the fluctuation regime (i.e., in the disordered state but near the ODT) may be considerably broader in block copolymer solutions than in melts. Furthermore, the onset of structure in the solution is accompanied by substantial form birefringence. In general, the optical signals are more complicated than the Theological ones, but also much more sensitive to small changes in temperature or concentration.     

Fddd network phase in ABA triblock copolymer melts

Using self‐consistent field theory, we investigate the stability of the orthorhombic Fddd network phase (O⁷⁰) in ABA triblock copolymer melt systems. Consistent with previous findings, we observe that the gross topology of phase behavior is unchanged with varying chain asymmetry. However, the mean field critical point is displaced from the diblock copolymer value of f_A = 0.5 (f_A is the A segment volume fraction) to larger values as the triblock copolymer symmetry is broken with unequal A block lengths. This deviation significantly shifts the order‐order phase boundaries, resulting in an appreciable region of O⁷⁰ stability in the phase diagram of asymmetric ABA triblock copolymers. More importantly, the stability of the O⁷⁰ phase extends to the intermediate segregation regime for select chain asymmetries. Both features are desirable for achieving a synthetic realization of the phase in binary AB block copolymer systems. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1112–1117     

Maximizing the grain growth rate during the disorder‐to‐order transition in block copolymer melts

The factors controlling grain growth during the disorder‐to‐order transition in a polystyrene‐block‐polyisoprene copolymer melt were studied with time‐resolved depolarized light scattering. The ordered phase consisted of hexagonally packed polyisoprene cylinders, and the order–disorder‐transition temperature of the block copolymer (T_ODT) was 132 ± 1 °C. Our objective was to identify the temperature at which the grain growth rate was maximized (T_max) and compare it with theoretical predictions. We conducted seeded grain growth experiments, which comprised two steps. In the first step, which lasted for 43 min, the sample was cooled from the disordered state to 124 °C. This resulted in the formation of a small number of ordered grains or seeds. This was followed by a second step in which the sample was heated to temperatures between 124 and 132 °C and the seeds grew with time. Our objective was to study grain growth at different temperatures starting from the same initial condition. The value of T_max obtained experimentally was 128 °C. The theoretically predicted value of T_max, based entirely on the rheological properties of the disordered sample and T_ODT, was also 128 °C. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2231–2242, 2001     

Solid-supported block copolymer membranes through interfacial adsorption of charged block copolymer vesicles

The properties of amphiphilic block copolymer membranes can be tailored within a wide range of physical parameters. This makes them promising candidates for the development of new (bio)sensors based on solid-supported biomimetic membranes. Here we investigated the interfacial adsorption of polyelectrolyte vesicles on three different model substrates to find the optimum conditions for formation of planar membranes. The polymer vesicles were made from amphiphilic ABA triblock copolymers with short, positively charged poly(2,2-dimethylaminoethyl methacrylate) (PDMAEMA) end blocks and a hydrophobic poly( n-butyl methacrylate) (PBMA) middle block. We observed reorganization of the amphiphilic copolymer chains from vesicular structures into a 1.5+/-0.04 nm thick layer on the hydrophobic HOPG surface. However, this film starts disrupting and dewetting upon drying. In contrast, adsorption of the vesicles on the negatively charged SiO2 and mica substrates induced vesicle fusion and formation of planar, supported block copolymer films. This process seems to be controlled by the surface charge density of the substrate and concentration of the block copolymers in solution. The thickness of the copolymer membrane on mica was comparable to the thickness of phospholipid bilayers.     

Nonionic block copolymer antifoams

Aqueous dispersions of alkoxylated alcohol block copolymer (BCP) drops are investigated as antifoams. A model aqueous nonionic surfactant solution of Polysorbate 20 and an industrial white water suspension are used as foaming systems. Visual evidence obtained using a two-bubble technique involving a CCD camera coupled with high magnification lenses clearly revealed the role of BCP droplets in the bubble coalescence process. The enhancement of bubble coalescence decreased as the temperature increased from 25 to 60 degrees C, which is due to the corresponding decrease in the rigidity associated with the weak interfacial structure and reduced viscosity of the BCP drops. The antifoaming efficiency measured in the macroscopic recirculation foam column increased with temperature from about 13 to 26 degrees C (attaining a maximum) and decreased as temperature increased further. Oscillatory thermo-rheometric measurements showed a sudden increase in the storage modulus (G') by several orders of magnitude, indicating gel formation initiated at about 13 degrees C and having a maximum at around 26 degrees C for an aqueous solution of the BCP above a critical concentration of around 20 wt %. Results obtained using small-angle X-ray scattering, micro-differential scanning calorimetry, and proton nuclear magnetic resonance confirmed the existence of ordered gel-like structures. Furthermore, macroscopic tests using a sparged air foam column showed a significant increase in antifoaming efficiency when highly hydrophobic particles are embedded in the BCP drops dispersed in water.     

Reactive block copolymer scaffolds

Block copolymers with sequences of differential reactivity were synthesized, and the step-wise and selective derivatization to form a new block copolymer was demonstrated.     

Molecule-responsive block copolymer micelles

Ring-opening metathesis polymerization was used to generate an ABC triblock copolymer, containing complementary diamidopyridine (DAP) and thymine (THY) outer blocks, which assembles into spherical aggregates held together by DAP-THY noncovalent interactions. Addition of THY-containing small guest molecules results in complete opening and deaggregation of the block copolymer micelle. This molecular recognition and macroscopic response shows high selectivity to the guest structure, and tolerates only a small amount of conformational mobility in the THY guest. On the other hand, addition of a small DAP-containing guest does not break the aggregates, but instead, results in new micelles which show a different selectivity profile from the parent morphology. We have examined the effect of a number of structural features in the block copolymers, on both the extent and selectivity of their macroscopic response to guests (that is, opening of the micelle). This study has resulted in a set of structural guidelines, which help in the design of effective molecule-responsive micelles for applications in selective drug delivery, sensing, and surface patterning.     

Bactericidal block copolymer micelles

Block copolymer micelles with bactericidal properties were designed to deactivate pathogens such as E. coli bacteria. The micelles of PS‐b‐PAA and PS‐b‐P4VP block copolymers were loaded with biocides TCMTB or TCN up to 20 or 30 wt.‐%, depending on the type of antibacterial agent. Bacteria were exposed to loaded micelles and bacterial deactivation was evaluated. The micelles loaded with TCN are bactericidal; bacteria are killed in less than two minutes of exposure. The most likely interpretation of the data is that the biocide is transferred to the bacteria by repeated micelle/bacteria contacts, and not via the solution.

     

Morphology of microphase separated domains in rod-coil copolymer melts

We investigate the morphology of microphase separated domains in diblock copolymers where each chain consists of a stiff rod block and a flexible coil block. A simplified phenomenological model system is introduced, which is coarse-grained in terms of the local concentration difference between the two blocks and the local director field of the rod part. Computer simulations of this set of time-evolution equations in two dimensions show in the weak segregation regime that the elastic energy in the rod-block rich domains affects drastically the structures of microphase separated domains. A coil-to-rod transition is incorporated into the model system to examine the elastic and anisotropic effects. The effects of the external electric field are also investigated to control the domain morphology.     

Integral equation theory of randomly coupled multiblock copolymer melts: effect of block size on the phase behavior

The phase behavior of randomly coupled multiblock copolymer melts is studied using the polymer reference interaction site model integral equation theory. The molecules are modeled as flexible chains with random sequences of two types of blocks, each of which consists of the same number (R) of monomer beads. In the random copolymer (R=1) limit the theory predicts macrophase separation as the temperature is decreased for all values of the monomer correlation length lambda. For R>2, however, the theory predicts a microphase separation for values of lambda less than some critical value which increases as the block size increases.     

Coarse graining in block copolymer films

We present few ordering mechanisms in block copolymer melts in the coarse-graining approach. For chemically homogeneous or modulated confining surfaces, the surface ordering is investigated above and below the order–disorder temperature. In some cases, the copolymer deformation near the surface is similar to the copolymer morphology in bulk grain boundaries. Block copolymers in contact with rough surfaces are considered as well, and the transition from lamellae parallel to perpendicular to the surface is investigated as a function of surface roughness. Finally, we describe how external electric fields can be used to align block copolymer mesophases in a desired direction, or to induce an order–order phase transition, and dwell on the role of mobile dissociated ions on the transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2725–2739, 2006     

PVT properties of polyethylene copolymer melts

PVT properties of four polyethylene random copolymers (ethylene-propylene, ethylene-1-butene, ethylene-1-hexene, and ethylene-1-octene) and linear polyethylene were measured at temperatures from 313 to 493 K and pressures up to 200 MPa. Dependence of properties such as specific volume, thermal expansion coefficient, isothermal compressibility, and characteristic parameter of equations of state on the length of the polymer branched chains were examined. It was found that the length of the branched chain did not affect the thermal expansion coefficient and isothermal compressibility. The specific volume of copolymers having longer branched chains were slightly larger than those copolymers with short branched chains.