Interdiffusion and Composition Polydispersity in Diblock Copolymers above the Ordering Transition

Dynamic light scattering and transmission electron microscopy in drug delivery: a roadmap for correct characterization of nanoparticles and interpretation of results

In this focus article, we provide a scrutinizing analysis of transmission electron microscopy (TEM) and dynamic light scattering (DLS) as the two common methods to study the sizes of nanoparticles with focus on the application in pharmaceutics and drug delivery. Control over the size and shape of nanoparticles is one of the key factors for many biomedical systems. Particle size will substantially affect their permeation through biological membranes. For example, an enhanced permeation and retention effect requires a very narrow range of sizes of nanoparticles (50-200 nm) and even a minor deviation from these values will substantially affect the delivery of drug nanocarriers to the tumour. However, amazingly a great number of research papers in pharmaceutics and drug delivery report a striking difference in nanoparticle size measured by the two most popular experimental techniques (TEM and DLS). In some cases, this difference was reported to be 200-300%, raising the question of which size measurement result is more trustworthy. In this focus article, we primarily focus on the physical aspects that are responsible for the routinely observed mismatch between TEM and DLS results. Some of these factors such as concentration and angle dependencies are commonly underestimated and misinterpreted. We convincingly show that correctly used experimental procedures and a thorough analysis of results generated using both methods can eliminate the DLS and TEM data mismatch completely or will make the results much closer to each other. Also, we provide a clear roadmap for drug delivery and pharmaceutical researchers to conduct reliable DLS measurements.

Diffusion-induced growth of compositional heterogeneity in polymer blends containing random copolymers

The compositional relaxation in random copolymer systems on a macroscopic scale is considered in theory. A set of diffusion equations is derived that describes the motion of chains of different composition and then converted into coupled equations for statistical moments of the compositional distribution. Several ways to solve the closure problem for these equations are discussed. The simplest is the situation when the shape of the transient compositional distribution can be predicted a priori, for example, a bimodal distribution is kept during interdiffusion of two copolymers that are not very close in composition. For a general case, it is shown that the cumulant-neglect closure based on the truncation of high-order cumulants is an effective method to get an approximate solution in terms of the time-dependent local mean composition and its dispersion. This method is applied to non-homogeneous compatible polymer systems, such as a random copolymer AB of a composition varying in space, a bilayer of Bernoullian copolymers AB of different composition, and a bilayer of homopolymers A and B, in which an autocatalytic polymer-analogous reaction A --> B takes place, with possibility of the neighbor group effect. It is found that the interdiffusion can lead to a substantial broadening of the local compositional distribution, which, in turn, accelerates the system dynamics and promotes chemical reactions.

Effect of Polydispersity on the Phase Diagrams of Linear ABC Triblock Copolymers in Two Dimensions

By using a two-dimensional (2D) real-space self-consistent field theory, we present the phase diagrams of monodisperse ABC triblock copolymers in a three-component triangle style with the interaction energies given between the distinct blocks; this system displays richer phase behavior when compared with the corresponding diblock copolymers. Polydispersity of the end or middle blocks in the ABC linear block copolymer chains results in a completely different phase diagram. The presence of a polydisperse end block may cause strong segregation to occur among the three distinct components and larger domain sizes of the dispersed phases; a polydisperse middle block may allow a connection to form between the two phases of the two end blocks.

Continuous polydispersity in a self-consistent field theory for diblock copolymers

An efficient algorithm is presented for numerically evaluating a self-consistent field theoretic (SCFT) model of an AB diblock copolymer that incorporates continuous polydispersity in one of the blocks. An interesting segregation effect is found in which chains of intermediate molecular weight are concentrated at domain interfaces. This model of continuous polydispersity is also implemented in the random phase approximation (RPA) to study the order-disorder transition and predicts that the stability of the disordered, homogeneous phase decreases as the polydispersity in one of the blocks increases. The RPA predictions are confirmed by SCFT calculations. Our approach and results are particularly relevant to block copolymers prepared by quasiliving synthesis techniques, where the polymerization of one block is much more controlled than the other block.

Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation

An extended generalization of the dynamic random phase approximation (DRPA) for L-component polymer systems is presented. Unlike the original version of the DRPA, which relates the (LxL) matrices of the collective density-density time correlation functions and the corresponding susceptibilities of concentrated polymer systems to those of the tracer macromolecules and so-called broken-links system (BLS), our generalized DRPA solves this problem for the (5xL) x (5xL) matrices of the coupled susceptibilities and time correlation functions of the component number, kinetic energy and flux densities. The presented technique is used to study propagation of sound and dynamic form-factor in disentangled (Rouse) monodisperse homopolymer melt. The calculated ultrasonic velocity and absorption coefficient reveal substantial frequency dispersion. The relaxation time tau is proportional to the degree of polymerization N, which is N times less than the Rouse time and evidences strong dynamic screening because of interchain interaction. We discuss also some peculiarities of the Brillouin scattering in polymer melts. Besides, a new convenient expression for the dynamic structure function of the single Rouse chain in (q,p) representation is found.