Tatiana M. Birshtein

Stretching and compression of a macromolecule under different modes of mechanical manupulations

This review is concerned with the response of an isolated polymer chain subjected to the action of the two different modes of the mechanical impact on the chain ends. In one mode, the end-to-end distance is changed in a controlled fashion and the fluctuating response force is measured; in the second case, an external stress field is applied to the chain end, and the measured response of the system is the fluctuating end-to-end distance. The main attention is focused on the results of the computer-aided simulation experiments and theoretical results. Upon stretching of an ideal chain, a real chain in a good solvent, or a globule, the resultant strain-force and force-strain dependences are shown to be different for chains with finite length L; however, this difference diminishes with an increase in the length of a molecule. When the anchored Gaussian chain is separated from the adsorbing surface, this difference disappears in the limit of high L; however, in the neighborhood of the phase transition, some characteristics (fluctuations, distribution functions) appear to be critically different under different impact modes even in the thermodynamic limit. The example of an abnormal system is discussed: The behavior of a polymer chain compressed by a small piston is different in the conjugated ensembles, and, as the system increases in size, this difference becomes even more pronounced.

Mechanical unfolding of a homopolymer globule studied by self-consistent field modeling

We present results of numerical self-consistent field (SCF) calculations for the equilibrium mechanical unfolding of a globule formed by a single flexible polymer chain collapsed in a poor solvent. In accordance with earlier scaling theory and stochastic dynamics simulations findings we have identified three regimes of extensional deformation: (i) a linear response regime characterized by a weakly elongated (ellipsoidal) shape of the globule at small deformations, (ii) a tadpole structure with a globular “head” coexisting with a stretched “tail” at intermediate ranges of deformations, and (iii) an uniformly stretched chain at strong extensions. The conformational transition from the tadpole to the stretched chain is accompanied by an abrupt unfolding of the depleted globular head and a corresponding jump-wise drop in the intrachain tension. The unfolding-refolding cycle demonstrates a hysteresis loop in the vicinity of the transition point. These three regimes of deformation, as well as the first-order li...

A Quantitative Theory of Mechanical Unfolding of a Homopolymer Globule

We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to extensional deformation. We demonstrate that depending on the degree of polymerization and solvent quality (quantified by the Flory−Huggins χ parameter) the mechanical unfolding of the collapsed chain either may occur continuously (by passing a sequence of uniformly elongated configurations) or involves intramolecular microphase coexistence of a collapsed and a stretched segment followed by an abrupt unraveling transition. The force−extension curves are obtained and quantitatively compared to our recent results of numerical self-consistent-field (SCF) simulations. The phase diagrams for extended homopolymer chains in poor solvent comprising one- and two-phase regions are calculated for different chain length or/and solvent quality.

Conformations of polymer and polyelectrolyte stars

The structure of polymer and polyelectrolyte stars in solution was studied by means of joint analysis of the results of analytical consideration, allowing for nonlocal effects, and numerical simulation based on the Scheutjens-Fleer self-consistent field approach. A limitation of the theoretical treatment is the assumption that all ends of polymer chains are fixed onto the external surface and its benefit is the possibility of obtaining compact and interpretable results. The Scheutjens-Fleer approach makes it possible to study conformations without introduction of additional limitations. The combination of analytical methods and direct numerical calculation turns out to be especially informative.

Liquid-crystalline polymer brushes: deformation and microphase segregation☆

Abstract A statistical theory of the structure and thermodynamics of a planar brush (‘accordion’) formed by bridged polymer chains containing mesogenic segments and immersed in a solvent is developed. It is shown that deformation of an accordion can lead to the formation of a two-phase structure with coexisting liquid-crystalline (LC) and swollen microphases. Phase diagrams for accordions with different grafting densities are obtained. The influence of anisotropic interaction between mesogenic segments on the structure of phase diagrams is investigated.

Formation of a "Hollow" Interior in the Fourth-Generation Dendrimer with Attached Oligomeric Terminal Segments.

By using the Scheutjens-Fleer self-consistent field approach, the structure of the fourth-generation dendrimer with attached terminal chemically different oligomeric segments is studied theoretically. It is demonstrated that an incompatibility of terminal segments with inner dendrimer units leads to formation of a hollow core with reduced polymer density in the dendrimer center. This effect is enhanced with a deterioration in the solvent quality for terminal segments. This observation is in accordance with experimental results and molecular dynamics simulation data for an analogous system. It is established that the main factor determining the hollow core formation is the segregation between inner and terminal units because the main driving force for the effect is the localization of the terminal segments at the dendrimer periphery. The influence of structural parameters of dendrimer such as the number of generations and length of the terminal chain on this effect is also studied.

Theory of Mechanical Unfolding of Homopolymer Globule: All-or-None Transition in Force-Clamp Mode vs Phase Coexistence in Position-Clamp Mode

Equilibrium mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in a poor solvent and subjected to an extensional force f (force-clamp mode) or extensional deformation D (position-clamp mode) is studied theoretically. Our analysis, like all previous analysis of this problem, shows that the globule behaves essentially differently in two modes of extension. In the force-clamp mode, mechanical unfolding of the globule with increasing applied force occurs without intramolecular microphase segregation, and at certain threshold value of the pulling force the globule unfolds as a whole (“all-or-none” transition). The value of the threshold force and the corresponding jump in the distance between the chain ends increase with a deterioration of the solvent quality and/or with an increase in the degree of polymerization. In the position-clamp mode, the globule unfolding occurs via intramolecular microphase coexistence of globular and extended microphases followed by an abrupt unrav...

Modeling of Charged Amphiphilic Copolymer Stars near Hydrophobic Surfaces

Numerical self-consistent field theory has been applied to amphiphilic copolyelectrolyte stars in the solution and at interfaces both in one- and two-gradient coordinate systems. Our focus is on polymer stars for which the solvent is poor for the short blocks in the center and good for the longer charged chain parts at the periphery of the star. Both in solution as well as near an interface, the structure of the core is influenced by the hydrophobic interactions that tend to form a compact globule with size Rc and the forces exerted by the charged peripheral chain parts that like to expand the core. When the distance H of the center of the star to the surface becomes smaller than the total size R, the interaction force becomes significant; it is positive for Rc<H<R, and rather suddenly becomes strongly attractive at shorter distances when the core can adsorb. Hence, the adsorption as well as the desorption of stars involves the passing of an activation barrier. Details of this barrier are important for a rational design of polymer stars that are of use to modify surface properties.

Deformation of a Polymer Brush Immersed in a Binary Solvent

An analog of the Alexander-De Gennes box model is used for the theoretical investigation of an external deformation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory-Huggins parameter χAB = 3.5). The thermodynamics of a polymer in the solvents A and B is described by parameters χA and χB, χA > χB. The brush behavior under deformation is investigated with regard to solvent composition and polymer-solvent interactions. It is shown that in a pre-binodal range of the solvent composition ΦB < ΦB0 in the bulk (here ΦB0 is a binodal value) there is such a value of ΦB = Φxa0B* that deformation does not affect solvent composition inside the brush. This invariant quantity Φxa0B*, being a function of only thermodynamic parameters, is independent of the brush characteristics, such as grafting density. It is shown that two types of the first-order phase transitions can arise in the system considered: a compositional phase transition induced by a change in the solvent composition in the bulk, and a deformational phase transition caused by an external deformation of the brush. The value of Φxa0B* defines a borderline concentration of the admixture in the bulk; the brush behavior in the ranges 00 ⪇ ΦB ⪇ Φxa0B* and Φxa0B* ⪇ ΦB < ΦB0 are different. If no compositional phase transition occurs in the system, the deformational phase transition should arise under stretching at Φxa0B* ⪇ ΦB. If the compositional phase transition exists, it is realized in the range ΦB < Φxa0B* and causes the deformational phase transition in this concentration range, not only under stretching, but also under compression. Microphase segregation inside the brush is demonstrated for both phase transitions despite overestimation of the brush homogeneity in the box model.

Mixed supercrystalline structures in mixtures of ABC-triblock and AB(BC)-diblock copolymers, 1. Lamellar structures in bicomponent mixtures

The theory of lamellar superstructures in binary mixtures of AB diblock and linear ABC triblock copolymers under the condition of strong segregation between chemically different blocks is developed. This system is considered using Alexander-de Gennes (box-model) and self-consistent field (SCF) models. The formation of a mixed lamellar superstructure comprising both mixture components is proved. It is shown that a mixed lamella may be the only type of lamellae in the mixture, or it may coexist with pure diblock lamellae, depending on the mixture composition, local characteristics of blocks (thickness and Kuhn segment length), and surface tension coefficients at the A/B and B/C interfaces. Preliminary experimental results provide support of these theoretical estimations. The formation of mixed lamellae in a mixture of linear ABC and branched (AB) 2 C block copolymers is also considered.