Simulations and theory of self-organization of comblike macromolecules with stiff side chains in semi-dilute solution

Under supervision of Prof. I.I. Potemkin I studied the aggregates that are formed in the system mentioned above. The case of soluble backbone and insoluble side groups was considered. The idea to do that was the potential use of self-organizing aggregates that would be sensitive to the change of external conditions in sensors, nanochips and as containers in delivery problems (drugs, genes). Specifics of the macromolecular architecture chosen was dictated by the intention to benefit from a competition between liquid-crystal ordering and energetic self-assembly in the system. In comparison with comblike macromolecules with fully flexible side chains, in our case isotropic-nematic transition inside the aggregates can be realized and successfully exploited.

Moreover, our collegues from Prof. M. Möller's group (Aachen, Leibniz-Institut für Interaktive Materialien) experimentally showed the formation of onion-like multylayer vesicles in this system with the bilayers comprised of the stiff groups. This finding was rather exciting since geometrically it's clear that no dense packing inside the liquid-crystal bilayers can be achieved and thus there're many costly contacts with the solvent. But, besides this fact, the vesicles were still stable, seemingly due to the gain in backbone monomers distribution and flip-flop from concave to convex sides.

First I analyzed the free energy of the vesicle with certain sizes and aggregation number. The general thing is that under constant temperature and volume (and there's no particles flow out of the volume) the full free energy should achieve its minimum in equilibrium. Under the assumption that we only have the vesicle-like aggregates with the same aggregation numbers in the box I showed the presence of the minimum of free energy function about the sizes and the aggregation number and found these values. The equilibrium sizes achieved corresponded to huge micro-scale vesicles - just that had been previously detected by our German collegues.

As the next step, I investigated the other structures that can be formed with such macromolecules by means of computer modelling using dissipative particle dynamics technique. The sumulations were performed using Lomonosov Supercomputer's facilities (Moscow University). Though only the medium regime of grafting density was considered (the length of the side rods was the same as the length of the backbone's spacer), we showed that the system is higly sensetive to the change of the sovent quality, which can be tuned by the change of the temperature or by addition of other solvents. Namely, isotropic-nematic transition from sphere- to bundle-like structures was established. To measure the extent of nematic ordering, we calculated the eigen values of the aggregates' orientational tensor. It was shown that the change of the order parameter is as abrupt as if it was the 1st order transition (one has to be very careful when speculates on phase transitions in finite systems). The effect of the side chains number (branching) on the critical insolubility of the side chains for which the transition occurs was investigated also. As we figured out, branching leads to a greater stability region for the isotropic phase.

The results of this activity comprise my graduation work, which will be presented in the University at the end of December. The article on these results is in preparation. To have a deeper insight about the work, take a look on the slides for the St. Petersburg International Conference on polymer science, which was held in November, 2015.

The diblock copolymer melt swollen in solvent vapor as a nanopump system

Diblock copolymers consist of two chemically distinct polymer blocks joint by a covalent bond. Due to the natural incompatibility between the two blocks, they tend to self-separate in a particular way and result in a variety of micro- and nanostructures inside the sample at the equilibrium. Diblock copolymer thin films present the robust way to exploit the nanostructuring since they can be so prepared to ensure their resulting thermodynamical stability and have the appropriate nanoscale for further usage. Given the idea of diblock copolymer thin films one can achieve well-structured patterns through such means as spin-coating on a surface and the subsequent annealing procedures for further stabilization of the film.

With Prof. Potemkin and a PhD student from our lab, R. Gumerov, we analyzed the strong segregation regime for symmetric copolymer (a case of lamella phase) and showed that the solvent tends to concentrate predominantly on the lamellas' interfaces. Led by this idea, one can control the distribution of the solvent in the film that was found to effectively pump towards and backwards the lamella's interface under the switch from stretching to squeezing of the film correspondingly. This effect when macroscopic forces, applied to the block copolymer film, induce a strong directed response in the nanochannel is very promising, e.g., for the injection of reagents into diagnostic bio-sampling nanochips for following virus detection or in hydroelectric power generation on the nanoscale.

The fact that the solvent prefers to locate on the interfaces between the polymer domains had been previously established by our group using computer modelling and by Prof. Papadakis group in experiments. Thus in this activity we were driven to show this phenomenon analytically in the mean-field approach and studied the dependencies of the solvent profiles on parameters of the system. On this way we wrote down the free energy functional of the film which depends on the solvent and the polymers density distributions and on the equilibrium thickness of the domains as well. Minimizing it using Lagrange multipliers (in order to meet the dense packing condition) we achieved the system of differential equations that were solved numerically afterwards. You can look for the details of the approach here. The resulting inhomogeneous solvent profile can be physically explained as follows: because of the incompatibility, blocks are strongly extended near the domains interfaces. As a result, the total volume fraction of polymer in this zone appears to be less than inside the phases. The formed free space is filled by the solvent. A more naive (but actually the same) explanation points out that due to the high cost of polymer-polymer contacts on the interface, the system benefits from partial screening of them increasing the number of solvent molecules there.

The film's domains can be understood as containers for the solvent where the chains in the absence of forces, though strongly extended, still allocate space for solvent molecules and effectively store them. As we showed, when a swift extension applied to the film, the domains secrete some solvent molecules to the nanochannel between and when the film is swift compressed, the solvent reversely flows out towards the domains, slightly drying the channel. This gives rise for the pumping system that exhibits nanoscale response while is controlled on macro level. Our calculations predicted the change of the solvent fraction from a twice-squeezed to a twice-extended states in more than 12% that was an order of mean solvent fraction in the film.

The first part of our work was presented at the Lomonosov-2015 Conference on a poster session (in Russian). The paper on the nanopump effect is almost prepared and about to be submitted to the journal ACS Nano.

Mechanical models for cell proliferation under constraints

These are the interests that we share with Dr. S. Nechaev(CNRS, Université Paris-Sud, LPTMS).

The rise for this research has been recently proposed to us by a biophysicist, Prof. L. Mirny (MIT), who managed to elaborate the experimental technique for tumor tissues, showing that the crucial feature of diseased area is its fractal-like organization. Besides that, it is known that the general limitating the untrammeled growth mechanism is prohibited for cancer cells. Thus the tumor tissue should experience the growth under physical constraints since it's surrounded by other cell colonies. As a result, the tissue is getting more and more buckled along the way of continued growing.

Using geometrical and energetic approaches for resulting buckling shapes we showed that these two methods give consistent results and thus can be taken into account separetely. Coming up with the energetic approach, we proposed the model of inhomogeneously pre-stressed plate under exponential protocol of squeezing along one of its side. While three of four sides are clamped and the pre-stress applied, the plate experiences the buckling as it does in continious growth model. We explicitly showed that the profile on the growing edge exhibits truly self-similar behavior. Such hierarchy is generally the subject of wonder in plants of different biological kinds (think of amazing lettuce leaves or coral polyps). It seems that all this beauty is just what the exponential growth of cells under certain constraints puts on the table. We report that no fractal structure formed if there is another force protocol affecting the plate (say, linear or constant squeezing).

You can read the full paper on arXiv. There'll be a journal version in January also. Furthermore, we plan to proceed the current research in the nearest months as long as it has revealed many branching topics to speculate on.

List of works:

• Course work №1: Thin films for modern applications(in Russian), 2012

• Course work №2: A vesicular structure in semi-dilute solution of comblike macromolecules with stiff side chain groups(in Russian), 2014

• Oral presentation on the conference "Lomonosov-2014": A vesicular structure in semi-dilute solution of comblike macromolecules with stiff side chain groups(in Russian), 2014

• Poster presentation on the conference "Lomonosov-2015": Theoretical investigation of solvent distribution in thin diblock copolymer film, swollen in vapor of the non-selective solvent poster, abstract(in Russian), details, 2015

• Oral presentation on the 11th International Saint-Petersburg Conference of Young Scientists "Modern problems of polymer science": Computer simulations of aggregation of comblike macromolecules with liquid-crystalline side groups in selective solvent slides, 2015

• S. Nechaev, K. Polovnikov, Buckling and wrinkling from geometric and energetic viewpoints, arXiv:1511.07862v1, 2015

• R. Gumerov, K. Polovnikov, I.I. Potemkin, Nanopump based on lamellae-forming diblock copolymers, ACS Nano (to be submitted in a few weeks)