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Machine Learning of Soft Materials

Bayesian Modelling of Microphase Separation
Soft materials are complex and are difficult to describe by simple governing equations. Obtaining these equations is one of the most significant issues in soft materials, and is also challenging and attracting. Recent development of techniques of machine learning gives us hope to make an estimation. Nevertheless, the estimation of the governing equations, particularly for materials, is not a straightforward extension of conventional machine learning techniques. First, materials exist under physical laws and symmetry, which we should not look over. Second, all the models are, in some sense, approximation of real phenomena. The governing equations are important because they clarify the mechanism of physical phenomena, and they make a good prediction. In this sense, the estimation of equations with the lowest error is not necessarily appreciated, but generalisability can be more critical. Moreover, the definition of generalisability remains unclear. We have developed the method to estimate partial differential equations from “one” stationary structural data.

Inverse structural design of patchy particles
Colloidal particles may self-assemble into crystalline-like structures. Recently, it is becoming possible to control a shape, surface property, interaction with other particles of colloidal particles. Patchy particles have a patch on a particle so that the particles have anisotropic surface property. For example, a particle that has patches on its north and south poles, namely nematic symmetry, may self-assemble into Kagome lattice. Such an open structure used to be difficult to synthesise. For given patchy particles, intensive studies have clarified which and how they form specific self-assembly structures. However, the design of the self-assembly is still challenging. Can design patchiness of the particle to get desired structure? We are developing the method to achive the inverse structural design.

Phase-field crystal model
The phase-field crystal model is a minimal model for pattern formation. The model may reproduce various crystalline structures, such as hexagonal lattice, square lattice, and stripe in 2D, BCC, FCC, double gyroid, Frank-Kasper in 3D. The model can also reproduce quasicrystals. Althouhg the model was originally proposed for the surface pattern of Faraday waves, the model is now used to describe elasticity and defect dynamics of crystals. In materials science, the phase-field model has often been used for metallic alloys. In the phase-field model, the two phases are described by the two potential minimum of the free energy. Despite the success of the method, the internal structure cannot be treatted in the conventioanl phase-field model. The phase-field crystal model takes the crystalline structure into account, and therefore, defects (disclinations and dislocations) and grain boundaries are handled naturally. We are studying both forward and inverse problems of the phase-field crystal model, namely, in the forward problem, we study the dynamics of defects, and in the inverse problem, we estimate the necessary terms and parameters to reproduce a desired pattern.



The defects may feel the underlying space where they live. The movies below demonstrate that the disclination is associated with positive Gaussina curvature.





Active Soft Materials

self-propulsion of an active polar drop
Active nematic/polar fluids are typical model for cytoskelton and dense suspension of self-propelled particles. The system is away from an equilibrium state due to the active stress. The bulk properties of this have been extensively studied. When the active fluid is confined in a drop, it may spontaneously move and deform due to the flow generated by the internal active stress. This is a very simple model of cell motility. We found various motion of the active drop depending on whether the active stress is contractile or extensile, and also on the strength of the active stress.

spontaneous motion and deformation of chemically driven drop: single drop and collective behaviours
Similar to the phoretic phenomena, a drop may move under a gradient of, for example, temperature and concentration. This is due to the surface tension depending on temperature and concentration of surfactants. When the surface tension is anisotropic on the drop surface, the tangential force acting on the surface occurs. This force drive flow inside and outside the drop. Of course, there is no external force acting on the drop, and therefore, the total force must be zero (the force-free condition). Under the gradient, the system has already broken symmetry. The direction of the motion is set by the gradient. When the drop has chemical reactions, for example, the drop produce chemical products which may change the surface tension. In this case, the nonliear effect plays a role. Even if the system including the chemical reaction is isotropic, the stationary state may become unstable. Becuase of the small initial perturbation, the produced concentration field may be anisotropic, which results in anisotropic surface tension. If the parameters are chosen appropriately, the anisotropic induces further motion, and the concentration becomes more anisotropic. This mechanism explains self-propulsion of a chemically driven drop observed recent experiments. We have developed theory and numerical simulations (see the movies below).


phoresis and self-phoresis
Phoretic phenomena, such as electrophoresis, diffusionphoresis, and thermophoresis, are flux under a gradient. Although these phenomena have been known from long time ago, the mechanism is, in fact, found recently. When a particle move under a gradient, the particle does not feel an external force. This force-free condition plays a crucial role.


Pattern Formation in Biology

Polarity pattern of stress fibers
Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns.









Polymer Translocation
Macromolecules assume compact conformations in certain situations. Examples include DNA in living cells, proteins in native states, and other polymers in poor solvent conditions or under a compression field. Once released from the condition, these polymers expand to swollen coiled state, which is characterized by developed fluctuations. This expansion process is of interest in two different contexts. First, this process is relevant to coil-globule transitions, thus, regarded as a fundamental topic in polymer science. Unfortunately, there are comparatively fewer past studies on this expansion process than on the folding (coil to globule) process. The second case of interest is encountered in the field of confined polymers. A recent advance in nanoscale fabrications and singlechain experiments allows one to manipulate and observe individual polymers, thereby facilitating a number of potential applications in biological as well as nanoscale sciences.


Polymers in nonequilibrium systems
Kinetics in soft matter is of importance for understanding of natural phenomena in biological systems and in daily lives. We know empirically shaving gel makes a transition into bubbles by rubbing with our hands. This shear-induced nonequilibrium phase transition is highly nonlinear and far-from equilibrium. Modelling its governing equations is difficult task. It is thus significant challenge as a theoretical modelling to work in the problems of kinetics in soft materials.
      I focus on kinetics of polymers. Even in this particular case, our understanding is quite primitive, while dynamical properties near equilibrium states have been investigated extensively. Recent experiments of single-molecule manipulation open investigations of the kinetics of soft materials including a single semiflexible polymer.


Polymer stretching
Kinetics of conformational change of a semiflexible polymer under mechanical external Field were investigated with Langevin dynamics simulations. It is found that a semiflexible polymer exhibits large hysteresis in mechanical folding/unfolding cycle even with a slow operation, whereas in a °exible polymer, the hysteresis almost disappears at a sufficiently slow operation. This suggests that the essential features of the structural transition of a semiflexible polymer should be interpreted at least on a two-dimensional phase space. The appearance of such large hysteresis is discussed in relation to different pathways in the loading and unloading processes. By using a minimal two-variable model, the hysteresis loop is described in terms of different pathways on the transition between two stable states.

The movie shows kinetics of comformational change during stretching a semiflexible polymer.


movie: mechanical unfolding of a semiflexible polymer


Rod-coil copolymer
We investigate the folding transition of a single diblock copolymer consisting of a semiflexible and a flexible blocks. We obtain the saturn shaped core-shell conformation in the folded state, where the flexible block form a core and the semiflexible block wrap around them. We find two distinctive features in the core-shell structures. (i) The kinetics of the folding transition in the copolymer are more efficient than that in a semiflexible homopolymer. (ii) The core-shell structure does not depend on pathways of the transition.


Two-state polymer
Monte Carlo simulation of annealed copolymers of solvophobic/solvophilic monomers show collapsed globular states having a dynamic core-shell structures. In these, the core is mostly solvophobic while the core boundary contains an excess of solvophilic monomers. This two state model, where each monomer undergoes interconversion between solvophobic and solvophilic state, is a minimal version of models of neutral water soluble polymers such as PEO. The reduced surface tension of such core-shell structures suggests an explanation of the stability of PNIPAM globules as observed in the experiments of X.Wang, X.Qiu, C.Wu, Macromolecules, 1998, 31, 2972. The statitistics of the monomeric states along the chain vary with the degree of chain swelling. They are differ from those of quenched copolymers designed to create water soluble globules though both systems involve a core-shell structures.

movie of a two-state polymer














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