@article{21006, abstract = {Modern experimental methods in programmable self-assembly make it possible to precisely design particle concentrations, shapes and interactions. However, more physical insight is needed before we can take full advantage of this vast design space to assemble nanostructures with complex form and function. Here we show how a substantial part of this design space can be quickly and comprehensively understood by identifying a class of thermodynamic constraints that act on it. These thermodynamic constraints form a high-dimensional convex polyhedron that determines which nanostructures can be assembled at high equilibrium yield and reveals limitations that govern the coexistence of structures. We validate our predictions through detailed, quantitative assembly experiments of nanoscale particles synthesized using DNA origami. Our results uncover physical relationships underpinning many-component programmable self-assembly in equilibrium and form the basis for robust inverse design, applicable to various systems from biological protein complexes to synthetic nanomachines.}, author = {Hübl, Maximilian and Videbæk, Thomas E. and Hayakawa, Daichi and Rogers, W. Benjamin and Goodrich, Carl Peter}, issn = {1745-2481}, journal = {Nature Physics}, publisher = {Springer Nature}, title = {{A polyhedral structure controls programmable self-assembly}}, doi = {10.1038/s41567-025-03120-3}, year = {2026}, } @article{21408, abstract = {Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge, especially in programmable systems and the so-called semi-addressable regime, where binding is often nondeterministic and the formation of off-target structures negatively influences the assembly. Here, we show that it is possible to simultaneously sculpt the assembly outcome and the assembly kinetics through the underexplored design space of binding energies and particle concentrations. By formulating the assembly process as a complex reaction network, we calculate and optimize the tradeoff between assembly speed and quality and show that parameter optimization can speed up assembly by many orders of magnitude without lowering the yield of the target structure. Although the exact speedup varies from design to design, we find the largest speedups for nondeterministic systems where unoptimized assembly is the slowest, sometimes even making them assemble faster than optimized, fully addressable designs. Therefore, these results not only solve a key challenge in semi-addressable self-assembly but further emphasize the utility of semi-addressability, where designs have the potential to be faster as well as cheaper (fewer particle species) and better (higher yield). More broadly, our results highlight the importance of parameter optimization in programmable self-assembly and provide practical tools for simultaneous optimization of kinetics and yield in a wide range of systems.}, author = {Hübl, Maximilian and Goodrich, Carl Peter}, issn = {1089-7690}, journal = {Journal of Chemical Physics}, number = {8}, publisher = {AIP Publishing}, title = {{Simultaneous optimization of assembly time and yield in programmable self-assembly}}, doi = {10.1063/5.0304731}, volume = {164}, year = {2026}, } @article{21482, abstract = {Controlling the size and shape of assembled structures is a fundamental challenge in self-assembly and is highly relevant in material design and biology. Here, we show that specific but promiscuous short-range binding interactions make it possible to economically assemble linear filaments of user-defined length. Our approach leads to independent control over the mean and width of the filament size distribution and allows us to smoothly explore design trade-offs between assembly quality (spread in size) and cost (number of particle species). We employ a simple hierarchical assembly protocol to minimize assembly times and show that multiple stages of hierarchy make it possible to extend our approach to the assembly of higher-dimensional structures. Our work provides a conceptually simple solution to size control that is applicable to a broad range of systems, from DNA nanoparticles to supramolecular polymers and beyond.}, author = {Hübl, Maximilian and Goodrich, Carl Peter}, issn = {2643-1564}, journal = {Physical Review Research}, publisher = {American Physical Society}, title = {{Entropic size control of self-assembled filaments}}, doi = {10.1103/68rs-3qgn}, volume = {8}, year = {2026}, } @article{19856, abstract = {Unlike in crystals, it is difficult to trace emergent material properties of amorphous solids to their underlying structure. Nevertheless, one can tune features of a disordered spring network, ranging from bulk elastic constants to specific allosteric responses, through highly precise alterations of the structure. This has been understood through the notion of independent bond-level response—the observation that, in many cases, different springs have different effects on different properties. While this idea has motivated inverse design in numerous contexts, it has not been formalized and quantified in a general context that not just informs but enables and predicts inverse design. Here, we show how to quantify independent response by linearizing the simultaneous change in multiple emergent features, and introduce the much stronger notion of fully independent response. Remarkably, we find that the mechanical properties of disordered solids are always fully independent across a wide array of scenarios, regardless of the target features, tunable parameters, system size, dimensionality, and class of interactions. Furthermore, our formulation quantifies the susceptibility of features to parameter changes, which is correlated with the maximum linear tunability. We also demonstrate the implications for multifeature inverse design beyond the linear regime. These results formalize our understanding of a key fundamental difference between ordered and disordered solids while also creating a practical tool to both understand and perform inverse design.}, author = {Zu, Mengjie and Desai, Aayush A and Goodrich, Carl Peter}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {23}, publisher = {American Physical Society}, title = {{Fully independent response in disordered solids}}, doi = {10.1103/PhysRevLett.134.238201}, volume = {134}, year = {2025}, } @article{20727, abstract = {Acoustic levitation provides a unique method for manipulating small particles as it completely evades effects from gravity, container walls, or physical handling. These advantages make it a tantalizing platform for studying complex phenomena in many-particle systems. In most standing-wave traps, however, particles interact via acoustic scattering forces that cause them to merge into a single dense object. Here, we introduce a complementary approach that combines acoustic levitation with electrostatic charging to assemble, adapt, and activate complex, separated many-particle systems. The key idea is to superimpose electrostatic repulsion on the intrinsic acoustic attraction, rendering a so-called “mermaid” potential where interactions are attractive at short range and repulsive at long range. By controlling the attraction–repulsion balance, we can levitate expanded structures where all particles are separated, collapsed structures where they are in contact, and hybrid ones consisting of both expanded and collapsed components. We find that collapsed and expanded structures are inherently stable, whereas hybrid ones exhibit transient stability governed by acoustically unstable dimers. Furthermore, we show how electrostatics allow us to adapt between configurations on the fly, either by quasistatic discharge or discrete up/down charge steps. Finally, we demonstrate how large structures experience selective energy pumping from the acoustic field—thrusting some particles into motion while others remain stationary—leading to complex dynamics including coupled rotations and oscillations. Our approach establishes a design space beyond acoustic collapse, offering possibilities to study many-particle systems with complex interactions, while suggesting pathways toward scalable integration into materials processing and other applications.}, author = {Shi, Sue and Hübl, Maximilian and Grosjean, Galien M and Goodrich, Carl Peter and Waitukaitis, Scott R}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {50}, pages = {e2516865122}, publisher = {National Academy of Sciences}, title = {{Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter}}, doi = {10.1073/pnas.2516865122}, volume = {122}, year = {2025}, } @misc{20749, abstract = {Datasets and code for publication "Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter"}, author = {Shi, Sue}, publisher = {Zenodo}, title = {{Datasets and code for manuscript "Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter"}}, doi = {10.5281/ZENODO.15752991}, year = {2025}, } @article{19067, abstract = {Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of this inverse problem start with the so-called fully addressable limit, where every particle in a target structure is different. This leads to clear design principles that often result in high assembly yield, but it is not a scalable approach—at some point, one must grapple with “reusing” building blocks, which lowers the degree of addressability and may cause a multitude of off-target structures to form, complicating the design process. Here, we solve a key obstacle preventing robust inverse design in the “semiaddressable regime” by developing a highly efficient algorithm that enumerates all structures that can be formed from a given set of building blocks. By combining this with established partition-function-based yield calculations, we show that it is almost always possible to find economical semiaddressable designs where the entropic gain from reusing building blocks outweighs the presence of off-target structures and even increases the yield of the target. Thus, not only does our enumeration algorithm enable robust and scalable inverse design in the semiaddressable regime, our results demonstrate that it is possible to operate in this regime while maintaining the level of control often associated with full addressability.}, author = {Hübl, Maximilian and Goodrich, Carl Peter}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {5}, publisher = {American Physical Society}, title = {{Accessing semiaddressable self-assembly with efficient structure enumeration}}, doi = {10.1103/PhysRevLett.134.058204}, volume = {134}, year = {2025}, } @article{21237, abstract = {Intelligent soft matter lies at the intersection of materials science, physics, and cognitive science, promising to change how we design and interact with materials. This transformative field aims to create materials with life-like capabilities, such as perception, learning, memory, and adaptive behavior. Unlike traditional materials, which typically perform static or predefined functions, intelligent soft matter can dynamically interact with its environment, integrating multiple sensory inputs, retaining past experiences, and making decisions to optimize its responses. Inspired by biological systems, these materials leverage the inherent properties of soft matter such as flexibility, adaptability, and responsiveness to perform functions that mimic cognitive processes. By synthesizing current research trends and projecting their evolution, we present a forward-looking perspective on how intelligent soft matter could be constructed, with the aim of inspiring innovations in areas such as biomedical devices, adaptive robotics, and beyond. We highlight new pathways for integrating sensing, memory and actuation with low-power internal operations, and we discuss key challenges in realizing materials that exhibit truly “intelligent behavior”. These approaches outline a path toward more robust, versatile, and scalable materials that can potentially act, compute, and “think” through their inherent intrinsic material properties—moving beyond traditional smart technologies that rely on external control.}, author = {Baulin, Vladimir A. and Giacometti, Achille and Fedosov, Dmitry A. and Ebbens, Stephen and Varela-Rosales, Nydia R. and Feliu, Neus and Chowdhury, Mithun and Hu, Minghan and Füchslin, Rudolf and Dijkstra, Marjolein and Mussel, Matan and van Roij, René and Xie, Dong and Tzanov, Vassil and Zu, Mengjie and Hidalgo-Caballero, Samuel and Yuan, Ye and Cocconi, Luca and Ghim, Cheol-Min and Cottin-Bizonne, Cécile and Miguel, M. Carmen and Esplandiu, Maria Jose and Simmchen, Juliane and Parak, Wolfgang J. and Werner, Marco and Gompper, Gerhard and Hanczyc, Martin M.}, issn = {1744-6848}, journal = {Soft Matter}, number = {21}, pages = {4129--4145}, publisher = {Royal Society of Chemistry}, title = {{Intelligent soft matter: Towards embodied intelligence}}, doi = {10.1039/d5sm00174a}, year = {2025}, } @article{17407, abstract = {The ability to control forces between sub-micron-scale building blocks offers significant potential for designing new materials through self-assembly. Traditionally, this involves identifying a crystal structure with a desired property and then designing building-block interactions so that it assembles spontaneously. However, this paradigm fails for structurally disordered solids, which lack a well-defined structure. Here, we show that disordered solids can still be treated from an inverse self-assembly perspective by bypassing structure and directly targeting material properties. Using the Poisson’s ratio as a primary example, we demonstrate how differentiable programming links interaction parameters with emergent behavior, enabling iterative training to achieve the desired Poisson’s ratio. We also tune other properties, including pressure and local 8-fold structural order, and can even control multiple properties simultaneously. This robust, transferable, and scalable approach can handle a wide variety of systems and properties, demonstrating the utility of disordered solids as a practical avenue for self-assembly platforms.}, author = {Zu, Mengjie and Goodrich, Carl Peter}, issn = {2662-4443}, journal = {Communications Materials}, publisher = {Springer Nature}, title = {{Designing athermal disordered solids with automatic differentiation}}, doi = {10.1038/s43246-024-00583-4}, volume = {5}, year = {2024}, } @article{14710, abstract = {The self-assembly of complex structures from a set of non-identical building blocks is a hallmark of soft matter and biological systems, including protein complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence of the equilibrium assembly yield on the concentrations and interaction energies of building blocks is highly challenging, owing to the difficulty of computing the entropic contributions to the free energy of the many structures that compete with the ground state configuration. While these calculations yield well known results for spherically symmetric building blocks, they do not hold when the building blocks have internal rotational degrees of freedom. Here we present an approach for solving this problem that works with arbitrary building blocks, including proteins with known structure and complex colloidal building blocks. Our algorithm combines classical statistical mechanics with recently developed computational tools for automatic differentiation. Automatic differentiation allows efficient evaluation of equilibrium averages over configurations that would otherwise be intractable. We demonstrate the validity of our framework by comparison to molecular dynamics simulations of simple examples, and apply it to calculate the yield curves for known protein complexes and for the assembly of colloidal shells.}, author = {Curatolo, Agnese I. and Kimchi, Ofer and Goodrich, Carl Peter and Krueger, Ryan K. and Brenner, Michael P.}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{A computational toolbox for the assembly yield of complex and heterogeneous structures}}, doi = {10.1038/s41467-023-43168-4}, volume = {14}, year = {2023}, } @article{9257, abstract = {The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.}, author = {Goodrich, Carl Peter and King, Ella M. and Schoenholz, Samuel S. and Cubuk, Ekin D. and Brenner, Michael P.}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {10}, publisher = {National Academy of Sciences}, title = {{Designing self-assembling kinetics with differentiable statistical physics models}}, doi = {10.1073/pnas.2024083118}, volume = {118}, year = {2021}, } @phdthesis{10422, abstract = {Those who aim to devise new materials with desirable properties usually examine present methods first. However, they will find out that some approaches can exist only conceptually without high chances to become practically useful. It seems that a numerical technique called automatic differentiation together with increasing supply of computational accelerators will soon shift many methods of the material design from the category ”unimaginable” to the category ”expensive but possible”. Approach we suggest is not an exception. Our overall goal is to have an efficient and generalizable approach allowing to solve inverse design problems. In this thesis we scratch its surface. We consider jammed systems of identical particles. And ask ourselves how the shape of those particles (or the parameters codifying it) may affect mechanical properties of the system. An indispensable part of reaching the answer is an appropriate particle parametrization. We come up with a simple, yet generalizable and purposeful scheme for it. Using our generalizable shape parameterization, we simulate the formation of a solid composed of pentagonal-like particles and measure anisotropy in the resulting elastic response. Through automatic differentiation techniques, we directly connect the shape parameters with the elastic response. Interestingly, for our system we find that less isotropic particles lead to a more isotropic elastic response. Together with other results known about our method it seems that it can be successfully generalized for different inverse design problems.}, author = {Piankov, Anton}, issn = {2791-4585}, publisher = {Institute of Science and Technology Austria}, title = {{Towards designer materials using customizable particle shape}}, doi = {10.15479/at:ista:10422}, year = {2021}, }