Robert Style

Last Name

Style

First Name

Robert

ORCID

0000-0001-5305-7658

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09455 - Isa, Lucio / Isa, Lucio

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Publications 1 - 10 of 32

Stress accumulation by confined ice in a temperature gradient
Gerber, Dominic; Wilen, Lawrence A.; Poydenot, Florian; et al. (2022)
Proceedings of the National Academy of Sciences of the United States of America
When materials freeze, they often undergo damage due to ice growth. Although this damage is commonly ascribed to the volumetric expansion of water upon freezing, it is usually driven by the flow of water toward growing ice crystals that feeds their growth. The freezing of this additional water can cause a large buildup of stress. Here, we demonstrate a technique for characterizing this stress buildup with unprecedented spatial resolution. We create a stable ice-water interface in a controlled temperature gradient and measure the deformation of the confining boundary. Analysis of the deformation field reveals stresses applied to the boundary with [Formula: see text](micrometers) spatial resolution. Globally, stresses increase steadily over time as liquid water is transported to more deeply undercooled regions. Locally, stresses increase until ice growth is stalled by the confining stresses. Importantly, we find a strong localization of stresses, which significantly increases the likelihood of damage caused by the presence of ice, even in apparently benign freezing situations. Ultimately, the limiting stress that the ice exerts is proportional to the local undercooling, in accordance with the Clapeyron equation, which describes the equilibrium between a stressed solid and its melt. Our results are closely connected to the condensation pressure during liquid-liquid phase separation and the crystallization pressure for growing crystals. Thus, they are highly relevant in fields ranging from cryopreservation and frost heave to food science, rock weathering, and art conservation.
It's Harder to Splash on Soft Solids
Howland, Christopher J.; Antkowiak, Arnaud; Castrejón-Pita, J. Rafael; et al. (2016)
Physical Review Letters
Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity, and air pressure. By imaging ethanol drops impacting silicone gels of different stiffnesses, we show that substrate stiffness also affects the splashing threshold. Splashing is reduced or even eliminated: droplets on the softest substrates need over 70% more kinetic energy to splash than they do on rigid substrates. We show that this is due to energy losses caused by deformations of soft substrates during the first few microseconds of impact. We find that solids with Young’s moduli ≲ 100 kPa reduce splashing, in agreement with simple scaling arguments. Thus, materials like soft gels and elastomers can be used as simple coatings for effective splash prevention. Soft substrates also serve as a useful system for testing splash-formation theories and sheet-ejection mechanisms, as they allow the characteristics of ejection sheets to be controlled independently of the bulk impact dynamics of droplets.
The generalized Clapeyron equation and its application to confined ice growth
Style, Robert; Gerber, Dominic; Rempel, Alan W.; et al. (2023)
Journal of Glaciology
Most theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice.
Dynamics of spontaneous wrapping of microparticles by floppy lipid membranes
Spanke, Hendrik; Agudo-Canalejo, Jaime; Tran, Daniel; et al. (2022)
Physical Review Research
Lipid membranes form the barrier between the inside and outside of cells and many of their subcompartments. As such, they bind to a wide variety of nano- and micrometer sized objects and, in the presence of strong adhesive forces, strongly deform and envelop particles. This wrapping plays a key role in many healthy and disease-related processes. So far, little work has focused on the dynamics of wrapping. Here, using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure the velocity of the particle during wrapping as well as the forces exerted on it by the lipid membrane. Dissipation near the contact line appears to be the main factor determining the wrapping velocity and time to wrap an object.
Surface Passivation Method for the Super-repellence of Aqueous Macromolecular Condensates
Testa, Andrea; Spanke, Hendrik T.; Jambon-Puillet, Etienne; et al. (2023)
Langmuir
Solutions of macromolecules can undergo liquid-liquid phase separation to form droplets with ultralow surface tension. Droplets with such low surface tension wet and spread over common surfaces such as test tubes and microscope slides, complicating in vitro experiments. The development of a universal super-repellent surface for macromolecular droplets has remained elusive because their ultralow surface tension requires low surface energies. Furthermore, the nonwetting of droplets containing proteins poses additional challenges because the surface must remain inert to a wide range of chemistries presented by the various amino acid side chains at the droplet surface. Here, we present a method to coat microscope slides with a thin transparent hydrogel that exhibits complete dewetting (contact angles θ ≈ 180°) and minimal pinning of phase-separated droplets in aqueous solution. The hydrogel is based on a swollen matrix of chemically cross-linked polyethylene glycol diacrylate of molecular weight 12 kDa (PEGDA), and can be prepared with basic chemistry laboratory equipment. The PEGDA hydrogel is a powerful tool for in vitro studies of weak interactions, dynamics, and the internal organization of phase-separated droplets in aqueous solutions.
Strain stiffening elastomers with swelling inclusions
Heyden, Stefanie; Style, Robert; Dufresne, Eric (2023)
Soft Matter
Inhomogeneously swollen elastomers are an emergent class of materials, comprising elastic matrices with inclusion phases in the form of microgel particles or osmolytes. Inclusion phases can undergo osmotically driven swelling and deswelling over orders of magnitude. In the swollen state, the inclusions typically have negligible Young's modulus, and the matrix is strongly deformed. In that regime, the effective mechanical properties of the composite are governed by the matrix. Laying the groundwork for a generic analysis of inhomogeneously swollen elastomers, we develop a model based on incremental mean-field homogenization of a hyperelastic matrix. The framework allows for the computation of the macroscopic effective stiffness for arbitrary hyperelastic matrix materials. For an in-depth quantification of the local effective stiffness, we extend the concept of elastic stiffness maps to incompressible materials. For strain-stiffening materials, stiffness maps in the swollen state highlight pronounced radial stiffening with a non-monotonic change in stiffness in the hoop direction. Stiffening characteristics are sensitive to the form of constitutive models, which may be exploited in the design of hydrated actuators, soft composites and metamaterials. For validation, we apply this framework to a Yeoh material, and compare to recently published data. Model predictions agree well with experimental data on elastomers with highly swollen embedded microgel particles. We identify three distinct regimes related to an increasing degree of particle swelling: first, an initial decrease in composite stiffness is attributed to particle softening upon liquid intake. Second, dilute particle swelling leads to matrix stiffening dominating over particle softening, resulting in an increase in composite stiffness. Third, for swelling degrees beyond the dilute limit, particle interactions dominate further matrix stiffening.
Ice and air: Visualisation of freezing spread and freeze-thaw embolism in young Liriodendron tulipifera leaves
Johnson, Kate M.; Scherer, Muriel; Gerber, Dominic; et al. (2025)
Journal of Experimental Botany
Spring freezing is an unforgiving stress for young leaves, often leading to death and with consequences for tree productivity and survival. While both the water-transport system and living tissues are vulnerable to freezing, we do not currently know whether damage to one or both of these systems causes death in leaves exposed to freezing. In this study, whole saplings of Liriodendron tulipifera were exposed to freezing and thawing trajectories designed to mimic natural spring freezes. We monitored the formation of freeze-thaw xylem embolism and damage to photosynthetic tissues and found a predictable progression of ice formation across the leaf surface that was strongly influenced by leaf- vein architecture, notably the presence or absence of bundle-sheath extensions. Our results also showed that freeze-thaw embolism occurred only in the lowest vein orders where mean vessel diameter exceeded 30μm. With evidence of both freeze-thaw embolism and damage to photosynthetic tissue, we conclude that this dual-mode of lethality in leaves might be common among other wide-vesseled angiosperm leaves, potentially playing a role in limiting geographic distributions, and demonstrate that bundle sheath extensions might stall or even prevent freezing spread.
Dynamic Shape Modulation of Deflated and Adhered Lipid Vesicles
Wolfisberg , Gianna; Agudo-Canalejo , Jaime; Bittmann , Pablo C.; et al. (2025)
Journal of the American Chemical Society
Lipid membrane-bounded organelles often possess intricate morphologies with spatially varying curvatures and large membrane surface areas relative to internal volume (small reduced volumes). These features are thought to be essential for protein sorting and vesicle trafficking, but challenging to reproduce in vitro. Here, we show that weakly adhered giant unilamellar vesicles (GUVs) can be osmotically deflated to reduced volumes as low as 0.1, similar to what is found in flattened, disc-shaped organelles such as Golgi cisternae and ER sheets. Using shape analysis with the Canham-Helfrich model, we determine mechanical parameters including adhesion strength, membrane tension, and pressure of individual vesicles. We find that the rate of shape flattening during deflation is governed by a normalized adhesion strength that combines vesicle size, adhesion energy, and bending rigidity. For highly flattened disc-like vesicles, we identify a geometric relationship that allows the adhesion strength to be estimated solely from the vesicle’s aspect ratio, size, and bending rigidity. These results provide a quantitative experimental platform for bottom-up studies of membrane shaping mechanisms and shape-dependent phenomena, such as curvature-mediated protein sorting.
Thermodynamics of microphase separation in a swollen, strain-stiffening polymer network
Fernández Rico, Carla; Style, Robert; Heyden, Stefanie; et al. (2026)
Soft Matter
Elastic MicroPhase separation (EMPS) provides a simple route to create soft materials with homogeneous microstructures by leveraging the supersaturation of crosslinked polymer networks with liquids. At low supersaturation, network elasticity stabilizes a uniform mixture, but beyond a critical threshold, metastable microphase-separated domains emerge. While previous theories have focused on describing qualitative features about the size and morphology of these domains, they do not make quantitative predictions about EMPS phase diagrams. In this work, we extend Flory-Huggins theory to quantitatively capture EMPS phase diagrams by incorporating strain-stiffening effects. This model requires no fitting parameters and relies solely on independently measured solubility parameters and large-deformation mechanical responses. Our results confirm that strain-stiffening enables metastable microphase separation within the swelling equilibrium state and reveal why the microstructures can range from discrete droplets to bicontinuous networks. This works highlights the critical role of nonlinear elasticity in controlling phase-separated morphologies in polymer gels.
Hydroelastomers: soft, tough, highly swelling composites
Moser, Simon; Feng, Yanxia; Yasa, Öncay; et al. (2022)
Soft Matter
Inspired by the cellular design of plant tissue, we present an approach to make versatile, tough, highly water-swelling composites. We embed highly swelling hydrogel particles inside tough, water-permeable, elastomeric matrices. The resulting composites, which we call hydroelastomers, combine the properties of their parent phases. From their hydrogel component, the composites inherit the ability to highly swell in water. From the elastomeric component, the composites inherit excellent stretchability and fracture toughness, while showing little softening as they swell. Indeed, the fracture properties of the composite match those of the best-performing, tough hydrogels, exhibiting fracture energies of up to 10 kJ m(-2). Our composites are straightforward to fabricate, based on widely-available materials, and can easily be molded or extruded to form shapes with complex swelling geometries. Furthermore, there is a large design space available for making hydroelastomers, since one can use any hydrogel as the dispersed phase in the composite, including hydrogels with stimuli-responsiveness. These features make hydroelastomers excellent candidates for use in soft robotics and swelling-based actuation, or as shape-morphing materials, while also being useful as hydrogel replacements in other fields.

Publications 1 - 10 of 32

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