1
|
Wang J, Wang X, Liu W, Hu H. Percolation thresholds of disks with random nonoverlapping patches on four regular two-dimensional lattices. Phys Rev E 2024; 109:064104. [PMID: 39020913 DOI: 10.1103/physreve.109.064104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Accepted: 05/13/2024] [Indexed: 07/20/2024]
Abstract
In percolation of patchy disks on lattices, each site is occupied by a disk, and neighboring disks are regarded as connected when their patches contact. Clusters of connected disks become larger as the patchy coverage of each disk χ increases. At the percolation threshold χ_{c}, an incipient cluster begins to span the whole lattice. For systems of disks with n symmetric patches on Archimedean lattices, a recent work [Wang et al., Phys. Rev. E 105, 034118 (2022)2470-004510.1103/PhysRevE.105.034118] found symmetric properties of χ_{c}(n), which are due to the coupling of the patches' symmetry and the lattice geometry. How does χ_{c} behave with increasing n if the patches are randomly distributed on the disks? We consider two typical random distributions of the patches, i.e., the equilibrium distribution and a distribution from random sequential adsorption. Combining Monte Carlo simulations and the critical polynomial method, we numerically determine χ_{c} for 106 models of different n on the square, honeycomb, triangular, and kagome lattices. The rules governing χ_{c}(n) are investigated in detail. They are quite different from those for disks with symmetric patches and could be useful for understanding similar systems.
Collapse
|
2
|
Torre KW, de Graaf J. Hydrodynamic lubrication in colloidal gels. SOFT MATTER 2023; 19:7388-7398. [PMID: 37740405 PMCID: PMC10548787 DOI: 10.1039/d3sm00784g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Accepted: 09/15/2023] [Indexed: 09/24/2023]
Abstract
Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.
Collapse
Affiliation(s)
- K W Torre
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
| | - J de Graaf
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
| |
Collapse
|
3
|
Müller FJ, Isa L, Vermant J. Toughening colloidal gels using rough building blocks. Nat Commun 2023; 14:5309. [PMID: 37652918 PMCID: PMC10471594 DOI: 10.1038/s41467-023-41098-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 08/22/2023] [Indexed: 09/02/2023] Open
Abstract
Colloidal gels, commonly used as mesoporous intermediates or functional materials, suffer from brittleness, often showing small yield strains on the order of 1% or less for gelled colloidal suspensions. The short-range adhesive forces in most such gels are central forces-combined with the smooth morphology of particles, the resistance to yielding and shear-induced restructuring is limited. In this study, we propose an innovative approach to improve colloidal gels by introducing surface roughness to the particles to change the yield strain, giving rise to non-central interactions. To elucidate the effects of particle roughness on gel properties, we prepared thermoreversible gels made from rough or smooth silica particles using a reliable click-like-chemistry-based surface grafting technique. Rheological and optical characterization revealed that rough particle gels exhibit enhanced toughness and self-healing properties. These remarkable properties can be utilized in various applications, such as xerogel fabrication and high-fidelity extrusion 3D-printing, as we demonstrate in this study.
Collapse
Affiliation(s)
| | - Lucio Isa
- Department of Materials, ETH Zurich, Switzerland
| | - Jan Vermant
- Department of Materials, ETH Zurich, Switzerland.
| |
Collapse
|
4
|
Gallegos JAS, Martínez-Rivera J, Valadez-Pérez NE, Castañeda-Priego R. Patchy colloidal gels under the influence of gravity. J Chem Phys 2023; 158:114907. [PMID: 36948838 DOI: 10.1063/5.0130796] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023] Open
Abstract
In this contribution, gravitational effects in gel-forming patchy colloidal systems are studied. We focus on how the gel structure is modified by gravity. Through Monte Carlo computer simulations of gel-like states recently identified by the rigidity percolation criterion [J. A. S. Gallegos et al., Phys. Rev. E 104, 064606 (2021)], the influence of the gravitational field, characterized by the gravitational Péclet number, Pe, on patchy colloids is studied in terms of the patchy coverage, χ. Our findings point out that there exists a threshold Péclet number, Peg, that depends on χ above which the gravitational field enhances the particle bonding and, in consequence, promotes the aggregation or clustering of particles; the smaller the χ value, the higher the Peg. Interestingly, when χ ∼ 1 (near the isotropic limit), our results are consistent with an experimentally determined threshold Pe value where gravity affects the gel formation in short-range attractive colloids. In addition, our results show that the cluster size distribution and the density profile undergo variations that lead to changes in the percolating cluster, i.e., gravity is able to modify the structure of the gel-like states. These changes have an important impact on the structural rigidity of the patchy colloidal dispersion; the percolating cluster goes from a uniform spatially network to a heterogeneous percolated structure, where an interesting structural scenario emerges, namely, depending on the Pe value, the new heterogeneous gel-like states can coexist with both diluted and dense phases or they simply reach a crystalline-like state. In the isotropic case, the increase in the Pe number can shift the critical temperature to higher temperatures; however, when Pe > 0.01, the binodal disappears and the particles fully sediment at the bottom of the sample cell. Furthermore, gravity moves the rigidity percolation threshold to lower densities. Finally, we also note that within the values of the Péclet number here explored, the cluster morphology is barely altered.
Collapse
Affiliation(s)
- Javier A S Gallegos
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| | - Jaime Martínez-Rivera
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| | - Néstor E Valadez-Pérez
- Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, 29050 Tuxtla Gutiérrez, Chiapas, Mexico
| | - Ramón Castañeda-Priego
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| |
Collapse
|
5
|
de Graaf J, Torre KW, Poon WCK, Hermes M. Hydrodynamic stability criterion for colloidal gelation under gravity. Phys Rev E 2023; 107:034608. [PMID: 37072990 DOI: 10.1103/physreve.107.034608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2022] [Accepted: 03/15/2023] [Indexed: 04/20/2023]
Abstract
Attractive colloids diffuse and aggregate to form gels, solidlike particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever-decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.
Collapse
Affiliation(s)
- Joost de Graaf
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Kim William Torre
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Wilson C K Poon
- SUPA, School of Physics and Astronomy, The University of Edinburgh, King's Buildings, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Michiel Hermes
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| |
Collapse
|
6
|
Antonov AP, Schweers S, Ryabov A, Maass P. Brownian dynamics simulations of hard rods in external fields and with contact interactions. Phys Rev E 2022; 106:054606. [PMID: 36559370 DOI: 10.1103/physreve.106.054606] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 10/24/2022] [Indexed: 11/12/2022]
Abstract
We propose a simulation method for Brownian dynamics of hard rods in one dimension for arbitrary continuous external force fields. It is an event-driven procedure based on the fragmentation and mergers of clusters formed by particles in contact. It allows one to treat particle interactions in addition to the hard-sphere exclusion as long as the corresponding interaction forces are continuous functions of the particle coordinates. We furthermore develop a treatment of sticky hard spheres as described by Baxter's contact interaction potential.
Collapse
Affiliation(s)
- Alexander P Antonov
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Sören Schweers
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| |
Collapse
|
7
|
Cai P, Su B, Zou L, Webber MJ, Heilshorn SC, Spakowitz AJ. Rheological Characterization and Theoretical Modeling Establish Molecular Design Rules for Tailored Dynamically Associating Polymers. ACS CENTRAL SCIENCE 2022; 8:1318-1327. [PMID: 36188349 PMCID: PMC9523779 DOI: 10.1021/acscentsci.2c00432] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Indexed: 05/15/2023]
Abstract
Dynamically associating polymers have long been of interest due to their highly tunable viscoelastic behavior. Many applications leverage this tunability to create materials that have specific rheological properties, but designing such materials is an arduous, iterative process. Current models for dynamically associating polymers are phenomenological, assuming a structure for the relationship between association kinetics and network relaxation. We present the Brachiation model, a molecular-level theory of a polymer network with dynamic associations that is rooted in experimentally controllable design parameters, replacing the iterative experimental process with a predictive model for how experimental modifications to the polymer will impact rheological behavior. We synthesize hyaluronic acid chains modified with supramolecular host-guest motifs to serve as a prototypical dynamic network exhibiting tunable physical properties through control of polymer concentration and association rates. We use dynamic light scattering microrheology to measure the linear viscoelasticity of these polymers across six decades in frequency and fit our theory parameters to the measured data. The parameters are then altered by a magnitude corresponding to changes made to the experimental parameters and used to obtain new rheological predictions that match the experimental results well, demonstrating the ability for this theory to inform the design process of dynamically associating polymeric materials.
Collapse
Affiliation(s)
- Pamela
C. Cai
- Department
of Chemical Engineering, Stanford University, Stanford, California 94305, United States
| | - Bo Su
- Department
of Chemical & Biomolecular Engineering, University of Notre Dame, Notre
Dame, Indiana 46556, United States
| | - Lei Zou
- Department
of Chemical & Biomolecular Engineering, University of Notre Dame, Notre
Dame, Indiana 46556, United States
| | - Matthew J. Webber
- Department
of Chemical & Biomolecular Engineering, University of Notre Dame, Notre
Dame, Indiana 46556, United States
| | - Sarah C. Heilshorn
- Department
of Materials Science and Engineering, Stanford
University, Stanford, California 94305, United States
| | - Andrew J. Spakowitz
- Department
of Chemical Engineering, Stanford University, Stanford, California 94305, United States
| |
Collapse
|
8
|
Wang Q, He Z, Wang J, Hu H. Percolation thresholds of randomly rotating patchy particles on Archimedean lattices. Phys Rev E 2022; 105:034118. [PMID: 35428067 DOI: 10.1103/physreve.105.034118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
We study the percolation of randomly rotating patchy particles on 11 Archimedean lattices in two dimensions. Each vertex of the lattice is occupied by a particle, and in each model the patch size and number are monodisperse. When there are more than one patches on the surface of a particle, they are symmetrically decorated. As the proportion χ of the particle surface covered by the patches increases, the clusters connected by the patches grow and the system percolates at the threshold χ_{c}. We combine Monte Carlo simulations and the critical polynomial method to give precise estimates of χ_{c} for disks with one to six patches and spheres with one to two patches on the 11 lattices. For one-patch particles, we find that the order of χ_{c} values for particles on different lattices is the same as that of threshold values p_{c} for site percolation on these lattices, which implies that χ_{c} for one-patch particles mainly depends on the geometry of lattices. For particles with more patches, symmetry becomes very important in determining χ_{c}. With the estimates of χ_{c} for disks with one to six patches, using analyses related to symmetry, we are able to give precise values of χ_{c} for disks with an arbitrary number of patches on all 11 lattices. The following rules are found for patchy disks on each of these lattices: (1) as the number of patches n increases, values of χ_{c} repeat in a periodic way, with the period n_{0} determined by the symmetry of the lattice; (2) when mod(n,n_{0})=0, the minimum threshold value χ_{min} appears, and the model is equivalent to site percolation with χ_{min}=p_{c}; and (3) disks with mod(n,n_{0})=m and n_{0}-m (m<n_{0}/2) share the same χ_{c} value. The results can be useful references for studying the connectivity of patchy particles on two-dimensional lattices at finite temperatures.
Collapse
Affiliation(s)
- Quancheng Wang
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei, Anhui 230601, China
| | - Zhenfang He
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei, Anhui 230601, China
| | - Junfeng Wang
- School of Physics, Hefei University of Technology, Hefei, Anhui 230009, China
| | - Hao Hu
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei, Anhui 230601, China
| |
Collapse
|
9
|
Protein microparticles visualize the contact network and rigidity onset in the gelation of model proteins. NPJ Sci Food 2021; 5:32. [PMID: 34903742 PMCID: PMC8668889 DOI: 10.1038/s41538-021-00111-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Accepted: 08/31/2021] [Indexed: 11/08/2022] Open
Abstract
Protein aggregation into gel networks is of immense importance in diverse areas from food science to medical research; however, it remains a grand challenge as the underlying molecular interactions are complex, difficult to access experimentally, and to model computationally. Early stages of gelation often involve protein aggregation into protein clusters that later on aggregate into a gel network. Recently synthesized protein microparticles allow direct control of these early stages of aggregation, decoupling them from the subsequent gelation stages. Here, by following the gelation of protein microparticles directly at the particle scale, we elucidate in detail the emergence of a percolating structure and the onset of rigidity as measured by microrheology. We find that the largest particle cluster, correlation length, and degree of polymerization all diverge with power laws, while the particles bind irreversibly indicating a nonequilibrium percolation process, in agreement with recent results on weakly attractive colloids. Concomitantly, the elastic modulus increases in a power-law fashion as determined by microrheology. These results give a consistent microscopic picture of the emergence of rigidity in a nonequilibrium percolation process that likely underlies the gelation in many more systems such as proteins, and other strongly interacting structures originating from (bio)molecules.
Collapse
|
10
|
Gallegos JAS, Perdomo-Pérez R, Valadez-Pérez NE, Castañeda-Priego R. Location of the gel-like boundary in patchy colloidal dispersions: Rigidity percolation, structure, and particle dynamics. Phys Rev E 2021; 104:064606. [PMID: 35030878 DOI: 10.1103/physreve.104.064606] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Accepted: 11/19/2021] [Indexed: 06/14/2023]
Abstract
During the past decade, there has been a hot debate about the physical mechanisms that determine when a colloidal dispersion approaches the gel transition. However, there is still no consensus on a possible unique route that leads to the conditions for the formation of a gel-like state. Based on gel states identified in experiments, Valadez-Pérez et al. [Phys. Rev. E 88, 060302(R) (2013)PLEEE81539-375510.1103/PhysRevE.88.060302] proposed rigidity percolation as the precursor of colloidal gelation in adhesive hard-sphere dispersions with coordination number 〈n_{b}〉 equal to 2.4. Although this criterion was originally established to describe mechanical transitions in network-forming molecular materials with highly directional interactions, it worked well to explain gel formation in colloidal suspensions with isotropic short-range attractive forces. Recently, this idea has also been used to account for the dynamical arrest experimentally observed in attractive spherocylinders. Then, by assuming that rigidity percolation also drives gelation in spherical colloids interacting with short-ranged and highly directional potentials, we locate the thermodynamic states where gelation seems to occur in dispersions made up of patchy colloids. To check whether the criterion 〈n_{b}〉=2.4 also holds in patchy colloidal systems, we apply the so-called bond-bending analysis to determine the fraction of floppy modes at some percolating clusters. This analysis confirms that the condition 〈n_{b}〉=2.4 is a good approximation to determine those percolating clusters that are either mechanically stable or rigid. Furthermore, our results point out that not all combinations of patches and coverages lead to a gel-like state. Additionally, we systematically study the structure and the cluster size distribution along those thermodynamic states identified as gels. We show that for high coverage values, the structure is very similar for systems that have the same coverage regardless the number or the position of the patches on the particle surface. Finally, by using dynamic Monte Carlo computer simulations, we calculate both the mean-square displacement and the intermediate scattering function at and in the neighborhood of the gel-like states.
Collapse
Affiliation(s)
- Javier A S Gallegos
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| | - Román Perdomo-Pérez
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| | - Néstor Enrique Valadez-Pérez
- Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, 29050 Tuxtla Gutiérrez, Chiapas, Mexico
| | - Ramón Castañeda-Priego
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| |
Collapse
|
11
|
Bantawa M, Fontaine-Seiler WA, Olmsted PD, Del Gado E. Microscopic interactions and emerging elasticity in model soft particulate gels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:414001. [PMID: 34265744 DOI: 10.1088/1361-648x/ac14f6] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 07/15/2021] [Indexed: 06/13/2023]
Abstract
We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model parameters allows us to sample, for a given gelation protocol, a variety of gel morphologies. For a specific set of the model parameters, we identify the local elastic structures that get interlocked in the gel network. Using the analytical expression of their elastic energy from the microscopic interactions, we can estimate their contribution to the emergent elasticity of the gel and gain new insight into its origin.
Collapse
Affiliation(s)
- Minaspi Bantawa
- Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, 37th and O Streets, N.W., Washington, D.C. 20057, United States of America
| | - Wayan A Fontaine-Seiler
- Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, 37th and O Streets, N.W., Washington, D.C. 20057, United States of America
| | - Peter D Olmsted
- Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, 37th and O Streets, N.W., Washington, D.C. 20057, United States of America
| | - Emanuela Del Gado
- Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, 37th and O Streets, N.W., Washington, D.C. 20057, United States of America
| |
Collapse
|
12
|
Lemaalem M, Hadrioui N, El Fassi S, Derouiche A, Ridouane H. An efficient approach to study membrane nano-inclusions: from the complex biological world to a simple representation. RSC Adv 2021; 11:10962-10974. [PMID: 35423551 PMCID: PMC8695885 DOI: 10.1039/d1ra00632k] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2021] [Accepted: 03/04/2021] [Indexed: 01/14/2023] Open
Abstract
Membrane nano-inclusions (NIs) are of great interest in biophysics, materials science, nanotechnology, and medicine. We hypothesized that the NIs within a biological membrane bilayer interact via a simple and efficient interaction potential, inspired by previous experimental and theoretical work. This interaction implicitly treats the membrane lipids but takes into account its effect on the NIs micro-arrangement. Thus, the study of the NIs is simplified to a two-dimensional colloidal system with implicit solvent. We calculated the structural properties from Molecular Dynamics simulations (MD), and we developed a Scaling Theory to discuss their behavior. We determined the thermal properties through potential energy per NI and pressure, and we discussed their variation as a function of the NIs number density. We performed a detailed study of the NIs dynamics using two approaches, MD simulations, and Dynamics Theory. We identified two characteristic values of number density, namely a critical number density n c = 3.67 × 10-3 Å-2 corresponded to the apparition of chain-like structures along with the liquid dispersed structure and the gelation number density n g = 8.40 × 10-3 Å-2 corresponded to the jamming state. We showed that the aggregation structure of NIs is of fractal dimension d F < 2. Also, we identified three diffusion regimes of membrane NIs, namely, normal for n < n c, subdiffusive for n c ≤ n < n g, and blocked for n ≥ n g. Thus, this paper proposes a simple and effective approach for studying the physical properties of membrane NIs. In particular, our results identify scaling exponents related to the microstructure and dynamics of membrane NIs.
Collapse
Affiliation(s)
- M Lemaalem
- Laboratoire de Physique des Polymères et Phénomènes Critiques, Sciences Faculty Ben M'Sik, Hassan II University P.O. Box 7955 Casablanca Morocco
| | - N Hadrioui
- Laboratoire de Physique des Polymères et Phénomènes Critiques, Sciences Faculty Ben M'Sik, Hassan II University P.O. Box 7955 Casablanca Morocco
| | - S El Fassi
- Laboratoire de Physique des Polymères et Phénomènes Critiques, Sciences Faculty Ben M'Sik, Hassan II University P.O. Box 7955 Casablanca Morocco
| | - A Derouiche
- Laboratoire de Physique des Polymères et Phénomènes Critiques, Sciences Faculty Ben M'Sik, Hassan II University P.O. Box 7955 Casablanca Morocco
| | - H Ridouane
- Laboratoire de Physique des Polymères et Phénomènes Critiques, Sciences Faculty Ben M'Sik, Hassan II University P.O. Box 7955 Casablanca Morocco
| |
Collapse
|
13
|
Kim S, Sureka HV, Kayitmazer AB, Wang G, Swan JW, Olsen BD. Effect of Protein Surface Charge Distribution on Protein–Polyelectrolyte Complexation. Biomacromolecules 2020; 21:3026-3037. [DOI: 10.1021/acs.biomac.0c00346] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Sieun Kim
- Department of Chemical Engineering, Massachusetts Institute of Technology, 02139 Cambridge, Massachusetts, United States
| | - Hursh V. Sureka
- Department of Chemical Engineering, Massachusetts Institute of Technology, 02139 Cambridge, Massachusetts, United States
| | | | - Gang Wang
- Department of Chemical Engineering, Massachusetts Institute of Technology, 02139 Cambridge, Massachusetts, United States
| | - James W. Swan
- Department of Chemical Engineering, Massachusetts Institute of Technology, 02139 Cambridge, Massachusetts, United States
| | - Bradley D. Olsen
- Department of Chemical Engineering, Massachusetts Institute of Technology, 02139 Cambridge, Massachusetts, United States
| |
Collapse
|
14
|
Rouwhorst J, Ness C, Stoyanov S, Zaccone A, Schall P. Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction. Nat Commun 2020; 11:3558. [PMID: 32678089 PMCID: PMC7367344 DOI: 10.1038/s41467-020-17353-8] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Accepted: 06/21/2020] [Indexed: 11/25/2022] Open
Abstract
The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. In particular, for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, numerical simulations, and analytical modeling with a master kinetic equation to show that cluster sizes and correlation lengths diverge with exponents ~1.6 and 0.8, respectively, consistent with percolation theory, while detailed balance in the particle attachment and detachment processes is broken. Cluster masses exhibit power-law distributions with exponents -3/2 and -5/2 before and after percolation, as predicted by solutions to the master kinetic equation. These results revealing a nonequilibrium continuous phase transition unify the structural arrest and yielding into related frameworks.
Collapse
Affiliation(s)
- Joep Rouwhorst
- Institute of Physics, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands
| | - Christopher Ness
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, CB3 0AS, UK
- School of Engineering, University of Edinburgh, Edinburgh, EH9 3FB, UK
| | - Simeon Stoyanov
- Unilever R&D Vlaardingen, Olivier van Noortlaan 120, Vlaardingen, 3133 AT, The Netherlands
| | - Alessio Zaccone
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, CB3 0AS, UK.
- Department of Physics "A. Pontremoli'", University of Milan, via Celoria 16, Milan, 20133, Italy.
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK.
| | - Peter Schall
- Institute of Physics, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands.
| |
Collapse
|
15
|
Thiel A, Atherton TJ, Spicer PT, Hartel RW. Aggregation in viscoelastic emulsion droplet gels with capillarity-driven rearrangements. SOFT MATTER 2020; 16:5506-5513. [PMID: 32495759 DOI: 10.1039/c9sm02134e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Arrested, or partial, coalescence of viscoelastic emulsion droplets can occur when elastic resistance to deformation offsets droplet surface area minimization. Arrest is a critical element of food and consumer product microstructure and performance, but direct studies of structural arrest and rearrangement have been carried out using only two or three droplets at a time. The question remains whether the behavior of small numbers of droplets also occurs in larger, more realistic many-droplet systems. Here we study two-dimensional aggregation and arrested coalescence of emulsions containing ∼1000 droplets and find that the restructuring mechanisms observed for smaller systems have a large effect on local packing in multidroplet aggregates, but surprisingly do not significantly alter overall mass scaling in the aggregates. Specifically, increased regions of hexagonal packing are observed as the droplet solids level, and thus elasticity, is decreased because greater degrees of capillary force-driven restructuring are possible. Diffusion-limited droplet aggregation simulations that account for the restructuring mechanisms agree with the experimental results and suggest a basis for prediction of larger-scale network properties and bulk emulsion behavior.
Collapse
Affiliation(s)
- Abigail Thiel
- Department of Food Science, University of Wisconsin-Madison, Madison, WI, USA
| | | | | | - Richard W Hartel
- Department of Food Science, University of Wisconsin-Madison, Madison, WI, USA
| |
Collapse
|
16
|
Kamp M, de Nijs B, van der Linden MN, de Feijter I, Lefferts MJ, Aloi A, Griffiths J, Baumberg JJ, Voets IK, van Blaaderen A. Multivalent Patchy Colloids for Quantitative 3D Self-Assembly Studies. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:2403-2418. [PMID: 32097015 PMCID: PMC7202687 DOI: 10.1021/acs.langmuir.9b03863] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Revised: 01/23/2020] [Indexed: 06/10/2023]
Abstract
We report methods to synthesize sub-micron- and micron-sized patchy silica particles with fluorescently labeled hemispherical titania protrusions, as well as routes to efficiently characterize these particles and self-assemble these particles into non-close-packed structures. The synthesis methods expand upon earlier work in the literature, in which silica particles packed in a colloidal crystal were surface-patterned with a silane coupling agent. Here, hemispherical amorphous titania protrusions were successfully labeled with fluorescent dyes, allowing for imaging by confocal microscopy and super-resolution techniques. Confocal microscopy was exploited to experimentally determine the numbers of protrusions per particle over large numbers of particles for good statistical significance, and these distributions were compared to simulations predicting the number of patches as a function of core particle polydispersity and maximum separation between the particle surfaces. We self-assembled these patchy particles into open percolating gel networks by exploiting solvophobic attractions between the protrusions.
Collapse
Affiliation(s)
- Marlous Kamp
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
- NanoPhotonics
Centre, Department of Physics, University
of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Bart de Nijs
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
- NanoPhotonics
Centre, Department of Physics, University
of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Marjolein N. van der Linden
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Isja de Feijter
- Laboratory
of Self-Organizing Soft Matter, Laboratory of Macromolecular and Organic
Chemistry, Department of Chemical Engineering and Chemistry, Institute
for Complex Molecular Systems, Eindhoven
University of Technology, Post Office
Box 513, 5600 MB Eindhoven, The Netherlands
| | - Merel J. Lefferts
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Antonio Aloi
- Laboratory
of Self-Organizing Soft Matter, Laboratory of Macromolecular and Organic
Chemistry, Department of Chemical Engineering and Chemistry, Institute
for Complex Molecular Systems, Eindhoven
University of Technology, Post Office
Box 513, 5600 MB Eindhoven, The Netherlands
| | - Jack Griffiths
- NanoPhotonics
Centre, Department of Physics, University
of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Jeremy J. Baumberg
- NanoPhotonics
Centre, Department of Physics, University
of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Ilja K. Voets
- Laboratory
of Self-Organizing Soft Matter, Laboratory of Macromolecular and Organic
Chemistry, Department of Chemical Engineering and Chemistry, Institute
for Complex Molecular Systems, Eindhoven
University of Technology, Post Office
Box 513, 5600 MB Eindhoven, The Netherlands
| | - Alfons van Blaaderen
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| |
Collapse
|
17
|
Immink JN, Maris JJE, Schurtenberger P, Stenhammar J. Using Patchy Particles to Prevent Local Rearrangements in Models of Non-equilibrium Colloidal Gels. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:419-425. [PMID: 31763852 PMCID: PMC6994064 DOI: 10.1021/acs.langmuir.9b02675] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Revised: 10/30/2019] [Indexed: 06/10/2023]
Abstract
Simple models based on isotropic interparticle attractions often fail to capture experimentally observed structures of colloidal gels formed through spinodal decomposition and subsequent arrest: the resulting gels are typically denser and less branched than their experimental counterparts. Here, we simulate gels formed from soft particles with directional attractions ("patchy particles"), designed to inhibit lateral particle rearrangement after aggregation. We directly compare simulated structures with experimental colloidal gels made using soft attractive microgel particles, by employing a "skeletonization" method that reconstructs the three-dimensional backbone from experiment or simulation. We show that including directional attractions with sufficient valency leads to strongly branched structures compared to isotropic models. Furthermore, combining isotropic and directional attractions provides additional control over aggregation kinetics and gel structure. Our results show that the inhibition of lateral particle rearrangements strongly affects the gel topology and is an important effect to consider in computational models of colloidal gels.
Collapse
Affiliation(s)
- Jasper N. Immink
- Division
of Physical Chemistry, Lund University, 22100 Lund, Sweden
| | - J. J. Erik Maris
- Inorganic
Chemistry and Catalysis Group, Utrecht University, 3584 CG Utrecht, The Netherlands
| | - Peter Schurtenberger
- Division
of Physical Chemistry, Lund University, 22100 Lund, Sweden
- Lund
Institute of advanced Neutron and X-ray Science (LINXS), Lund University, 22100 Lund, Sweden
| | | |
Collapse
|
18
|
Nguyen HT, Graham AL, Koenig PH, Gelb LD. Computer simulations of colloidal gels: how hindered particle rotation affects structure and rheology. SOFT MATTER 2020; 16:256-269. [PMID: 31782472 DOI: 10.1039/c9sm01755k] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The effects of particle roughness and short-ranged non-central forces on colloidal gels are studied using computer simulations in which particles experience a sinusoidal variation in energy as they rotate. The number of minima n and energy scale K are the key parameters; for large K and n, particle rotation is strongly hindered, but for small K and n particle rotation is nearly free. A series of systems are simulated and characterized using fractal dimensions, structure factors, coordination number distributions, bond-angle distributions and linear rheology. When particles rotate easily, clusters restructure to favor dense packings. This leads to longer gelation times and gels with strand-like morphology. The elastic moduli of such gels scale as G'∝ω0.5 at high shear frequencies ω. In contrast, hindered particle rotation inhibits restructuring and leads to rapid gelation and diffuse morphology. Such gels are stiffer, with G'∝ω0.35. The viscous moduli G'' in the low-barrier and high-barrier regimes scale according to exponents 0.53 and 0.5, respectively. The crossover frequency between elastic and viscous behaviors generally increases with the barrier to rotation. These findings agree qualitatively with some recent experiments on heterogeneously-surface particles and with studies of DLCA-type gels and gels of smooth spheres.
Collapse
Affiliation(s)
- Hong T Nguyen
- Department of Materials Science and Engineering, University of Texas at Dallas, Richardson, Texas 75080, USA.
| | - Alan L Graham
- Department of Mechanical Engineering, University of Colorado - Denver, Denver, CO, USA
| | - Peter H Koenig
- Beauty Care Modeling and Simulation, Mason Business Center, 8700 Mason-Montgomery Rd, Mason, OH 45040, USA
| | - Lev D Gelb
- Department of Materials Science and Engineering, University of Texas at Dallas, Richardson, Texas 75080, USA.
| |
Collapse
|
19
|
Cerbelaud M, Lebdioua K, Tran CT, Crespin B, Aimable A, Videcoq A. Brownian dynamics simulations of one-patch inverse patchy particles. Phys Chem Chem Phys 2019; 21:23447-23458. [PMID: 31616876 DOI: 10.1039/c9cp04247d] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Inverse patchy particles are promising colloids to develop new architectures in ceramic materials based on their self-assembly. Nonetheless, a good understanding of their aggregation is required. Several previous studies have shown that the behavior of ceramic colloids can be well described by the DLVO interaction potential. In the present paper, we develop new coarse-grained Brownian dynamics simulations, where particles are represented by an assembly of beads interacting via DLVO interactions, whose parameters can be directly linked to experimental characterization. First, the validity of the simulations is proved by studying the heteroaggregation of homogeneously charged particles. Then, simulations are applied to one-patch inverse patchy particles to study the effect of the patch size. They show that the smaller the patch, the more elongated the aggregates. Simulations are also performed to understand the role of the Debye screening length in the particular case of large patches and they show that aggregation leads always to compact aggregates.
Collapse
|