Spontaneous Formation of Eutectic Crystal Structures in Binary And
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Depletion Forces Due to Image Charges Near Dielectric Discontinuities
Depletion forces due to image charges near dielectric discontinuities Robin A. Curtisa, Leo Lueb,∗ a School of Chemical Engineering and Analytical Science, The University of Manchester Oxford Road, Manchester M13 9PL, United Kingdom b Department of Chemical and Process Engineering, University of Strathclyde James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, United Kingdom Abstract The depletion force is an effective inter-particle attractive interaction that is en- tropically driven by the exclusion of co-solvent molecules. For large co-solvents, such as polymers, the exclusion is primarily driven by excluded volume interac- tions. However, the exclusion of co-solvents, such as electrolytes, can be caused by other mechanisms. In this review, we summarize the literature on inter- particle depletion forces that arise from repulsive image-charge forces between low-dielectric particles and electrolytes. In particular, we emphasize the results from a variational perturbation theory for describing the salting-out behavior observed in moderately concentrated salt solutions. The theory predicts an unscreened force with a range given by the Bjerrum length and a magnitude proportional to the osmotic pressure of the salt solution. The force becomes sig- nificant at the same salt concentration where salting-out behavior is typically observed. Keywords: depletion force, dielectric, electrolyte, colloids 1. Introduction The depletion force was originally used to describe the attraction between colloidal particles induced by the addition of small polymer molecules [1]. In ∗Corresponding author Email address: [email protected] ( Leo Lue ) Preprint submitted to Curr. Opin. Colloid Interface Sci. December 1, 2014 this case, the force is driven by polymer exclusion from the colloidal particles. -
Recent Progress on Deep Eutectic Solvents in Biocatalysis Pei Xu1,2, Gao‑Wei Zheng3, Min‑Hua Zong1,2, Ning Li1 and Wen‑Yong Lou1,2*
Xu et al. Bioresour. Bioprocess. (2017) 4:34 DOI 10.1186/s40643-017-0165-5 REVIEW Open Access Recent progress on deep eutectic solvents in biocatalysis Pei Xu1,2, Gao‑Wei Zheng3, Min‑Hua Zong1,2, Ning Li1 and Wen‑Yong Lou1,2* Abstract Deep eutectic solvents (DESs) are eutectic mixtures of salts and hydrogen bond donors with melting points low enough to be used as solvents. DESs have proved to be a good alternative to traditional organic solvents and ionic liq‑ uids (ILs) in many biocatalytic processes. Apart from the benign characteristics similar to those of ILs (e.g., low volatil‑ ity, low infammability and low melting point), DESs have their unique merits of easy preparation and low cost owing to their renewable and available raw materials. To better apply such solvents in green and sustainable chemistry, this review frstly describes some basic properties, mainly the toxicity and biodegradability of DESs. Secondly, it presents several valuable applications of DES as solvent/co-solvent in biocatalytic reactions, such as lipase-catalyzed transester‑ ifcation and ester hydrolysis reactions. The roles, serving as extractive reagent for an enzymatic product and pretreat‑ ment solvent of enzymatic biomass hydrolysis, are also discussed. Further understanding how DESs afect biocatalytic reaction will facilitate the design of novel solvents and contribute to the discovery of new reactions in these solvents. Keywords: Deep eutectic solvents, Biocatalysis, Catalysts, Biodegradability, Infuence Introduction (1998), one concept is “Safer Solvents and Auxiliaries”. Biocatalysis, defned as reactions catalyzed by bio- Solvents represent a permanent challenge for green and catalysts such as isolated enzymes and whole cells, has sustainable chemistry due to their vast majority of mass experienced signifcant progress in the felds of either used in catalytic processes (Anastas and Eghbali 2010). -
Phase Diagrams
Module-07 Phase Diagrams Contents 1) Equilibrium phase diagrams, Particle strengthening by precipitation and precipitation reactions 2) Kinetics of nucleation and growth 3) The iron-carbon system, phase transformations 4) Transformation rate effects and TTT diagrams, Microstructure and property changes in iron- carbon system Mixtures – Solutions – Phases Almost all materials have more than one phase in them. Thus engineering materials attain their special properties. Macroscopic basic unit of a material is called component. It refers to a independent chemical species. The components of a system may be elements, ions or compounds. A phase can be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics i.e. it is a physically distinct from other phases, chemically homogeneous and mechanically separable portion of a system. A component can exist in many phases. E.g.: Water exists as ice, liquid water, and water vapor. Carbon exists as graphite and diamond. Mixtures – Solutions – Phases (contd…) When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient. A solution (liquid or solid) is phase with more than one component; a mixture is a material with more than one phase. Solute (minor component of two in a solution) does not change the structural pattern of the solvent, and the composition of any solution can be varied. In mixtures, there are different phases, each with its own atomic arrangement. It is possible to have a mixture of two different solutions! Gibbs phase rule In a system under a set of conditions, number of phases (P) exist can be related to the number of components (C) and degrees of freedom (F) by Gibbs phase rule. -
Irilll SDI: 0378-4371(92)00312-H
Physica A 195 (1993) 387-397 North-Holland IRIlll SDI: 0378-4371(92)00312-H On the spinodal instability of highly asymmetric hard sphere suspensions H.N.W. Lekkerkerker and A. Stroobants Van't Hoff Laboratory for Physical and Colloid Chemistry, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands Received 21 December 1992 A new treatment of the binodal instability of suspensions containing a highly asymmetric mixture of hard spheres is presented. The origin of the instability is the attractive depletion interaction between the larger spheres, which is caused by the presence of the smaller spheres. 1. Introduction Until recently it was generally believed that hard sphere mixtures are stable with respect to phase separation into two fluid phases. Indeed, at least within the Percus-Yevick closure of the Ornstein-Zernike equation and using the compressibility theorem to calculate the thermodynamic quantities this is true [1,2]. However, recently Biben and Hansen [3] have shown that starting from the Rogers-Young closure [4], which is known to be more accurate for hard spheres than the Percus-Yevick closure, such mixtures do seem to become unstable for diameter ratios larger than 5 at sufficiently high volume fractions. A direct experimental test of the prediction of Biben and Hansen is obviously not any easy task as hard sphere atoms do not exist in reality. However, recently strong experimental evidence for phase separation in bimodal disper- sions of sterically stabilized silica particles was obtained in our laboratory [5]. The short-ranged harshly repulsive interactions between these sterically stabil- ized colloidal particles closely approximate that of hard spheres [6] and therefore the thermodynamic properties of such bimodal suspensions are closely related to those of hard sphere mixtures [7]. -
Arxiv:2012.01639V4 [Cond-Mat.Soft] 29 Jun 2021 T =Kbt/Ε, Where Kb and T Are the Boltzmann Constant and the Temperature of System, Respectively
Self-Assembly of Isostatic Self-Dual Colloidal Crystals Qun-Li Lei,1, 2, ∗ Wei Zheng,1, 2, ∗ Feng Tang,1 Xiangang Wan,1 Ran Ni,2, y and Yuqiang Ma1, z 1National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China 2School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore Self-dual structures whose dual counterparts are themselves possess unique hidden symmetry, beyond the description of classical spatial symmetry groups. Here we propose a strategy based on a nematic monolayer of attractive half-cylindrical colloids to self-assemble these exotic structures. This system can be seen as a 2D system of semi-disks. By using Monte Carlo simulations, we discover two isostatic self-dual crystals, i.e., an unreported crystal with pmg space-group symmetry and the twisted Kagome crystal. For the pmg crystal approaching the critical point, we find the double degeneracy of the full phononic spectrum at the self-dual point, and the merging of two tilted Weyl nodes into one critically-tilted Dirac node. The latter is `accidentally' located on the high-symmetry line. The formation of this unconventional Dirac node is due to the emergence of the critical flat bands at the self-dual point, which are linear combinations of finite-frequency floppy modes. These modes can be understood as mechanically-coupled self-dual rhomb chains vibrating in some unique uncoupled ways. Our work paves the way for designing and fabricating self-dual materials with exotic mechanical or phononic properties. -
Section 1 Introduction to Alloy Phase Diagrams
Copyright © 1992 ASM International® ASM Handbook, Volume 3: Alloy Phase Diagrams All rights reserved. Hugh Baker, editor, p 1.1-1.29 www.asminternational.org Section 1 Introduction to Alloy Phase Diagrams Hugh Baker, Editor ALLOY PHASE DIAGRAMS are useful to exhaust system). Phase diagrams also are con- terms "phase" and "phase field" is seldom made, metallurgists, materials engineers, and materials sulted when attacking service problems such as and all materials having the same phase name are scientists in four major areas: (1) development of pitting and intergranular corrosion, hydrogen referred to as the same phase. new alloys for specific applications, (2) fabrica- damage, and hot corrosion. Equilibrium. There are three types of equili- tion of these alloys into useful configurations, (3) In a majority of the more widely used commer- bria: stable, metastable, and unstable. These three design and control of heat treatment procedures cial alloys, the allowable composition range en- conditions are illustrated in a mechanical sense in for specific alloys that will produce the required compasses only a small portion of the relevant Fig. l. Stable equilibrium exists when the object mechanical, physical, and chemical properties, phase diagram. The nonequilibrium conditions is in its lowest energy condition; metastable equi- and (4) solving problems that arise with specific that are usually encountered inpractice, however, librium exists when additional energy must be alloys in their performance in commercial appli- necessitate the knowledge of a much greater por- introduced before the object can reach true stabil- cations, thus improving product predictability. In tion of the diagram. Therefore, a thorough under- ity; unstable equilibrium exists when no addi- all these areas, the use of phase diagrams allows standing of alloy phase diagrams in general and tional energy is needed before reaching meta- research, development, and production to be done their practical use will prove to be of great help stability or stability. -
PHYSICA ELSEVIER Physica a 222 (1995) 10-24
PHYSICA ELSEVIER Physica A 222 (1995) 10-24 Depletion force in colloidal systems Y. Mao a'*, M.E. Cates b, H.N.W. Lekkerkerker c a Cavendish Laboratory, Madingley Road, Cambridge, CB30HE, UK bDepartment of Physics and Astronomy. University of Edinburgh, King "s Buildings, Mayfield Road, Edinburg EH9 3JZ, UK c Van "t Haft Laboratory, University of Utrecht, Padualaan 8, 3584 Utrecht, The Netherlands Received: 31 May 1995 Abstract The entropic depletion force, in colloids, arises when large particles are placed in a solution of smaller ones, and sterically constrained to avoid them. We calculate the interaction between large spheres (of radius R) in a dilute solution of mutually avoiding small spheres (of diameter a ,~ R and volume fraction ~b), to third order in ~b. In addition to the well-known attractive force for 0 < h < a, we find a repulsive barrier at larger separations, and beyond that a secondary minimum. Except for unusually large size ratios (perhaps abetted by relatively high density qS), these features of the interaction potential are too small, compared to kBT, for kinetic stabili- zation (arising from the barrier) or flocculation into the secondary minimum, to be widespread, although such effects are possible in principle. For feasible size ratios, the same features should have observable consequences for the radial distribution function of the large spheres. Such effects can be viewed as precursors, at low density, of liquidlike structuring (solvation forces) expected at higher q~. Our third order calculation gives satisfactory agreement with a recent computer simulation at moderate density and size ratio (2R/a = 10; ~b = 7z/15). -
Chapter 10 Gibbs Free Energy Composition and Phase Diagrams of Binary Systems 10.2 Gibbs Free Energy and Thermodynamic Activity
Chapter 10 Gibbs Free Energy Composition and Phase Diagrams of Binary Systems 10.2 Gibbs Free Energy and Thermodynamic Activity The Gibbs free energy of mixing of the components A and B to form a mole of solution: If it is ideal, i.e., if ai=Xi, then the molar Gibbs free energy of mixing, Figure 10.1 The molar Gibbs free energies of Figure 10.2 The activities of component B mixing in binary systems exhibiting ideal behavior obtained from lines I, II, and III in Fig. 10.1. (I), positive deviation from ideal behavior (II), and negative deviation from ideal behavior (III). 10.3 The Gibbs Free Energy of Formation of Regular Solutions If curves II and III for regular solutions, then deviation of from , is ∆ ∆ For curve II, < , , and thus is a positive quantity ( and Ω are positive quantities). ∆ ∆ ∆ Figure 10.3 The effect of the magnitude of a on the integral molar heats and integral molar Gibbs free energies of formation of a binary regular solution. 10.3 The Gibbs Free Energy of Formation of Regular Solutions The equilibrium coexistence of two separate solutions at the temperature T and pressure P requires that and Subtracting from both sides of Eq. (i) gives 0 or Similarly Figure 10.4 (a) The molar Gibbs free energies of mixing of binary components which form a complete range of solutions. (b) The molar Gibbs free energies of mixing of binary components in a system which exhibits a miscibility gap. 10.4 Criteria for Phase Stability in Regular Solutions For a regular solution, and 3 3 At XA=XB=0.5, the third derivative, / XB =0, 2 2 and thus the second derivative, / XB =0 at XA=0.5 ∆ When α=2 ⇒ the critical value of ∆αabove which phase separation occurs. -
Interplay of Motility and Polymer-Driven Depletion Forces in the Initial Stages of Bacterial Cite This: DOI: 10.1039/C9sm00791a Aggregation†
Soft Matter View Article Online PAPER View Journal Interplay of motility and polymer-driven depletion forces in the initial stages of bacterial Cite this: DOI: 10.1039/c9sm00791a aggregation† Michael K. Porter, a Asher Preska Steinberg a and Rustem F. Ismagilov *ab Motile bacteria are often found in complex, polymer-rich environments in which microbes can aggregate via polymer-induced depletion forces. Bacterial aggregation has many biological implications; it can promote biofilm formation, upregulate virulence factors, and lead to quorum sensing. The steady state aggregation behavior of motile bacteria in polymer solutions has been well studied and shows that stronger depletion forces are required to aggregate motile bacteria as compared with their nonmotile analogs. However, no one has studied whether these same trends hold at the initial stages of aggregation. We use experiments and numerical calculations to investigate the polymer-induced depletion aggregation of motile Escherichia coli in polyethylene glycol solutions on short experimental Creative Commons Attribution 3.0 Unported Licence. Received 17th April 2019, timescales (B10 min). Our work reveals that in the semi-dilute polymer concentration regime and at Accepted 29th July 2019 short timescales, in contrast to what is found at steady state, bacterial motility actually enhances DOI: 10.1039/c9sm00791a aggregate formation by increasing the collision rate in viscous environments. These unexpected findings have implications for developing models of active matter, and for understanding -
Continuous Eutectic Freeze Crystallisation
CONTINUOUS EUTECTIC FREEZE CRYSTALLISATION Report to the Water Research Commission by Jemitias Chivavava, Benita Aspeling, Debbie Jooste, Edward Peters, Dereck Ndoro, Hilton Heydenrych, Marcos Rodriguez Pascual and Alison Lewis Crystallisation and Precipitation Research Unit Department of Chemical Engineering University of Cape Town WRC Report No. 2229/1/18 ISBN 978-1-4312-0996-5 July 2018 Obtainable from Water Research Commission Private Bag X03 Gezina, 0031 [email protected] or download from www.wrc.org.za DISCLAIMER This report has been reviewed by the Water Research Commission (WRC) and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the WRC nor does mention of trade names or commercial products constitute endorsement or recommendation for use. Printed in the Republic of South Africa © Water Research Commission ii Executive summary Eutectic Freeze Crystallisation (EFC) has shown great potential to treat industrial brines with the benefits of recovering potentially valuable salts and very pure water. So far, many studies that have been concerned with the development of EFC have all been carried out (1) in batch mode and (2) have not considered the effect of minor components that may affect the process efficiency and product quality. Brines generated in industrial operations often contain antiscalants that are dosed in cooling water and reverse osmosis feed streams to prevent scaling of heat exchangers and membrane fouling. These antiscalants may affect the EFC process, especially the formation of salts. The first aim of this work was to understand the effects of antiscalants on thermodynamics and crystallisation kinetics in EFC. -
Entropic Effects in Polymer Nanocomposites
Review Entropic Effects in Polymer Nanocomposites Xiaobin Dai 1,†, Cuiling Hou 1,†, Ziyang Xu 1, Ye Yang 1, Guolong Zhu 1, Pengyu Chen 1, Zihan Huang 1 and Li-Tang Yan 1,* 1 State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China; [email protected] (X.D.); [email protected] (C.H.); [email protected] (Z.X); [email protected] (Y.Y.); [email protected] (Z.G.); [email protected] (P.C.); [email protected] (Z.H.) * Correspondence: [email protected] † These authors contributed equally. Received: 14 December 2018; Accepted: 11 February 2019; Published: 15 February 2019 Abstract: Polymer nanocomposite materials, consisting of a polymer matrix embedded with nanoscale fillers or additives that reinforce the inherent properties of the matrix polymer, play a key role in many industrial applications. Understanding of the relation between thermodynamic interactions and macroscopic morphologies of the composites allow for the optimization of design and mechanical processing. This review article summarizes the recent advancement in various aspects of entropic effects in polymer nanocomposites, and highlights molecular methods used to perform numerical simulations, morphologies and phase behaviors of polymer matrices and fillers, and characteristic parameters that significantly correlate with entropic interactions in polymer nanocomposites. Experimental findings and insight obtained from theories and simulations are combined to understand how the entropic effects are turned into effective interparticle interactions that can be harnessed for tailoring nanostructures of polymer nanocomposites. Keywords: entropy; nanocomposites; thermodynamics; nanostructure; morphology 1. Introduction Entropy (S), the measure of possible states that a system can take, has drawn intense research interest in polymer nanocomposites (PNCs), owing to their rich fundamental behaviors associated with self-assembly [1–6], stimulus-response [7–9], and so on. -
Chapter 9. Phase Diagrams
Chapter 9. Phase Diagrams 9.1 Introduction Good understanding of phase diagrams will help engineers to design and control heat treatment procedures:- some properties of materials are functions of their microstructures, and hence of their thermal histories. The development of microstructure of an alloy is related to the characteristics of its phase diagram. Phase diagrams provide valuable information about melting, casting, crystallization, and other phenomenon. Topics to be discussed are: terminology of phase diagrams and phase transformations, interpretation of phase, simple binary phase diagrams, and development of equilibrium microstructures upon cooling. DEFINITIONS AND BASIC CONCEPTS “Components”: pure metals and/or compounds of which an alloy is composed (Ex.: solute and solvent in Cu-Zn brass). A “System”: a specific body of material under consideration (Ex.: ladle of molten steel) or a series of alloys consisting of the same components but without regard to alloy composition (Ex.: the iron- carbon system). “Solid solution”: consists of atoms of at least two different types; the solute atoms (minor component) occupy either substitutional or interstitial positions in the solvent lattice (host or major component). 9.2 Solubility Limit Solubility limit is the maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution at a specific temperature. Adding more solute in excess of this limit results in forming another solid solution or compound with different composition. Consider sugar-water (C12H22O11 – H2O) system. As sugar is added to water Æ sugar-water solution (syrup). Adding more sugar Æ solution becomes more concentrated until solubility limit is reached (solution is saturated with sugar).