Comparison of surface energy values for Au, Pb, and Bi [8]
\r\n\t
",isbn:"978-1-83969-561-2",printIsbn:"978-1-83969-560-5",pdfIsbn:"978-1-83969-562-9",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"65f2a1fef9c804c29b18ef3ac4a35066",bookSignature:"Dr. Luis Loures",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10756.jpg",keywords:"Urban Processes, Urban Patterns, Redevelopment Strategies, Landscape, Land Transformation, Urban Models, Urban Evolution, Urban Organisation, Legislation, Sustainable Development, Green Infrastructure, Regional Planning",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 23rd 2021",dateEndSecondStepPublish:"March 22nd 2021",dateEndThirdStepPublish:"May 21st 2021",dateEndFourthStepPublish:"August 9th 2021",dateEndFifthStepPublish:"October 8th 2021",remainingDaysToSecondStep:"a month",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Dr. Loures has worked on pioneering research on circular planning applied to post-industrial landscape redevelopment. Since he graduated he has published several peer-reviewed papers at the national and international levels and he has been a guest researcher and lecturer both at Michigan State University (USA) and at the University of Toronto (Canada) where he has developed part of his Ph.D. research with the Financial support from the Portuguese Foundation for Science and Technology (Ph.D. grant).",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"108118",title:"Dr.",name:"Luis",middleName:null,surname:"Loures",slug:"luis-loures",fullName:"Luis Loures",profilePictureURL:"https://mts.intechopen.com/storage/users/108118/images/system/108118.png",biography:"Luís Loures is a Landscape Architect and Agronomic Engineer, Vice-President of the Polytechnic Institute of Portalegre, who holds a Ph.D. in Planning and a Post-Doc in Agronomy. Since he graduated, he has published several peer reviewed papers at the national and international levels and he has been a guest researcher and lecturer both at Michigan State University (USA), and at University of Toronto (Canada) where he has developed part of his Ph.D. research with the Financial support from the Portuguese Foundation for Science and Technology (Ph.D. grant).\nDuring his academic career he had taught in several courses in different Universities around the world, mainly regarding the fields of landscape architecture, urban and environmental planning and sustainability. Currently, he is a researcher both at VALORIZA - Research Centre for Endogenous Resource Valorization – Polytechnic Institute of Portalegre, and the CinTurs - Research Centre for Tourism, Sustainability and Well-being, University of Algarve where he is a researcher on several financed research projects focusing several different investigation domains such as urban planning, landscape reclamation and urban redevelopment, and the use of urban planning as a tool for achieving sustainable development.",institutionString:"Polytechnic Institute of Portalegre",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"8",totalChapterViews:"0",totalEditedBooks:"2",institution:{name:"Polytechnic Institute of Portalegre",institutionURL:null,country:{name:"Portugal"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"10",title:"Earth and Planetary Sciences",slug:"earth-and-planetary-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"205697",firstName:"Kristina",lastName:"Kardum Cvitan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/205697/images/5186_n.jpg",email:"kristina.k@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"7476",title:"Land Use",subtitle:"Assessing the Past, Envisioning the Future",isOpenForSubmission:!1,hash:"5b0c406adac8447ffeb089e29eac8ea9",slug:"land-use-assessing-the-past-envisioning-the-future",bookSignature:"Luís Carlos Loures",coverURL:"https://cdn.intechopen.com/books/images_new/7476.jpg",editedByType:"Edited by",editors:[{id:"108118",title:"Dr.",name:"Luis",surname:"Loures",slug:"luis-loures",fullName:"Luis Loures"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8295",title:"Landscape Reclamation",subtitle:"Rising From What's Left",isOpenForSubmission:!1,hash:"1fb7d9e280708a190a90c3b352c93d45",slug:"landscape-reclamation-rising-from-what-s-left",bookSignature:"Luis Loures",coverURL:"https://cdn.intechopen.com/books/images_new/8295.jpg",editedByType:"Edited by",editors:[{id:"108118",title:"Dr.",name:"Luis",surname:"Loures",slug:"luis-loures",fullName:"Luis Loures"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"5962",title:"Estuary",subtitle:null,isOpenForSubmission:!1,hash:"43058846a64b270e9167d478e966161a",slug:"estuary",bookSignature:"William Froneman",coverURL:"https://cdn.intechopen.com/books/images_new/5962.jpg",editedByType:"Edited by",editors:[{id:"109336",title:"Prof.",name:"William",surname:"Froneman",slug:"william-froneman",fullName:"William Froneman"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"314",title:"Regenerative Medicine and Tissue Engineering",subtitle:"Cells and Biomaterials",isOpenForSubmission:!1,hash:"bb67e80e480c86bb8315458012d65686",slug:"regenerative-medicine-and-tissue-engineering-cells-and-biomaterials",bookSignature:"Daniel Eberli",coverURL:"https://cdn.intechopen.com/books/images_new/314.jpg",editedByType:"Edited by",editors:[{id:"6495",title:"Dr.",name:"Daniel",surname:"Eberli",slug:"daniel-eberli",fullName:"Daniel Eberli"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"48911",title:"Surface Energy and Wetting in Island Films",doi:"10.5772/60900",slug:"surface-energy-and-wetting-in-island-films",body:'Surface energy is one of the most important characteristics of condensed matter. While methods available for the liquid phase enable to determine reliably not only the value but also the temperature dependence of surface energy [1–3], for the solid phase the accuracy of existing methods, as a rule, does not allow to trace its temperature dependence [4, 5]. Therefore, the following approach is justified: what information can be obtained about surface energy of the condensed matters on studies of various properties and processes in small size samples [6–9]. This article considers mainly the investigations of temperature and size dependence of surface energy of condensed matter based on the analysis of surface phenomena and phase transitions in nano-sized systems.
Wetting of solid surfaces with a liquid as well as spreading of a liquid over solid surfaces as a manifestation of interaction between the solid and liquid phases is one of the universal phenomena and covers a wide variety of both fundamental and technological processes. Despite their crucial importance, these processes are still unclear [1, 2, 10]. Therefore, this paper focuses on effects of wetting in nanodispersed systems and considers various physical and chemical factors affecting it. Such statement of the problems seems actual since these details are important to describe a wide range of processes and phenomena, whereas the available data are disembodies and often ambiguous or even lacking.
In the framework of the Gibbs thermodynamics of heterophase systems, the size dependence of surface energy is due to the curvature of the phase interface. The Gibbs method applied to interfaces with a small curvature radius was first developed by Tolman [11], who derived the equation relating the surface energy σ of a spherical particle with its radius
where δ is the difference between the radii of equimolecular surface and surface of tension. Since the function δ = δ(
For particles with
In this approach the parameter α = 2δ∞ has a definite physical meaning as a width of the respective phase interface for any condensed phases. Character of the dependence σ(
Calculations of δ∞ for plane liquid–vapor interfaces made by statistical methods [12] has shown that the quantity δ∞ > 0 and has a value of approximately a few tenth of nanometer (e.g., according to [12] for argon at 90 K δ∞ = 0.36 nm). Further research with use of a computer simulation [13–17], electron theory of surface energy of metals [18, 19], the thermodynamic perturbation theory [20, 21] is consistent with the results in terms of the type of the dependence σ(
Qualitatively, the decrease in the surface energy of small particles can be explained as follows. For the condensed phase being in equilibrium with its own vapor, the interface surface energy at first approximation is proportional to the difference between the number of atoms (molecules) per unit volume of the condensed and vapor phases. With decreasing particle size of the condensed phase vapor pressure increases, and, consequently, its density increases, which causes decrease of the surface energy of the particle – saturated vapor interface approximately in inverse proportion to the particle radius.
In this way, theoretical studies suggest the existence of the size dependence of surface energy in the nanodispersed systems. According to estimates made using different methods, dependencies of σ on size for particles and films are manifested as a monotone decrease with decreasing size starting from a radius of less than 20 nm for particles and a thickness of < 5 nm for films.
Experimental determination of surface energy of solid bodies is a challenging task. Experimental methods available to scientists today offer the measurement of values of surface energy of liquid-phase matters with a reasonable degree of accuracy and in a broad temperature band, which is not the case for the crystalline phase. Known experimental methods for the determination of the surface energy for the crystalline phase are limited, and, as a rule, have a very narrow range of pre-melting temperatures and provide precision of not more than 10–20% [4]. This is largely due to the fact that surface energy is not a directly measurable value, but in most cases it is estimated as an adjustable parameter in various processes such as, for example, wetting, spreading, melting, crystallization, dissolution, analysis of high-temperature creep, electronic work function, etc. Among the best-known methods are the following: the crystal cleavage method, the dispersed powder dissolution method, the “neutral” droplet method, the multiphase equilibrium method, the growth and evaporation steps method, the “healing” scratch method, and, finally, the zero creep method [4]. Surface energy may also be evaluated by the measurement of electronic work function [18, 19]. However, the analysis of these methods shows that they are not applicable to the measurement of surface energies of small particles.
Surface energy of small particles can be determined by kinetics of evaporation in vacuum at a constant temperature [6]. The method is based on the concepts of the molecular-kinetic theory that supposes that the rate of evaporation from a unit of free surface in vacuum is defined by the expression
where
(va is atomic volume). The evaporation rate will be equal to
For an array of particles on the substrate it is more practicable to measure not the evaporation rate
where
According to (5) and (6), knowing the temperature, particle size reduction rate
Electron microscope investigation of the kinetics of particle evaporation was later used to register the melting temperature of small crystalline Au particles by breaks in dependencies
This method was used to determine the surface energy of small particles in Bi, Pb, and Au island films [8, 9]. The sample film was heated in the electron microscope by electron beam up to the onset temperatures of evaporation. The temperature and, hence, evaporation rate was controlled with beam density. The particles radius variation rate ∆
Where
Tabular data are available for the function
Figure 1а presents an example of a series of successive micrographs of Bi island films obtained in the process of their evaporation with the time interval of 15 s, and Figure 1b, c present the results of analysis of evaporation of Au island films. These data were used to find values of ∆
Values of surface energies σ for Au, Pb, and Bi found as a result of the preceding experiments are presented in Table 1, which also presents available literature data for σ at similar temperatures. Comparison of values of σ obtained by kinetics of evaporation of small particles with available data for bulk samples shows their satisfactory fit.
Electron micrographs of successive stages of evaporation of Bi island films on amorphous Si films (а); change of particle size in the process of evaporation (temperatures are given in the charts) (b), and relations of evaporation rate to reciprocal size of particles for gold island films on carbon substrates (c)
Ме | \n\t\t\t\n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t||
\n\t\t\t\t | \n\t\t\tσ, mJ/m2\n\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t\tσ, mJ/m2\n\t\t\t | \n\t\t|
Au | \n\t\t\t1245 | \n\t\t\t1410±20 | \n\t\t\t1240 | \n\t\t\t1410 [5] | \n\t\t
1260 | \n\t\t\t1430 | \n\t\t\t1176–1306 | \n\t\t\t1390±80 [5] | \n\t\t|
1310 | \n\t\t\t1320±100 | \n\t\t\t1297 | \n\t\t\t1137 [6] | \n\t\t|
1350 | \n\t\t\t1230±100 | \n\t\t\t1348 | \n\t\t\t1135 [6] | \n\t\t|
1510 | \n\t\t\t1160 | \n\t\t\t\n\t\t\t | \n\t\t | |
Pb | \n\t\t\t670 | \n\t\t\t385 | \n\t\t\t557–589 | \n\t\t\t560 [5] | \n\t\t
720 | \n\t\t\t484 | \n\t\t\t735 | \n\t\t\t438 [7] | \n\t\t|
740 | \n\t\t\t452 | \n\t\t\t730 | \n\t\t\t439 [7] | \n\t\t|
750 | \n\t\t\t450 | \n\t\t\t748 | \n\t\t\t436 [7] | \n\t\t|
770 | \n\t\t\t447 | \n\t\t\t\n\t\t\t | \n\t\t | |
Bi | \n\t\t\t650 | \n\t\t\t386 | \n\t\t\t509–518 | \n\t\t\t501 [5] | \n\t\t
Comparison of surface energy values for Au, Pb, and Bi [8]
Available experimental data, for example, [8, 9, 24, 25], offer contradictory conclusions regarding the sign of the size dependence of the surface energy of small particles.
The preceding paragraph demonstrates that the surface energy of small particles can be directly determined using the kinetics of their evaporation in vacuum. Table 1 presents the results of such experiments for nanoparticles over 20 nm in size. At the same time, the kinetics of evaporation of Pb and Au nanoparticles with the size below 20 nm both in liquid and crystalline state was investigated in works [6, 7]. The authors of these studies used these results to test the applicability of the Kelvin equation (3) and to estimate values of σ at temperatures at which the evaporation of particles is observed. However, the authors [6, 7] did not analyze the dependence of particle evaporation rates on particle size. Such analysis was offered by the authors in [8, 9], where they demonstrate that for particles with a size of less than 10 nm their surface energy decreases. Figure 2а presents an example of the plot of
Change of the radius of Pb particles in the process of evaporation (a) and the plot of their evaporation rate against size on the coordinate “ln│
It is evident that at sizes of particles less than 10 nm significant deviation of the preceding relationship from linear is observed, which in accordance to (5) is an evidence of decreasing σ. Values of σ calculated using expression (5) are presented in Figure 3 (Curve 5), which also shows calculation data of the relation σ(
The plot of surface energy against microparticles size: a – Au (1 – calculation using the Tolman equation at
Comparison of these dependencies produces qualitatively the same result, that is, the surface energy of small particles decreases with decrease of their size, but nanoparticles evaporation experiments suggest a stronger relationship σ(
It is common knowledge that melting temperature of small particles, thin metal, and alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of thermodynamics, there exist several models to describe the size dependence of melting temperature of small particles [27]; however, as the quantitative analysis of experimental data shows, the triple point model proves to be the most feasible. Within the framework of this model the problem of the melting temperature of the small particle was first solved by Pavlov [37], who obtained expression for the size dependence of melting temperature
where
where ∆Ω0 =
It follows from (9) that using the experimental relation
Considering the preceding, we calculated values of surface energies for a number of metals (In, Sn, Bi, Pb, Al, Au) in crystalline state over the temperature interval of (0.6–1)
Surface energy temperature dependence for different metals according to the TR(R) data [
It is evident that there is a common tendency observed for all of the preceding metals manifested in the fact that the values of σ
The nonlinear increment effect │∂σ
Information on values of surface energy and interfacial energy of contacting phases can be obtained when studying wetting in solid–liquid systems. Analysis of known methods for the determination of the wetting contact angles θ shows that the use of traditional methods [1, 40] for studying wetting in ultradispersed systems is quite limited. In view of these, new methods [41, 42] were developed that allowed to investigate wetting in ultradispersed systems with different types of contact interaction (i.e., applicable both at θ < 90°, and for θ > 90°), with typical phase size changing over a broad range.
Test samples were island films of various metals condensed in vacuum by vapor–liquid method on solid substrates, which, as a rule, were prepared using vacuum condensation as well [9, 42–44]. The substance substrate was deposited on the NaCl (or KCl) cleavages in a vacuum of 10-7–10-9 mm Hg. After that the investigated metal was condensed at a substrate temperature that ensured condensation of the metal into liquid phase. The obtained films were cooled in vacuum to room temperature and the crystallized particles were further analyzed using the methods of optical, scanning, and transmission electron microscopy. According to the estimates and data of experimental research [42–44] (Figure 5) contact angle measurement error due to changing droplet volume during its solidification on the substrate is not more than 2°. In this way one can discard the variation of the angle during crystallization of liquid droplets and relate the values of θ found for crystallized particles to values of the contact angles of liquid droplets at the temperature of their formation.
Electron microscope images of crystalline (a) and liquid (b) lead particles on a carbon substrate and a schematic representation of a liquid droplet on a solid substrate (c)
In the case when the gravity effect can be disregarded, the shape of small droplets is a segment of a sphere (estimations show that this is knowingly true for metals with particle size below 105 nm). To find the angle θ it is sufficient to measure any two of the three quantities that define droplets on the substrate: the radius of droplet surface curvature
The methods suggested in [41, 42] differ in approaches to measure geometric parameters of droplets. The most frequently used cleavage and convolution methods are based on measurement of the said parameters during direct observation of droplet profiles with an optical or electron microscope [41, 42]. In this case, the contact angle is determined from the relations
The developed complex of methods [41, 42] makes it possible to investigate the wetting of surfaces with small droplets, with the size of the latter ranging within 3–105 nm.
Wetting in the liquid–solid system is defined by the equilibrium contact angle θ, which is related to surface energies of contact phases with Young’s equation
where the indices
Consider, following [42, 43, 45], a small droplet of liquid on a flat solid surface. The total free energy of the system
where S is the interfacial area.
In accordance with existing concepts [11, 45] the surface energy σl is viewed as dependent on the average surface curvature C at a given point
For spherical surface (
When finding equilibrium conditions, one should take account of the size dependence of the interfacial energy of droplet – substrate boundary σul. It would be natural to consider this dependence as a relation not to the radius of the surface curvature
Expressions (12) and (13) apply at 1/
Due to the axiality of the problem, it can be solved using polar coordinates with their origin in the center of the circle of the wetted perimeter and the vertical axis
The equilibrium shape of the droplet is found by minimizing the functional (11), which, with regard to relations for droplet volume and areas of its boundary surfaces, is written as follows:
The summand (σ
Functional variation (14) in δ
The integration constant in (15) is equal to zero from the equal-zero condition of one of the non-integral summands δF at the point
which solution by separation of variables gives equilibrium shape of the droplet surface in the form of a sphere truncated by plane
The sphere radius satisfies the relation
which shows that the undetermined Lagrange multiplier p is nothing, but the Laplace pressure adjusted for the dependence σ(
The wetting angle θ can be found from the boundary condition or, since function
By setting the derivative
Equation (17), naturally, is different from Young’s equation (10) by presence of summands containing surface energy derivatives with respect to size.
By using expressions (12) and (13) for σ
Naturally, in the extreme case at σ → σ∞ (α/
The size effect in wetting of the flat surface of the solid substrate with small metal droplets was first found for vacuum-condensed island tin and indium on an amorphous carbon substrate [42–44]. A combination of optical and electron microscopy [41, 42] allowed to determine wetting contact angles over the range of particles of 1–104 nm. According to measurements using optical microscopy the contact angle in the Sn/C system for micron-sized droplets is constant and makes 151°±2°, which fact agrees with the known data for the tin-carbon system. For measurement of contact angle in islands of smaller size we applied the methods of convolution and photometric analysis of electron microscope pictures.
The results of measurement of θ for tin on carbon substrate are presented in Figure 6а, which demonstrates that for big particles (
The plots of the contact angle against the radius of particles of tin (a), bismuth (b), and led (c) on a carbon substrate (O – data using convolution method, ● – using photometric measurement of electron microscope pictures) [
The preceding research was followed later by the study of wetting in the systems of “island metal (Bi, Pb, Au) film–amorphous carbon film” and “Pb–amorphous silicon film” depending on the size of particles [9, 42–44]. For all investigated systems it was obtained that with particle sizes
Influence of sample preparation conditions on the contact angles of microparticles in the gold–carbon system was discussed in detail in [50]. It showed that the amount of pressure of residual gases during the preparation of gold island films has no effect on the values of surface energies corresponding to the bulk state, though it has a slight impact on their size dependence.
The results of the study of wetting obtained [9, 42–44] and presented in Figure 6 are of separate interest, in particular, for some practical applications (e.g., the formation of ordered nanostructures by film melting [51–53]), but at the same time allow to obtain new physical information regarding properties of microparticles. Thus, using the experimental relations θ(R) and σ
For analysis of results of the size effect of wetting in island films expression (18) was used, from which, using the relation θ(R) at known quantities of the parameter α and the value of the surface energy σu, the value of the interfacial energy of the microparticle–substrate boundary and its size dependence were found. The parameter α can be found from data on the kinetics of evaporation of small particles [8]. It may be evaluated using the relation α ≈ 0.916
Using these data authors of work [45] found values of σul and the parameter β, which are presented for the investigated metal-carbon systems in Table 2.
The parameters α and β are positive, which is an evidence of decreasing surface energy of microparticles and interfacial energy at the substrate boundary with a decrease of the radius. Values of α approximately correspond to the thickness of the surface layer at the liquid–vacuum boundary. The value β, which defines the width of the transition zone between the liquid particle and the substrate and depends on the nature of contacting phases, is 2–4 times as big as α.
\n\t\t\t\t | \n\t\t\t\n\t\t\t\t \n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t\t\n\t\t\t\t \n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t|
Calculated | \n\t\t\tExperiment [8] | \n\t\t|||||
Au | \n\t\t\t1130 | \n\t\t\t0.24 | \n\t\t\t0.23 | \n\t\t\t955 | \n\t\t\t1.0 | \n\t\t\t138.4 | \n\t\t
Sn | \n\t\t\t531 | \n\t\t\t0.28 | \n\t\t\t- | \n\t\t\t574 | \n\t\t\t0.53 | \n\t\t\t152.4 | \n\t\t
Pb | \n\t\t\t450 | \n\t\t\t0.29 | \n\t\t\t0.27 | \n\t\t\t463 | \n\t\t\t0.91 | \n\t\t\t140.9 | \n\t\t
Bi | \n\t\t\t376 | \n\t\t\t0.30 | \n\t\t\t- | \n\t\t\t407 | \n\t\t\t0.5 | \n\t\t\t141.0 | \n\t\t
In | \n\t\t\t559 | \n\t\t\t0.27 | \n\t\t\t- | \n\t\t\t566 | \n\t\t\t0.55 | \n\t\t\t143 | \n\t\t
The observed reduction of the contact angle θ with decreasing radius of the droplet is accounted for by the size dependence σ
At the same time, as a result of the small size of droplets and increased diffusion coefficients in nanodispersed systems [57–59], the wetting perimeter under the action of surface tension forces may experience irreversible changes, which may be registered with electron microscopy as circular traces on the substrate left after evaporated droplets. In addition, the plot of the radius of evaporating droplet against time at constant temperature, as a rule, has periodic deviations of experimental points from the continuous curve. Works dedicated to direct measurement of the wetting contact angle also demonstrate fluctuations ∆θ ≈ 10–15°, while the precision of the convolution and photometry methods makes 3–5° [41, 42]. In both cases these deviations may be accounted for by wetting hysteresis. This phenomenon consists in fixation of the wetting perimeter, which under certain conditions, for example, during evaporation, significantly changes the behavior of the liquid droplet. Work [60] examines the reasons causing this effect in microdroplets, it analyses the effect of wetting hysteresis on parameters of the droplet–substrate system.
A number of works were concerned with wetting hysteresis, for example [46, 61], and the commonest causes of this effect are considered to be microroughness and inhomogeneity of the substrate. However, many assumptions underlying these works, for example, the roughness height of ~ 1 µm cannot be applied to microdroplets. In several systems fixation of the wetting perimeter is achieved by partial mutual dissolution of solid and liquid phases. Nevertheless, hysteresis may be as well observed for systems with minor mutual solubility, such as Au/C. Some authors noted that at high temperatures under the action of liquid surface tension forces, the substrate may be subject to inelastic deformation. In this case the triple contact area develops a prominent welt. Comparison of different mechanisms of mass transfer at small (~10-8 m) distances implies a conclusion about the defining role of surface diffusion. As follows from estimations made in work [60] characteristic time of deformation in the Au/C systems makes about 0.1 s. Since the time of condensation of films is about 102 s, in the process of droplet growth the welt has enough time to form even with quite frequent jumps of the wetting perimeter, that is, the droplet creates substrate roughness itself.
The values of the contact angles corresponding to perimeter breakdown with changing volume of the droplet were received [60] from the condition of the system’s minimum free energy taking into account elastic deformations of the substrate and their partial relaxation in the triple contact area trough surface diffusion. According to [60] the contribution of relaxed elastic deformation energy reaches significant values, for example, for the Au/C system the wetting hysteresis, that is, difference between advancing θ
In this way, with changes of the volume of the droplet, for example, during evaporation, its wetting perimeter will be fixed until the contact angle is reduced to the critical value θ
Considerable amount of Laplace pressure in very small (less than 10 nm) droplets results in elastic deformation being able to relax not only in the triple contact area, but also directly under the droplet. In this case, along with the welt along the wetted perimeter dimples may form under the droplet, which causes higher hysteresis value, with the difference θ0 – θ
Among the factors that define wetting in dispersed metal–metal systems, in addition to size effect of wetting, one can single out the following: discontinuity of intermediate film and resulting heterogeneity of the substrate, mutual solubility of components in each other, formation of chemical compounds at the solid and liquid phase interface, and oxidation of the metal film. Therefore, wetting processes in ultradispersed systems are defined by a number of parameters, which are quite inseparable.
A case study research of the influence of fineness of the solid phase on the contact angle is presented in work [62], which investigated wetting of thin films of different thickness deposited on bulk substrate. It showed that in the melt (Ag, Cu, Sn, Pb)–metal film (Mo, V, Fe)–nonmetal substrate (sapphire, quartz, graphite) system the contact angle is subject to linear variation within the range of values corresponding to wetting of clean substrate (at thickness of film
Wetting in triple systems Pb/Ni/[NaCl, Si, GaAs], Sn/[C, Al, Al2O3]/KCl, Bi/Fe/KCl as a function of metal film thickness (2 nm < t < 200 nm) was investigated in [9, 42–44, 63]. These systems substantially differ by interaction behaviors: Sn–C, Sn–Al2O3, Bi–Fe – complete insolubility in solid and liquid states; Sn–Al – solubility 0.5 wt. % Al in Sn; and Pb–Ni – up to 4 wt. % Ni in Pb. Test samples were prepared as follows. Variable thickness intermediate film (Al, Fe, Ni, C, Al2O3) was condensed on monocrystal substrates (KCl, NaCl, Si, GaAs) in a vacuum of 10-6–10-8 mm Hg. The studied metal (Sn, Bi, Pb) was condensed on this film by the vapor–liquid mechanism without deterioration in vacuum. The substrate temperature during condensation was 653 K for Pb, 523 K for Sn, and 560 K for Bi.
In all investigated systems degree of wetting strongly depends on intermediate film thickness, though the range of thicknesses, on which change of θ occurs is different. The common feature for the analyzed systems is that the contact angle is defined at a fist approximation by heterogeneity of the wetted surface and changes within extreme limits corresponding to wetting of clean substrate (
Main types of dependencies
Wetting angle against thickness of intermediary film for systems Sn/C/KCl (а); Bi/Fe/KCl (1), Sn/Al/KCl (2), Pb/Ni/NaCl (3) (b); and Pb/Ni/GaAs (c) [9, 42–44, 63]
It should be noted that plots presented in Figure 7 are simplest and influence other factors, for example, interaction with the residual atmosphere (Sn/Al/KCl [42]) may cause a more complex variation of the contact angle with changing thickness of the intermediary film.
When interpreting results of wetting in three-component systems liquid–thin film–bulk substrate, it is difficult to separate effects due to film thickness itself and the influence of bulk substrate. Therefore, it was considered expedient to investigate wetting of thin free films depending on their thickness [42–44]. The obtained results did not make it possible to find size dependence of surface energies of thin carbon films. However, these results are of interest in themselves because it is possible for highly dispersed systems, when liquid particles wet not the surface of bulk solid bodies, but that of free thin films. In this case, specific effects connected to deformation of film under the liquid droplet are observed.
A theory of half-space wetting was constructed in [55]. It suggests that the droplet deforms the region near the line of contact of three phases to form a welt. In case of thin films deformation may be significant that makes it possible to find it by experiment. Therefore, in the following text we give an outline theoretical analysis of wetting of thin free films on assumption of constant surface energies σ
According to [42–44, 54], the equilibrium characteristic of the system comprised of free elastically deformed film with the thickness
where
Schematic diagram of a liquid droplet on a thin elastic film
The function ψ is equal to the sum of contributions of elastic energies of pure bending ψ1 and longitudinal extension of the film ψ2, written, according to [66], with regard to axiality in the following form:
where ν is Poisson’s ratio,
The shape of the free surface of liquid is found by variation of the functional
Variation of
The boundary conditions for equations (21) and (22) follow from non-integral summands of the variation δ
The condition of equilibrium value of the contact angle θ may be determined by variation of functional (19) with δ
Another relation connecting ϕ and θ follows from equation (21) and boundary conditions at the point
As it is seen from (21) and (23), the contact angle depends on film deformation and is determined by the jump of the third derivative ζ(
Features of deformation for small and big film deflections, that is, with prevailing bending and tensile deformation, respectively, were evaluated in [54]. In the case when the maximum film deflection δ is less than its thickness, equations (21) and (22) become linear, and their solution yields the following expression
which relates Young’s module to parameters measurable by experiment. At greater film bends (δ >
In the case of a very thin film
As already noted, experimental research of wetting of free amorphous carbon films of different thickness with island vacuum condensates aimed at obtaining data on surface energy of films was made in [42–44]. The research used test metals (In, Sn, Pb), which are inert to carbon films and forming with carbon films contact angles of 140°–150°.
Test samples were prepared by evaporation and condensation of carbon and metal in a vacuum of 10–6 mm Hg on carbon films of different thickness located on copper grids with the mesh size of 60 µm. During the experiment the temperature was kept above the melting point for the relevant metal. Carbon film thickness varied on the range of 4–30 nm, and the size of liquid metal particles was 30–500 nm and was limited, on the one hand, by the need to exclude size effect due to dispersity of the liquid phase, and by strength of carbon films on the other.
Electron microscope examination of profiles of crystallized metal droplets (Figure 10) revealed substantial difference in the shape of the interphase boundary droplet–substrate for microparticles condensed on free films and films on a solid surface. The difference is that when the film is thin enough it gets deformed by the droplet (Figure 10), while in particles condensed on a solid surface, liquid–substrate interface remained flat.
For the analyzed systems it was determined that at
The obtained results were interpreted in [42–44] within the framework of wetting of elastically deformable carbon films [54], whose basic concepts were given earlier. As follows from relations (24) and (25), at
Micrographs of tin droplets on free carbon films with the thickness of 20 (a) и 10 (b) nm
Experimental relations δ(
Dependence of the angle of wetting of free carbon films with tin (a), lead (b), and indium (c) on their thickness [
It follows from the same charts that
The relation
The results of theoretical consideration for very thin films were used to evaluate the surface energy of carbon films. As follows from (26) and (10), in the case when deformation energy in comparison with surface ones may be neglected, the quantity σ
The range of free films thickness on which this relation is satisfied is not attainable experimentally (
Variation of θ with thickness of free films as a result of theoretically predicted size dependence of their surface energy is about an order of magnitude smaller than the change in the contact angle due to deformation. Hence, the studies did not allow to trace the dependence of σ(
It is known that above the melting temperature the surface energy σl decreases linearly with increase of temperature. However, existing knowledge and experimental data on temperature dependence of surface energy of supercooled liquids are ambiguous [67]. According to [67] at significant supercooling values, one may expect inversion of the temperature dependence σ
The temperature dependence of the surface energy of metals (Ga, In, Sn, Bi, Pb) [68] has been studied only in the rage of small supercoolings down to 0.1
Measurement of surface energy of supercooled melts is hard to make because considerable supercoolings are normally obtained in microvolumes, and traditional methods to determine σl require large amount of melt [1, 40]. However, temperature dependence of surface energy on at
Contact pairs being island films of tin, indium, bismuth, and copper on amorphous carbon substrates and indium on aluminum substrate were investigated in [42, 43, 72]. The test samples were prepared by condensation in a vacuum of 5⋅10–6–2⋅10–8 mm Hg on the circular substrate with temperature gradient (200–900 K) set along it. As a result, condensation to equilibrium or supercooled phase with the formation of microdroplets occurred according to the condensation diagram [73–76]. The obtained samples were cooled to room temperature and then wetting contact angles on crystallized droplets condensed at different substrate temperatures were measured. Due to wetting hysteresis, which occurs even on an absolutely smooth and uniform surface because of deformation of the substrate in the region of triple contact [60], the droplet base radius remains constant during cooling. The contract angles were measured on electron microscope pictures of droplet profiles (Figure 13) and averaged for 10–20 droplets. As long as condensation takes place on a substrate with temperature gradient, the relation θ(
Micrographs of tin particles condensed in a vacuum of 5⋅10-6 mm Hg at temperatures 400 K (a), 570 K (b), and 730 K (c) [
The results of measurement of wetting angles in the Sn/C and In/C systems [72] are presented in Figure 14a, b. The obtained dependencies are characterized by the maximum at temperatures 550 and 500 K for tin and indium, respectively. Below
Temperature dependencies of wetting for island condensates of metals on different substrates. On the left – Sn/C (a) (base substrate: O – NaCl; ● – Al2O3; vacuum 5 10-6 mm Hg) and In/C (b), on the right – Bi/C (c), and In/Al (d) [
In the Bi/C system temperature dependence of wetting, similarly to the In/C and Sn/C systems considered earlier, is nonmonotonic and is characterized by considerable decrease of the contact angle when approaching the temperature of maximum supercooling (Figure 14c). However, the maximum value of θ for bismuth is achieved at
Nonmonotonic dependence of the contact angle on temperature is also a feature of In/Al system (Figure 14d). This is similar to the relation θ(
For the Cu/C system wetting temperature dependence does not have any peculiarities: on the interval 1200 <
Observed changes of the contact angle in the supercooled region, as noted in [42, 43, 72], is probably stipulated by abnormal behavior of either liquid metal surface energy or interface energy of the metal–carbon boundary. If σ
The plots of liquid phase surface energy [
Among the reasons causing such a significant decrease in interfacial energy works [42, 43, 72] cite adsorption of gaseous impurities, which value increases with decrease of temperature or inversion of the surface energy of metal in supercooled state. However, considering the fact that for a number of analyzed metals (In, Sn, Bi) inversion of wetting temperature dependence occurs within approximately the same temperature range, while in the Cu/C system at high temperature it was not found at all, one should probably consider the adsorption of impurities from residual gases that grows at such temperatures crucial and causing decrease of interfacial energy on the carbon substrate boundary with increased supercooling, and hence, better wetting observed experimentally. The increase of temperature of the substrate above 500–600 K increases σ
The experimental relations θ(
The samples were prepared using the technique described earlier [72] at the pressure of residual gases of 10–7–10–9 mm Hg. A mass spectrometer was employed to control residual atmosphere, and its content was changed by leaking gas into the unit pumped to a pressure of 10–9 mm Hg. The wetting contact angles were measured on micrographs of particle profiles on rolled-up (Figure 16) or inclined (Figure 17) spots of carbon film (convolution and angular observation methods [41, 42]); the quantity θ for a fixed temperature was found by averaging the contact angle values for 10–20 microparticles.
Micrographs of crystallized tin droplets condensed in a vacuum of 2⋅10–8 mm Hg on carbon substrates at temperatures 350 K (a), 410 K (b), and 500 K (c) [
The results of measurement of θ(
At substrate temperatures
It is worth noting that for a supercooled state of tin decrease of temperature in all cases leads to a decrease of the contact angles. At the pressure of residual gases of 10–8 mm Hg improvement of wetting gets quite significant and makes ∆θ ≈ 50°. Variation of wetting with temperature is well illustrated by micrographs of particle profiles (Figure 16) and inclined spots of film near the temperature of maximum supercooling (Figure 17). In this case, as could be seen from the chart (Figure 18, Curve 3) and micrographs (Figs. 16, 17), transition from nonwetting (θ > 90°, i.e., σ
Micrographs of tin island film condensed in a vacuum of 2⋅10–8 mm Hg on a carbon substrate at the temperature of 315 K (θ = 82°)
Temperature dependence of the contact angle of wetting of carbon substrates with tin islands prepared under different pressure of residual gases: 1 – 5⋅10–6 mm Hg [
The analysis of the outlined results allows us to assume that the supercooled state of the metal itself is not the main cause of sharp improvement of wetting with decrease of temperature for fusible metals. This is also suggested by the fact that inversion of wetting temperature dependence is observed both above (Sn/C, In/C, In/Al) and below (Bi/C) of melting point, while for the Cu/C system there is no inversion at all. However, this conclusion may not be considered final since for the Cu/C system the relation θ(
As it has been shown earlier using the contact systems (Sn/C, In/C, Bi/C, Pb/C, Au/C, Pb/Si) as a case study, wetting of amorphous neutral substrates with liquid metals is improving with decrease of the size of microdroplets [9, 42–44]. This effect is a result of decrease in surface energy of metal droplets σ
Such investigations for island tin films on amorphous carbon substrate were made in [72, 78]. The results of measurement of contact angles in the Sn/C system at temperatures 400 K and 315 K are presented in Figure 19, which shows that for supercooled droplets as well as for equilibrium ones (see Figure 6a) the contact angle decreases with decrease of droplets size. However, numerical values of the contact angles for droplets of equal size turn out to be different, and the relation θ(
The plot of wetting angle against the radius of supercooled (1 – Т = 315 K, 2 – T = 400 K [
Comparison with known results regarding the size effect of wetting at
The experimental data and their analysis outlined herein show that the application of island vacuum condensates to study surface energy and wetting allowed to obtain a number of general results of crucial importance for physics and chemistry of surface phenomena.
Quantitative data of surface energies of solid Au, Pb, and Bi nanoparticles and parameters that define size dependence of surface energy of small particles have been obtained from the investigations of evaporation processes in condensed films.
Options for measuring surface energy in the solid phase and its temperature dependence are discussed and are based on the data regarding the decrease of melting temperature of small metal particles. Temperature dependencies of surface energy for In, Sn, Bi, Pb, Al, Au, and Pt have been calculated on the basis of the preceding consideration. The significant reduction of surface energy for all metals studied when approaching melting temperature has been shown.
The detailed investigation and theoretical description of the size effect of wetting, which consists in the decrease of the wetting angle with the decrease of particles size, have been provided. Size dependencies of wetting angle in In/C, Sn/C, Bi/C, Pb/C, Pb/Si, and Au/C have been obtained for equilibrium and supercooled (Sn/C) liquid microdroplets. On the basis of these studies, size dependencies of interfacial energy of In/C, Sn/C, Bi/C, Pb/C, Au/C couples were obtained.
Experimental data and theoretical description of the effect of thickness of free carbon film on wetting angle have been obtained for In/C, Sn/C, and Pb/C couples. These studies enabled to determine the surface energy of thin carbon films, which makes σu = 120±30 mJ/m2.
Temperature dependencies of contact angle in In/C, Sn/C, Bi/C, In/Al, and Cu/C couples have been obtained for equilibrium and supercooled liquid microdroplets.
Cells are pre-programmed to carry out certain functions – this represents their potential. At the same time, they are sensitive to physical or biological changes in their surrounding environment and will modify their function accordingly – and this becomes their constantly changing actuality. Cells
In the early days of cell culture in the 1950’s the focus was to get cells to propagate rapidly and reliably in flasks, facilitated by the destruction of their ECM. With the realisation that cells grown in 3D conditions are more mimetic of human cell biology, the focus has changed away from getting the cells to propagate to getting the cells to function (physiologically). These two conditions mark the extremes in a spectrum of cellular activity [1].
\nBearing this in mind, there are a number of factors that should be considered when changing this focus and transitioning from the classical 2D cell culture to 3D cell culture. These factors not only indicate which 3D culture systems could be expected to be advantageous over others but also indicate which should generate data that is more representative of the
Perhaps, the most significant difference between 2D and 3D culture is the establishment of longer diffusion gradients for the majority of cells and thus the cells will experience significantly different levels of oxygen, CO₂, nutrients and waste products.
\nRelated to the diffusion gradients is the amounts of various compounds in the environment around cells: cells in 2D are typically exposed to levels of for example O₂ and glucose which are not seen in the intact, healthy organism.
\nAnother very significant difference will be the establishment of channels of communication between cells that are not only juxtapositioned but also further away. In 2D, immortal cells are typically passaged roughly every week (and shorter for faster growing cells). At the end of this cycle, cells are usually treated with enzymes or cocktails (containing trypsin, collagenases or other compounds) that damage proteins protruding from the plasma membrane and which dissolve or fragment the ECM. Similar cocktails may be used to produce cell suspensions from tissue biopsies, or these biopsies may be pressed through a mesh to ‘liberate’ cells. All these treatments release proapoptotic factors, damage cells and have a significant impact on gene expression. Cells will attempt to repair this damage and recover, but need time to do so. So, the final factor to consider is time.
\nWhile there are numerous publications illustrating that 3D cell culture can mimic functionalities of human tissues, perhaps one of the most graphic is shown in \nFigure 1\n where a freshly extirpated human liver biopsy and 29 day old C3A spheroids have been biosynthetically labelled with [35S]-methionine and their proteins extracted and run on high resolution two-dimensional gels (IPG-SDS). Notice that, not only are the proteins expressed in very similar amounts, but also that their post-translationally modifications are very similar.
\n(next page.) Human biopsy tissue (ca. 0.5 mm3) and spheroids (29 day-old, ca. 1 mm3) were biosynthetically labelled for 20 hrs with [35S]-methionine. Some of the proteins are named for reference: ACTB, Actin beta; ALBU, Albumin; ALDH2, Aldehyde dehydrogenase 2; APE, Apolipoprotein E; CCND1, Cyclin D; HSPA8, Heat shock protein 8; HSPH1, Heat shock protein H1; HYOU1, Hypoxia up-regulated protein 1; PSMA5, Proteasome subunit alpha type-5; SAHH, S-adenosyl-L-homocysteine hydrolase; TUBB5, Tubulin beta chain 5; VCL, Vinculin; YWHAH, 14–3-3 protein eta.
For many purposes in medical research, what is needed is a model system that accurately reflects what happens in the living organism - more often than not a human being – to shed light on many different processes, whether normal physiology or what goes wrong in disease, or infections by microorganisms, or the effects of compounds during treatment or poisoning.
\n3D cell culture promises to offer what is needed, but the field is still relatively new and many of the products used are small modifications of existing products that have been available for many years and as such, many have not been ideally suited to the purpose.
\nFor these reasons, when we started to design some equipment specifically designed to support 3D cell culture. In doing so, we used four aims to guide the process. These were:
Use
Allow the cells to do what they want. Do not provide unnecessary compounds and do not stress them in any unphysiological way.
Keep the culture conditions as close to that seen
Keep it simple (both for the cells and the user).
The main requirements that we addressed were: diffusion gradients, shear stress and time.
\nAtmospheric oxygen (21%) provides a partial pressure (pO₂) of about 145 mm Hg (ca. 190 μM) to cells grown in 2D cultures. This is considerably more than the partial pressure of oxygen measured in tissues (11% to 0.1%) which should be considered as normoxic for cell culture [3]. Thus, cells grown in 2D cultures are exposed to unphysiological, hyperoxic conditions.
\nIn the human body cells are usually located within 200 μm of a capillary [4] (corresponding to only 10 to 40 cell layers thick). Because cells are actively consuming oxygen, there will be a diffusion gradient into the cell. This is not problematic in 2D because the cultures are typically only one cell layer thick, but it becomes a challenge in 3D because there the spheroids can become tens or hundreds of cell layers thick. Despite that there may be a preferential transport of oxygen through cells and tissues by hydrophobic channelling within membranes, suggesting that oxygen diffusion within cells and tissues may be faster than through water, there will clearly be a limit [5].
\nIn seminal work, Sutherlands group clearly demonstrated that the pO₂ in the centre of a spheroid fell to 0% when the radius was greater than 250 μm, corresponding quite well with the
A flow of media past a spheroid significantly reduced this zone and had a very significant effect on the oxygenation of the spheroid. This allowed the spheroids to become larger before their cores reached anoxia. The beneficial effect of flow was almost completely negated if the spheroid was resting on a gas impermeable surface (e.g. glass or a gas-impermeable membrane) [6]. Spheroids appear to have a large capacity to adapt and significantly reduce their consumption when the supply of either O₂ or glucose or both is restricted [7, 8, 9].
\nInterestingly, hepatocytes, (which express haemoglobin
Exactly the same arguments apply to CO₂: it has been demonstrated that CO₂ (as HCO3\n−) diffuses through spheroids of many cell types essentially as if the cells are not there [11]. Cells in clusters increase their aerobic respiration and decrease oxidative phosphorylation as they reprogram to a more anabolic based metabolism. This reduces their need for O₂ and their production of CO₂. Although this was first noted by Warburg in relation to cancer [12], it probably more strongly reflects the effects of ‘mis-culture’ of tumour cells in 2D rather than a metabolic style reflective of tumours
Interestingly the rate of glucose diffusivity through spheroids of different cell types has been shown to differ by a factor of up to 4. The diffusion into a spheroid is quite rapid and an equilibrium is established after about 1 hour (single cells reach this equilibrium within a minute) [13]. These differences may be correlated to how tightly connected the cells become. C3A spheroids have been shown to rapidly deplete normoglycaemic media (5.5 mM) of glucose within 8 hours, converting much of it to glycogen. The cells were then able to reconvert the glycogen to glucose and survive for the next 40 (or 64 hrs) hrs until the next media exchange [9].
\nDiffusion gradients will also apply to nutrients and waste products. For example, NH3 is produced by transamination followed by deamination, from biogenic amines and purine and pyrimidine bases. NH3 (as NH4OH) is a smaller and less lipophilic molecule and thus its diffusivity five times slower than CO₂ through cells than through pure water at 37 °C making it more difficult to ‘escape’ [11].
\nThe conclusions are clear for 3D cell culture: without a vasculature, cell clusters should not be too big in order to avoid anoxia (and ensuing necrosis) and should be irrigated on all sides to diminish the depletion zone and accelerate gas, substrate and metabolite exchange.
\nThere is a growing appreciation that the mechanical properties and cell mechanics, play an important role in gene expression and cell development. The concept that is emerging is that cell types which experience shear stress
Thus, in some cases shear stress is positive: see-saw shaking of induced pluripotent stem cell (iPSC) constructs for 17 days promoted cell aggregation, and induced significantly higher expression of chondrogenic-related marker genes than observed in static cultures [15]. A platform rocking at 7 ° with a 3 second cycle results in an average shear stress of about 0.01 Pascal [16]. These shear forces are however distributed unevenly – both spatially and temporally during the motion of the container (bag, or flask) [17]. A similar, ultra-low shear stress is also seen in clinostat cultures. In this case though, the shear stress is distributed essentially homogeneously spatially and temporarily throughout the culture [9].
\nFluid-induced shear stress (ca. 0.02–0.06 Pa) in microfluidic devices
Stirred tank suspension bioreactors and orbital shakers are used widely [21, 22, 23] but both result in significantly higher shear forces (0.3–0.66 Pa and 0.6–1.6 Pa respectively) and are considered to be in the critical/lethal range for mammalian cells [24].
\nSince most cells are found in tissues which experience very little shear stress, equipment that is designed to cultivate cells from these tissues should expose cell clusters to as little shear stress as possible. It is easier to reintroduce shear stress if needed, than to struggle to remove it from a system not designed to be shear stress free.
\nAs mentioned above, enzymatic treatment of tissues or cells in 2D damages both the ECM and surface located proteins (including their modifications). This raises a number of questions.
\nThe first is as to whether this damage can be repaired, i.e. can the 3D cultures recover the metabolic or physiological properties that they exhibited
If the damage cannot be repaired, then the question raised is whether this failure is due to a limitation of the cells used, whether several cell types are needed, whether the procedures used prevent the recovery, or whether it is a true limitation that the performance cannot be replicated
If it can, the next question is how long do cells need to repair this damage?
\nA final question is that if the damage can be repaired, then once the cells have recovered, how stable is the 3D culture, i.e. for how long can the 3D culture be used?
\nThe answer to these questions depends very much on the origin of the cells. For immortal cells, there are now numerous publications suggesting that these cells need to grow as spheroids for at least 2 weeks to recover their
One observation that appears to be true for the majority of cells, irrespective of their origin, is that they grow considerably much slower as spheroids or organoids as they do in 2D cultures. Thus, doubling times in 3D may be as long as every 50 or 100 days rather than the 1 to 2 days seen in 2D [32, 33]. This makes sense: tissues and tumours
Starting with isolated cells in culture, it is necessary therefore to anticipate that the cells need to re-adapt to being in clusters once again. There is a lot that needs to occur in such a readaptation process: for example, isolated cells do not have tight junctions and so their import and export pumps will have mixed: and need to be ‘re-deployed’ to different regions of the plasma membrane once tight junction has been re-established [36]. While this is critically important for most cells, the specialisation of pumps in the liver cells is exquisite and intricate [37]. Redeployment of pumps might not be an active process – the cell after all was not designed to work in 2D cultures. Hence, the cell may have to rely on protein turnover to degrade the misplaced pumps and on membrane delivery processes to establish the pumps on the correct sides of the tight junctions. And there are innumerable other redeployments (changes to the cytoskeleton [1], organelle organisation, gene and protein expression, epigenetic marking [38], post-translational modifications and metabolic reprogramming [8, 9]) to complete.
\nThe take home message here is that researchers have to be much more patient and expect that they will need to maintain 3D cultures for extended periods of time (weeks or months). With this in mind, these extended periods will place a premium on cultures that are highly reproducible and preferably also high yield. Cultures that reach and maintain a dynamic equilibrium for weeks or months will be advantageous in that they will mimic the homeostasis seen in tissues and will provide a large window of utility. Within this window, it will be possible to for example collect multiple samples from the same culture (like collecting biopsies from the same animal at different times) or perform repeated treatment studies [39]. These samples could be used for the same assay at different times or multiple different assays at the same time, or both if there is sufficient biomass available. But the stability of the biological process needs to be documented throughout this window before perturbation experiments can be initiated [32, 40].
\nMaintaining cultures for extended times greatly increases the risk of infections, and thus requires great care. This can be facilitated if all aspects of a 3D culture system have to be considered so that the culture is well protected from external contamination.
\nSo – what does a cell culture system that addresses all of these issues look like?
\nFirst it is a CO₂ incubator. The incubator constructed can maintain a steady temperature both over time and within its volume. The inclusion of a powerful fan to mix the air within the incubator ensures no differences in temperature or gas partial pressures (and speed temperature recovery after the door has been opened). Measurements show that the difference in temperature between the top of the chamber and the bottom are less than 0.2 °C.
\n\n\nFigure 2\n illustrates that the incubator quickly reaches running conditions after about 15 minutes when it is first switched on and that it can maintain a steady temperature and CO₂ % (in the figure, over 12 hrs).
\n% CO₂
When the door is opened, the controlling software switches off the fan, heaters and the UV-C lamp (if active) and closes the CO₂ valve. Closing the door reactivates these functions. \nFigure 3\n illustrates the effect of opening the door wide open (90 °) for respectively either 30 seconds or two minutes showing that running conditions are re-established by about 4 or 6 minutes.
\nThe effect on CO₂ %
Note that the internal temperature in the culture vessel falls by a maximum of only 0.1 °C while the door is open illustrating that the cultures are not exposed to any cold shock which would affect their gene expression.
\nIn order to reduce the diffusion depleted zone to a minimum, we have adopted the clinostat technology. Introduced for cell culture more than 20 years ago, this technology has been used to culture hundreds of different types of cells and tissues (cell lines, stem cells, primary cells) as well as bacteria and viruses and produced some excellent research. The major limitation of the initial equipment was that it was difficult to use (for example the culture chamber could not be opened but had to be accessed via luer lock ports).
\nBasically, a clinostat keeps cell clusters in suspension by rotating the culture vessel in a vertical direction (like a wheel). At the right speed, the uplift caused by the effect of liquid viscosity between the vessel and the clusters is balanced by the effect of gravity (these systems are often referred to as ‘simulated microgravity’ because the clusters appear to float or be maintained in a ‘stationary orbit’ (relative to the culture vessel)). Thus, the incubator that has been built has been equipped with clinostat motors. These have to run very smoothly so that there is no vibration (which would otherwise shake the clusters apart). \nFigure 4\n A) would reveal 50/60 Hz mains ‘noise’ effects while B) would reveal high frequency noise.
\nVariations in the rotational speed of a clinostat motor. (A) Long term variations during 1 second: RPM (± STD) 5.03 ± 0.210; 10.03 ± 0.277; 30.21 ± 0.278; 100.38 ± 0.224. (B) Sort term variations during one thousandth of a second. RPM (± STD) 5.12 ± 0.002; 9.82 ± 0.004; 30.13 ± 0.008; 100.66 ± 0.007.
To retain ‘continuity’ with previously published data, we have maintained the basic geometry of the culture chamber.
\nThe next requirement is to be able to open the culture vessel easily for the purpose of introducing or removing cell clusters, for changing the media, or adding compounds or collecting samples.
\n\n\nFigure 5\n illustrates a culture vessel with a top access port for media exchange, a front access port for collecting individual cell clusters, and front window that can be removed to reveal a petri-dish like 10 mL culture chamber.
\nA culture vessel designed to provide easy access to the culture chamber. (A) Exploded view of parts. (B) Front view showing spheroids in the culture chamber (white spots).
Changing the growth media is illustrated in the video (https://bit.ly/2PkiE9m). The culture chamber is removed from the incubator and the spheroids are allowed to sink to the bottom. The top port plug is removed and 90–95% of the media is sucked away using a sterile syringe and long needle. Fresh media is introduced in the same way, making sure to overfill the growth chamber so that any bubbles are driven into the ‘drip-cup’ around the top port. The plug is then replaced, the drip cup emptied, washed with 70% ethanol for sterility and the culture vessel replaced in the clinostat incubator. The whole procedure takes less than 40 seconds, resulting in minimal stress for the cell clusters (a video of this can be seen on CelVivo’s website). Small samples of the media can be collected at any time using the same approach.
\nIn this design (\nFigure 5\n), the gas exchange membrane has been moved from its ‘cylinder end’ position to a circumferential ‘side’ position whilst still retaining essentially the same area to allow rapid gas exchange between the culture chamber and the humidification chamber. Relocating the gas exchange membrane allows the culture chamber to be illuminated from the back and observed from the front (using the cameras), facilitating inspection of the clusters without disturbing the culture, or even opening the incubator door. This also helps to minimise infection risks.
\nMost incubators are humidified with water trays or tanks, which usually increase the relative humidity close to 100% to prevent cultures from losing water and concentrating the media. This is fortunate because CO₂ normally does not transverse dry membranes very readily. By hydrating the atmosphere, CO₂ can dissolve into the water vapour (giving H2CO3) and then diffuse easily across the membrane [41].
\nUnfortunately, the combination of high humidity and the warm temperatures inside an incubator are strongly conducive to infections and so regular thorough cleaning is necessary to prevent contamination of the cultures.
\nMicrobial infection can be mitigated if the humidification of the incubator chamber can be reduced. For that reason, a culture vessel has been designed that can humidified itself. This permits the incubator to be run in a ‘dry state’ (i.e. with only ambient humidity). Assuming that the air around the incubator contains 40% relative humidity, (at 20 °C and normal pressure), then when this air enters the incubator and is warmed up to 37 °C, its relative humidity will fall to 13.9% making microorganism growth more difficult.
\nThe culture vessel is humidified by placing water beads in a circumferential chamber around the gas exchange membrane and allowing air exchange into this chamber. In use, the hydrated beads release water linearly with time to the atmosphere (1 mL water gives about 1.67 L water vapour) and maintain a very high humidity close to the membrane and facilitating gas exchange (\nFigure 6\n).
\nLoss of water from water beads in a culture vessel in a clinostat incubator at 37 °C.
The circumferential position of the gas exchange membrane facilitates another feature of the culture chamber. Because there is nothing on either planar side of the vessel, it is possible to provide uniform illumination from one side and observe the culture from the other side. Fey
A clinostat incubator, containing 6 culture vessels (one back illuminated).
Even though most modern incubators have a double door, with the inner door made of glass, it is difficult to see the cell clusters clearly often because of poor illumination. The use of an integrated back-light and a camera to inspect the cultures brings yet another advantage: it is not necessary to open the incubator to see the cultures. If these shadow area measurements are repeated over time it becomes possible to follow the growth curve of the clusters. The only manipulation required is to change the media (typically this would be every 2–3 days). If the media is changed for example on a 2, 2 and 3 day (weekly) cycle, then the incubator will need to be opened only 10 times during a 21 day culture. Since a practiced person can change the media within 1 minute each time, this means that the cells need to be out of the incubator for less than 10 minutes in the 21 day period.
\nThus, the construction using illumination and a camera for each cell culture vessel minimises the number of times that the incubator needs to be opened. This in turn further reduces the risk of infection, in addition to the effect gained by running the incubator ‘dry’.
\nAn extra source of illumination has been included on the same side as the camera so that it is possible to see the clusters by direct inspection and not just their silhouettes.
\nAll of the images are displayed on (and can be captured from) a tablet that also serves to regulate the temperature, CO₂ and rpm of the culture vessels (\nFigure 8\n).
\nThe tablet display showing regulation of the rpm and set value (left panel), culture vessel (main panel), clinostat incubator number (A-1, main panel top left), actual rpm (top right), actual temperature and CO₂ (bottom left). The front access port plug can be seen at the bottom right of the culture vessel.
One final step has been taken to reduce the risk of microorganism contamination even further. A UV-C light has been built into the incubator. The UV-C LED source itself is behind the bowl of the incubator but the UV-C light is led out through a fused silica light guide which passes along the shaft of the fan. UV-C capture from the LED was calculated to be 88%. By terminating the light guide in an arrow shape (with angles of 52 and 56 °), the emitted UV-C sweeps the incubator as the fan rotates. Normally, UV-C light reflectance from stainless steel is usually about 5% but this has been increased to about 75% by using a special ePTFE coating. Thus, the UV-C irradiation is reflected in all directions and will reach all surfaces. All clinostat motors are activate during decontamination so that all sides of the culture vessel holder will also be irradiated. The inner surface of the glass door is assumed to be totally absorbing for the UV-C. According to the specifications of the LED lamp, the UV-C light emitted will provide a dose of at least 12 mJ/cm2 everywhere in the incubator after 2 hours. This results in a log4 reduction (99.99% reduction) in viable bacteria. A log6 reduction is normally defined as sterile for medical facilities (and therefore this is classified only as a decontamination).
\nOne easy way to initiate spheroid cultures is to use embryoid body plates (\nFigure 9\n).
\nC3A spheroids at various times.
Here, cells are centrifuged into the bottom of inverted square-based pyramid micro-indentations in microtitre plate wells. Not surprisingly, the spheroids are somewhat squarish immediately after their release from the embryoid body plate and there is quite a lot of loose cells (seen most clearly in the ‘Day 0 and 2’ image in \nFigure 9\n).
\nThese loose cells do not sediment down as quickly as the spheroids and thus are lost during successive media changes. The remaining spheroids become steadily rounder and more robust as they grow. Starting from a single embryoid body plate well, these procedures have been shown to produce large numbers of spheroids (about 1200) similar to those shown in \nFigure 9\n after 21 days (these would normally be cultured in four culture vessels). At this stage, each spheroid contains about 82,300 cells and contains 12.31 μg protein (C3A spheroids). The standard deviation of their diameters is less than 21% (after 21 days in culture) and this approach thus provides large numbers of very reproducible spheroids for further experimentation [39, 43].
\nOnce C3A spheroids have recovered, they reach a metabolic equilibrium, characterised by a constant production of ATP, cholesterol and urea for at least 24 days [32]. During this period, treatment of these spheroids with for example any one of six commonly used drugs (acetaminophen (APAP), amiodarone, diclofenac, metformin, phenformin and valproic acid) causes them to respond (as shown by the increase in ATP production) and then recover to the pre-treatment conditions [43]. This can be repeated multiple times and has been proposed to be useful for assessing repeated-dose drug toxicity [39].
\nThe liver is the primary source of many of the proteins found in the blood. To illustrate just how stable C3A spheroids are, they have been kept alive for 302 days. Even after this length of time C3A spheroids are quite capable of synthesising and post translationally modifying these blood proteins (\nFigure 10\n).
\nProteins secreted from 302 day old C3A spheroids. Some of the proteins are named for reference: ACTB, actin beta; ALBU, albumen; APA4, apolipoprotein a I; APA4, apolipoprotein a IV; APOC3, apolipoprotein C III; APOE, apolipoprotein E, CO3 complement C3 alpha; CO4 complement C4; FETA Foetal albumen; FGL1, fibrinogen-like protein 1; FIBB, fibrinogen beta; FIBG, fibrinogen gamma; ITH4, inter alpha trypsin inhibitor heavy chain 4; MTN3, Matrilin3; PEDF, pigment epithelium derived factor; THRB, prothrombin; TRFE, Serotransferrin; TTHY, transthyretin.
Already 8 years ago, clinostat spheroids constructed from C3A cells were shown to be more effective of predicting drug toxicity than primary human hepatocytes
C3A spheroids have also been used to reveal novel signalling pathways involved in drug treatment (acetaminophen) [46].
\nCurrently one of the major weakness of testing for genotoxicity is the inability of indicator cells to express metabolic enzymes needed for the activation and detoxification of genotoxic compounds
Herbal medicines are often assumed to be safe because they are ‘natural products’, despite the lack of data. To reduce the cost and accelerate their testing, a C3A 3D spheroid model has been developed and benchmarked against Sprague Dawley rats to test one of the most widely used extracts, (
Heteromeric proteins from spheroids even been used as an internal quality control for proteomic data [49].
\nEpigenetic marking and histone clipping have been shown to be recovered in spheroids [38] and this has been shown to occur during intestinal differentiation
Spheroids and organoids are being used to investigate the self-organisation of multicellular tissues [53]. Human induced pluripotent stem cells (hiPS cells) have been used to generate neural spheroids that contain oligodendrocytes, neurons and astrocytes [28] and to mimic the blood brain barrier [54]. Primary and stem cells have been used to recapitulate the intricate pattern and functionality of pancreatic islets, working towards regenerative medicine for diabetes [55]. Progress is also being made towards producing transplantable photoreceptor precursors using pluripotent stem cell-derived retinal organoids to treat retinal degeneration diseases [56].
\nBacterial-host interactions during Salmonella infections are being studied using iPSCs organoids and stem cell enteroids to mimic the intestinal villus and crypt [57].
\nMulticellular, physiologically active organotypic cultures are being use to study a wide variety of human viral pathogens with a view to pre-clinical evaluation of vaccines, antivirals and therapeutics [58].
\nClinostat cultures are also being used in bone research. Low dietary intake of both vitamin D and K is negatively associated with fracture risk, often seen in persons suffering from osteoporosis. Treatment of primary human osteoblasts (hOBs) 3D multicellular spheroids with a combination of vitamin D and K, enhanced gene expression of periostin and collagen (COL-1), as well as inducing extended osteoid formation. The two vitamins apparently affected bone mechanical properties differently: vitamin D enhancing stiffness and K2 conveying flexibility to bone. It is anticipated that the combination of these effects may translate to increased fracture resistance
Clinostat bioreactors systems clearly provide readily controllable 3D cell culture conditions, needing small amounts of cells, media or other compounds and provide sufficient cellular material for a wide variety of assays. The culture vessels and clinostat incubator described here, would be beneficial for many
The advantages of culture stability for months, its reproducibility and the possibility to treat and then see the response and recovery (if necessary, for multiple times on the same culture) offer a great potential for future research. The novel equipment described here, will facilitate this research.
\nFurthermore, the fact that the clinostat system does not require changes in media, the use of scaffolds or special growth factors will not only facilitate the transition from other systems to this clinostat approach but will also allow the cells to respond in their own natural pre-programmed manner.
\nThanks to 3D cell culture, the border between basic research and clinical applications is dissolving – and this new era of self-assembling tissue mimetic structures requires a new range of purpose-built equipment.
\nThe authors are all employees of CelVivo ApS.
\nThe culture vessel and clinostat incubator illustrated in this chapter are sold under the ClinoReactor® and ClinoStar® trade names by CelVivo ApS.
\nVideo materials referenced in the text are available at: https://bit.ly/2PkiE9m.
\nSupporting women in scientific research and encouraging more women to pursue careers in STEM fields has been an issue on the global agenda for many years. But there is still much to be done. And IntechOpen wants to help.
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\n\nWe aim to publish 100 books in our Women in Science program over the next three years. We are looking for books written, edited, or co-edited by women. Contributing chapters by men are welcome. As always, the quality of the research we publish is paramount.
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