Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\n
We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\n
Throughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\n
We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
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1. Introduction
Lactic acid bacteria can be found in a diversity of ecosystems, which is consistent with their ability to adapt to highly variable environments. Among the various parameters that characterize these environments (temperature, pH, water activity), redox is relatively recent.It has however already been addressed indirectly in studies relating to the impact of oxidative stress on lactic acid bacteria. Indeed, the concept of oxidation has often been associated with the presence of oxygen; however, oxidoreductive effects on microorganisms must not be limited to oxygen.
A broader vision could be proposed concerning the adaptation of lactic acid bacteria to extracellular redox. The metabolism of lactic acid bacteria, chemosynthetic organisms, involves a series of dehydrogenation (oxidation) and hydrogenation (reduction)reactions. This metabolism follows the principle of conservation of energy and matter, and therefore requires the availability of a terminal electron acceptor. In lactic acid bacteria, a carbon metabolic intermediate is reduced (mainly pyruvate). In homofermentative lactic acid bacteria, redox coenzymes (NAD+/NADH) enable coupling between oxidation and reduction reactions. During anaerobic glycolysis, glucose is oxidized to 2 moles of pyruvate with the formation of 2 moles of NADH,which then further reduces pyruvate to form lactic acid. Consequently, the typical equation of homolactic fermentation is: 1 glucose 2 lactate.
Such a perfect matching, theoretically consistent, must be qualified according to the environmental conditions, including the redox state of the extracellular medium. The adaptation of lactic acid bacteria to extracellular redox depends on their ability to positively or negatively interfere with oxidants (electron acceptors) or reducing molecules (electron donors). Carbon and electron flow management by the cell will thus be highly dependent on the ability of the microorganisms to interact with the redox environment.
Potentially, all biochemical reactions in the cell, and therefore the enzymatic activity, may be influenced by the redox state of the environment. Dissolved oxygen is an oxidizer and can reach concentrations of 8 mg.L-1of medium (equilibrium with air). Despite the strict anaerobic metabolism of some lactic acid bacteria, the majority are aerotolerant and can react with dissolved oxygen at varying levels. Lactic acid bacteria provided with NADH oxidase can reduce oxygen to water (reduction reaction coupled with the re-oxidation of NADH). This process influences both the intracellular and extracellular redox environment, and will result in a change in the metabolism, cellular physiology and physico-chemical environment surrounding the microorganism.
Changes in the extracellular environment can be monitored by measuringthe redox potential (Eh). This parameter plays a key role in the quality of fermented dairy products, but is still rarely taken into consideration or is completely ignored during the manufacturing process. The reasons for this lack of interest can be attributed to difficulties associated with its measurement and control. Over thepast ten years, several studies advocate the monitoring and control of Eh in fermented products using lactic acid bacteria selected for their reducing ability, redox molecules, or heat treatment. In terms of food applications, the variation in Eh must involve compounds that do not alter the product characteristics. So, modifying the Ehusing gas, which enablesthe product characteristics to be maintained, may be advantageously exploited in industry.
The aim of this chapter is to present the latest knowledge concerning the adaptation of lactic acid bacteria to their redox environment, and the interest of modifying Eh using gas for lactic acid bacteria applications in the food industry.
2. Redox potential
Eh, like pH, is a parameter of the state of biological media which indicates the capacity to either gain or lose electrons. During oxidation, electrons are transferred from an electron donor to an electron acceptor, which is reduced. Electrochemical measurement of Eh is not new but has attracted little attention as a parameter for controlling fermentation processes due to the sensitivity of its measurement. However, Eh is already indirectly taken into account in industry through oxygen, of which the inhibitory effect on lactic acid bacteria is well-known. Indeed, oxygen modifies the growth capacity of microorganisms and the formation of end products, and so may contribute to the quality of fermented products [1, 2].
2.1. Definition of Eh
Oxidation is a reaction in which a molecule, atom or ion, loses electrons.
Reduction is a reaction in which a molecule, atom or ion, gains electrons.
An oxidant (also known as an oxidizing agent, oxidizer or oxidiser) can be defined as a substance that removes electrons from another reactant in a redox reaction.
A reductant (also known asa reducing agent or reducer) can be defined as a substance that donates an electron to another species in a redox reaction.
In the same way pH defines acid-base characteristics of a solution, Eh defines the reducing and oxidizing characteristics.
Presented below isthe reduction half-reaction of an oxidant (Ox) to its corresponding reduced species (Red):
Ox + ne−↔RedE1
The Nernst equation gives the relationship between the redox potential and the activities of the oxidised and reduced species:
Eh=Eh0+2.3×(RTnF)×log([Ox][Red])E2
where:
Eh = redox potential (mV) (in relation to a normal hydrogen electrode).
Eh0= standard redox potential (mV) (in relation to a normal hydrogen electrode) at pH 0
F = Faraday constant (96500 C.mol-1)
n = number of electrons exchanged
R = gas constant (8.31 J.mol-1.K-1)
T = temperature in K
2.3×RTF=59 mV (at 25 °C)
However, chemical reactions in aqueous media involve protons, and the following half-reaction:
Equation (4) is used to determine Eh0\' defined as the standard redox potential at pH 7, which is closer to biochemical and biological processes (Figure 1).
Figure 1.
Standard reduction potential Eh0\'(mV) of some important half-reactions involved in biological processes at 25 °C and pH 7.
2.2. Measurement of Eh
The first technique for measuringEh is based on the use of coloured indicators (redox indicators), which are mostly indophenols or indigo derivatives with a reversible structure between oxidized (coloured) and reduced (colourless) state. However, the use of coloured indicators for measuring Eh, including biological media or food, is limited. Indeed, these molecules behave as electron donors and acceptors; they affect and can change the equilibrium. These compounds can also catalyse or inhibit biological reactions and may be toxic to microorganisms. Furthermore, in some cases it is difficult to appreciate a significant colour change and some Eh indicators also change colour with the pH of the medium. For these reasons, redox indicators are rarely used. They are more often used as indicators of redox thresholds, especially in the manufacture of strictly anaerobic culture media (resazurin) where maintaining a minimum level of reduction is essential for the growth of anaerobic microorganisms. Resazurin is also used to evaluate the reducing activity of starter cultures, for sterility testing and for the detection of microorganisms in dairy milk.
The second method commonly used in microbiology is a potentiometric technique which, contrary to redox indicators, is a direct method. The principle consists in measuring a potential difference determined between an inert electrode (usually made of platinum or gold) in contact with a redox couple in solution and a reference electrode. Electron exchange with the reduced and oxidised species takes place at the inert electrode. The inert electrode is made of stainless metals with a high enough standard potential to be electrochemically stable. These metals act as electron conductors between the measuring medium and the reference electrode. The reference system is the standard hydrogen electrode, but in practice two other references are used: the calomel electrode and the silver / silver chloride (Ag/AgCl)electrode. The redox potential is expressed in volts or millivolts. Redox values should always be expressed in relation to the hydrogen electrode. Consequently, potential measurements (Em) using other references must be adjusted according to the reference potential of the hydrogen electrode (Er):
Eh=Em+ErE5
For example, Er of the Ag/AgCl electrode is equal to 207 mV at 25 °C [3]. According to data from Galster [3], we propose the following equations linking Er and temperature for the two reference electrodes:
Ag/AgCl (KCl 3M)Er=207+0.8×(25−T)E6
Calomel (Saturated KCl)Er=244+0.7×(25−T)E7
Before use, the redox electrodes must be polished with fine aluminium powder to restore the platinum surface, and controlled in tap water. Three measurements in tap water should be compared and need to be within the confidence interval around their mean value (calculated at 20 mV, 95% confidence level) to ensure correct measurement [4].
Equation (4) shows the dependence of Ehon pH. It is possible to overcome pH dependency by applying the Leistner and Mirna equation [5]:
Eh7=Ehβ−α x (7−β)E8
(
where:
Eh7 = redox potential (mV) at pH 7
Eh = redox potential (mV) at pH
= pH of medium
= Nernst Eh–pH correlation factor (mV/pH unit).
To calculate Eh7 in biological media, the Nernst factor (α) must be determined experimentally by measuring Eh variation as a function of pH using an acid or a base. This value may vary according to the nature of the oxido-reducing molecules in the media.For example, the Nernst factor is 40 mV/pH unit in milk [6].
2.3. Use of gas to modify Eh
Gas applications in the food industry are numerous: modified atmosphere packaging (MAP), beverage distribution, cooling, freezing or carbonation. The advantage of using gases such as hydrogen (H2), nitrogen (N2) or carbon dioxide (CO2) to modify Eh is that they are not directly toxic to microorganisms. There are no safety issues for the productwith these gases and they can be used sequentially. Finally, their use is authorized at European level. Of the gases used in the food industry, in this chapter we will focus more particularly on nitrogen and hydrogen.
Nitrogen (N2) is odourless, colourless, tasteless, non-toxic, and non-flammable. It is used to extend the life of packaged products (authorized additive E941). It is used to expel oxygen from the packaging before it is closed,which prevents oxidative phenomena involving pigmentation, flavours and fatty acids. It is also used for rapid freezing and refrigeration of food during transport.
Hydrogen (H2) hasmajor potential in food as it is colourless, odourless and has no known toxic effects. It is already used in the food industry for the hydrogenation of liquid oils and their transformation into solid products such as margarine or peanut butter. Hydrogen is a powerful reducer in solution, even at very low concentrations. It has been used to demonstrate the effect of Eh on the heat-resistance of bacteria [7]. Hydrogen is a special reducing agent: it imposes an Eh value on the medium associated with the introduction of the H+/H2 couple (Eh0\' = -414 mV). This Eh value is highly dependent on the concentration of this couple that mainly influences the stability of the Eh imposed.
With the prospect of food use, hydrogen has the advantage over chemical reducing agents of not changing the product formulation, and therefore not altering the taste. Its industrial use has been rarely seen in this context because of its low flammability limit of 4% in air at 20 °C [8], this is why N2-H2 (96%-4%) is preferred to pure hydrogen. Its use in food technology is authorised at the European level (E949).
3. Effect of Eh on a fermented dairy product: Yoghurt
3.1. Reminder regarding the manufacture of yoghurt
We chose to focus on the key steps in the manufacture of yoghurt, which are:
Delivery of milk: The raw material can be either fresh milk,reconstituted milk (from skim milk powder), or a mixture. In all cases, it is generally accepted that a quality product can be made froman extremely high qualityraw material. With this in mind, it is essential that when the milk and other raw materials are received methods are established to detect anypotentialdefects as early as possible. Two parameters must therefore be analysedas soon as the milk is received:
Its microbiology: to ensure consumer health, prevent the degradation of milk components that persist in the finished product and eliminate any possible competition between the starter culture and the endogenous flora that may involve bacteriophages.
Its chemistry: a rapid analysis of the chemical composition of the milk is necessary in order to identify any problems such as colostrum and late-lactation milk. Furthermore, these data concerning the chemistry of the milk can be useful in the standardization of the mixture.
Standardization of the mixture: each component in milk plays a role. Fat has an effect on the smoothness and the feeling of softness in the mouth, lactose is the raw material used by lactic acid bacteria for acidification, proteins act on the texture and minerals help stabilize the gel. These components vary in cow’s milk according to race, diet, stage of lactation of the animal and season, which is why, during yoghurt manufacture, it is necessary to standardize the milk fat and protein content to meet the nutritional and organoleptic characteristics of the product and obtain consistent quality throughout the year.
Homogenization: homogenization has two main effects on milk fat and proteins. The fragmentation of the fat globules prevents the separation of the lipid phase and the rest of the mixture, thus preventing the cream rising to the top during fermentation. Homogenization also stabilizes the proteins.
Heat treatment: This eliminates most of the microbial flora originally present in the milk, including pathogenic or spoilage flora. It denatures the whey proteins, improves the consistency and viscosity of fermented milks and prevents whey separation. The risk of syneresis is reduced.
Heat treatment of milk also has a positiveeffect on enzyme activity by providing a supportive environment. The environment becomes reductive through the elimination of a high proportion of oxygen. This medium is more conducive to fermentation that takes place under anaerobic conditions.
Cooling: After heat treatment, the mixture must be cooled to temperatures approaching 43 °C for inoculation and incubation of the starter culture.
Fermentation: "Yoghurt" refers to a product fermented by Streptococcus thermophilus (S. thermophilus) and Lactobacillus delbrueckii ssp. bulgaricus (Lb. bulgaricus). In general, milk is fermented at 40-45 °C, the optimum growth temperature, with an incubation time of 2 and a half hours. However, a longer incubation periodof 16-18 hours can be used at a temperature of 30 °C, or until the desired acidity is attained[9].
3.2. Yoghurt strains: Lactobacillus delbrueckii ssp. bulgaricus and Streptococcus thermophilus
The association of S. thermophilus and Lb. bulgaricus is called proto-cooperation. Each species produces one or moresubstances, initially absent from the culture medium, that stimulate the growth of the other species [10]. During the symbiosis observed in yoghurt, the growth phases of these two bacterial species arestaggered. Initially, growth of S. thermophilusis observed which is then slowed by the inhibitory effect of the lactic acid produced; the growth rate of Lb. bulgaricusthen increases [11].
S. thermophilus is a strain that often shows little proteolytic activity, due to general low activity or absence of a wall protease. Its growth is limited because the peptides and amino acids initially present in milk are insufficient to cover its needs. In contrast, Lb. bulgaricus membrane protease degrades milk caseins releasing small peptides and amino acids which can be used by S. thermophilus intracellular peptidases [12].
The cooperation between these two strains also involves the production by S. thermophilus of pyruvic acid, formic acid, and carbon dioxide (CO2obtained from the decarboxylation of milk urea by urease) which stimulates the growth of Lb. bulgaricus[9, 13]. However, formic acid is released late in fermentation and in small quantities. The two bacterial species also consume the formic acid resulting from the heat treatment of milk [14].
Some authors have also demonstrated that the association of S. thermophilus and Lb. bulgaricus affects the production of volatile compounds involved in flavour development in yoghurt [15]. S. thermophilus produces more acetaldehyde, acetoin and diacetyl than Lb. bulgaricus, contrary to the rest of the bibliography concerning acetaldehyde [9, 16, 17]. Quantities of these molecules and other carbonyl compounds are not crucial per se for yoghurt flavour, but there are relationships between them that give yoghurt its distinctive flavour.
Finally, Ebel et al.[18] showed that during the manufacture and storage of a fermented dairy product, the populations of Lb. bulgaricusandS. thermophilusare the samewhatever the Eh of the milk.
3.3. Texture
3.3.1. A look at yoghurt texture
The transformation of milk into yoghurt is called acid gelation. This gelation is a phenomenon that results in a remarkable change in the physical state of the system which changes from a liquid to a system with the characteristics of a solid. Several phases in the formation of a gel can be distinguished:
The "solution" phase, where the polymer forms a solution: the macromolecules are not held together;
The "gel" phase occurs when enough chains have joined together to form a network or gel, with dominant elastic rheological behaviour;
Sometimes, additional aggregation of associated areas is observed; the gel becomes increasingly rigid and syneresis may occur with time: the gel shrinks and exudes some of the liquid phase.
The slow acidification of milk is due to bacteria that metabolize lactose and produce lactic acid. While casein micelles are stable at normal milk pH and room temperature, this supramolecular structure becomes unstable and leads to the formation of a gelwith the slow progressive acidification of milk.
From pH 6.7 to pH 5.8, the casein micelles seem to retain their integrity, shape and size.
From pH 5.8 to pH 5.5, the micelles get closer togetherdue to the decrease in the potential ζ and begin to form groups of micelles.
From pH 5.5 to pH 5.0, significant changes in shape and size take place: micelle aggregates appear and these particles partially fuse. This is the phase transition between the solution and the acid gel.
When the pH reaches 5, the solubilisation of micellar calcium, which occurs steadily from pH 6.8, is complete. From pH 5 to pH 4.8, rearrangements of the aggregates take place. At pH 4.9, gelation is complete. At pH 4.6, the acid gel is definitively formed. Aggregation of casein micelles at pH 4.6 is irreversible. Hydrophobic interactions are facilitated at this pH due to reduced electrostatic repulsion, leading to micelle aggregation.
Rheology is used to characterize the texture of yoghurt that specifically targetsthe mechanical properties. The rheological characterization of a product involves the application of a shear stress and measurement ofthe deformation, or application of a deformation (compression, stretching or shear) and measurement of its ability to withstand this distortion. Yoghurt can be defined as a viscoelastic fluid. It therefore has both the viscous properties of a liquid and the elastic properties of a solid.
3.3.2. Effect of Eh on a model acid skim milk gel
It has been shown that dairy products are affected by Eh[4, 19]. Delbeau et al. [19] showed that the use of gas to change the Eh of milk can modify the sensory properties of a fermented dairy product.However, we do not know if these modifications are due to the impact of Eh on physicochemical phenomena, lactic acid bacteria, or both. For this purpose, Martin et al.[20] wanted to determine to what extent chemical phenomena affect acid milk gelation under different Eh conditions. Glucono-δ-lactone (GDL) was used to acidify milk to avoid variations caused by microorganisms sensitive to Eh.
Martin et al.[20] studied the effects of Eh on model acidified skim milk gels obtained using GDL and prepared under different gaseous conditions. The milk prepared in air is an oxidizing medium; nitrogen, which is a neutral gas, can be used to remove oxygen from milk - even so the milk Eh remains oxidizing in these conditions - and hydrogen leads to a reducing Eh (below 0). Martin et al.[20] focused on the effect of gas bubbling on gel structure through viscoelastic properties and measurement of whey separation (Table 1).
Gaseous conditions applied to milk
pH
Eh7 (mV)
η (Pa.s)
WS (g/100g of GDL-gel)
At t=0
At t=3.5 hours
At t=0
At t=3.5 hours
Air
6.80 ± 0.03
4.6a ± 0.0
405 ± 22
414 ± 8
0.039a ± 0.000
4.74a ± 1.42
Air bubbling
6.70 ± 0.04
4.6a ± 0.0
433 ± 6
430 ± 5
0.032c ± 0.001
1.26b ± 0.26
N2 bubbling
6.8 ± 0.06
4.6a ± 0.0
283 ± 13
288 ± 11
0.035b ± 0.001
1.93b ± 0.33
N2 – H2bubbling
6.73 ± 0.04
4.6a ± 0.0
- 349 ± 6
- 83 ± 18
0.032c ± 0.001
0.59c ± 0.12
Table 1.
Characteristics of gel structure depending on the different Eh conditions (milk acidified using GDL):
• Apparent viscosity η at 500 1/s of GDL-gel at pH 4.6 and 4 °C. Measurements were carried out 24 hours after addition of GDL.
• Evolution of average whey separation (WS) over 28 days in GDL-gels.
Values are means from triplicate experiments (mean value standard deviation).
The apparent viscosity of each gel was characterized at pH 4.6, 4 °C, 24 hours after addition of GDL under the different Ehconditions (Table 1). For GDL-gels, apparent viscosity ranged from 0.032 to 0.039 Pa.s. GDL-gels produced in air had the highest apparent viscosity,whereas values obtained with air and N2– H2 bubbling were similar and significantly lower than those obtained with N2bubbling. So, for GDL-gels,the viscosity was affected by bubbling. Martin et al.[20] showed that the type of gas used for bubbling has a significant influence but no clear trend can be deduced from these results in terms of the influence of an oxidizing or reducing environment.
The gel structure was then observed during storage for up to 28 days. The mean whey separation values of GDL-gels produced under different Eh conditions are presented in Table 1. For each gaseous condition, the authorsobserved that whey separation occurred from the very first day of storage and the volume of whey separation was relatively constant during the 28 days of storage [20]. Whey separation ranged from 0.59 to 4.74 g / 100 g of GDL-gels. The highest whey separation was obtained with air but this value was lower than values reported in the literature: 18.48% of GDL-gels in the work by Lucey et al. [21] and 10% in a study by Fiszman et al.[22]. One explanation for is that in the study by Lucey et al.[21] the method used to measure whey separationwas to remove the gels from their flasks and thus whey separation could have been over-estimated. Whey separation obtained with gas bubbling was lower (1.26 g / 100 g with air bubbling, 1.93 g / 100 g with N2 bubbling and 0.59 g / 100 g with N2 - H2bubbling). The lowest whey separation was observedwith GDL-gels made under N2– H2. Adjusting the Eh of milk to reducing conditions (under N2– H2) could be a possible way of significantly decreasing the phenomenon of whey separation.
3.3.3. Effect of Eh on a non-fat yoghurt
In a second step, the authors proposed studyingthe extent to which lactic acid bacteria affect acid milk gelation under different Eh conditions [23]. Indeed, oxygen modifies the growth capacity of bacteria and the formation of end products. So, Eh may contribute to the quality of fermented products [2, 24, 25]. Martin et al.[23] wanted to determine the effects of Eh on yoghurts made under various gaseous conditions. In this study they focused on exopolysaccharide production and gel structure (Table 2). The same gaseous conditions as in the study on the effect of Eh on model acid skim milk gels were chosen.
Lb. bulgaricus and S. thermophilus produce exopolysaccharides (EPS) which can contribute to improving the texture and viscosity of fermented dairy products [26].In standard yoghurts (produced in air) the concentration of EPS was 63.60 mg.L-1, in accordance with the literature (50 to 350 mg.L-1) [27, 28].The concentration was lower in yoghurts produced with air bubbling (15.22 mg.L-1) than in yoghurts produced with N2 bubbling, which was lower than those made with N2 – H2 bubbling. The EPS concentration of yoghurts made in Air and with N2 – H2bubbling were similar. In reducing Eh conditions, lactic acid bacteria produced the same amount of EPS as in ambient air. This result has already been observed in the literature. Indeed, Lactobacillus sake 0-1was reported to have optimal EPS production in anaerobic conditions [29], while higher EPS yields were correlated with a lower oxygen tension[30].
Gaseous conditions applied to milk
pH
Eh7 (mV)
CEPS (mg/L)
η (Pa.s)
WS (g/100g of yoghurt)
At t=0
At t=3.5 hours
At t=0
At t=3.5 hours
Air
6.80a ± 0.0
4.6a ± 0.0
425a ± 20
171a ± 2
63.60b ± 3.72
0.046a ± 0.00
1.98a ± 0.54
Air bubbling
6.80a ± 0.0
4.6a ± 0.0
435a ± 3
241a ± 8
15.22a ± 0.74
0.046a ± 0.00
1.76a ± 0.31
N2 bubbling
6.81a ± 0.0
4.6a ± 0.0
285b ± 11
139b ± 5
25.29c ± 0.40
0.035b ± 0.00
1.03ab ± 0.27
N2 – H2bubbling
6.81a ± 0.0
4.6a ± 0.0
-345c ± 4
-309c ± 10
62.70b ± 0.75
0.021c ± 0.01
0.59b ± 0.12
Table 2.
Characteristics of gel structure depending on the different Eh conditions (milk acidified using lactic starters):
• Concentrations of exopolysaccharides (CEPS) in yoghurts after one day of storage.
• Apparent viscosity η at 500 1/s of yoghurt at pH 4.6 and 4 °C. Measurements were made 24 hours after addition of starter culture.
• Evolution of average whey separation over 28 days (WS) in yoghurts.
Values are means from triplicate experiments.
The apparent viscosity of each yoghurt was characterized at pH 4.6 and 4 °C, 24 hours after addition of bacteria under the different Eh conditions (Table 2). The apparent viscosity ranged from 0.021 to 0.046 Pa.s. Yoghurts produced in air and with air bubbling had the highest apparent viscosity. The apparent viscosity of yoghurts made with N2bubbling was lower (0.035 Pa.s) than other oxidizing conditions (0.046 Pa.s), and values obtained with N2– H2bubbling were the lowest (0.021 Pa.s). Apparent viscosity is clearly affected by the gastype. A reducing environment reduces the apparent viscosity of yoghurt.
Apparent viscosity depends on the solid fraction in the gel as well as the relationships between the different solid elements. In yoghurt, solid particles include milk proteins, lactic acid bacteria and their EPS. Indeed,the gel of yoghurts produced under N2 – H2 conditionsis weaker despite greater EPSproduction [23]. It is a common assumption that EPS produced by bacteria contribute to the rheological properties of yoghurt [31-33] but, as reported by Hassan et al.[34], van Marle [35] and Martin et al.[23], no correlation between the viscosity of yoghurt and EPS concentrations was found.
Whey separation of yoghurts produced under different Eh conditions over 28 days of storage was then studied [23] (Table 2). Concerning GDL-gels, whey separation of yoghurts occurred from the very first day of storage and the volume of whey separation was relatively constant over the 28 days of storage. Whey separation ranged from 0.59 to 1.98 g/100 g of yoghurt. The highest whey separation was obtained with air and air bubbling and these values are in accordance with the literature [22]. Whey separation obtained with N2 bubbling(1.03 g / 100 g) and N2 - H2bubbling(0.59 g / 100 g) was lower. So, the more reducing the environment, the lower the whey separation. Adjusting the Eh of milk to reducing conditions (under N2– H2) could be a possible way of significantly decreasing the phenomenon of whey separation.
3.4. Aroma compounds
3.4.1. A look at yoghurt aroma compounds
The typical flavours of fermented milk are mainly due to a blend of the following compounds: lactic acid, carbon compounds such as acetaldehyde, acetone, acetate and diacetyl, non-volatile acids such as pyruvic, oxalic and succinic acids, volatile acids such as acetic, propionic and formic acids and products from the thermal degradation of proteins, lipids or lactose.
Ott et al.[36] identified 91 aroma compounds (GC-olfactometry) in yoghurt among which 21 were detected more frequently and would thus have a major impact on flavour. Acetaldehyde is found in significant quantities and is responsible for the characteristic smell of yoghurt. Diacetyl, pentane-2,3-dione, and dimethyl sulphide also have a major impact on yoghurtflavour [36, 37].
Acetaldehyde was firstly reported by Pette et al. [38] as the main aromatic compound in yoghurt. During manufacture, production of this compound is only highlighted when a certain level of acidification is reached (pH 5.0). Concentrations found in the final product are 0.7 to 15.9 mg.kg-1.The maximum amount is obtained at pH 4.2 and stabilizes at pH 4.0. The production of acetaldehyde and other flavour compounds by S. thermophilus and Lb. bulgaricus occurs during yoghurt fermentation and the final amount is dependent on specific enzymes which are able to catalyse the formation of carbon compounds from the various milk constituents.
Three metabolic pathways producing acetaldehyde were identified and some pathways may take place simultaneously [39]:
From glucose in the glycolytic pathway,
From the degradation of DNA,
From L-threonine with threonine aldolase.
However, 90% of acetaldehyde produced by Lb. bulgaricus comes from glucose and 100% in the case ofS. thermophilus [39].
Diacetyl and pentane-2,3-dione also have a significant impact on the final aroma of yoghurt: 1 mg of diacetyl and 0.1 mg of pentane-2, 3-dione per kg of yoghurt are produced by lactic acid bacteria during fermentation.These diketones are produced by decarboxylation of their precursors, 2-acetolactate and 2-aceto-hydroxybutyrate [39]. These compounds are thermally unstable and in the presence of oxygen are converted into their corresponding diketones[40, 41]. Moreover, during storage at 4 °C, the concentration of the two diketones increases slightly [41] due to the basal metabolic activity of the bacteria.
Agitating a mixed culture of Lactococcus and Leuconostoc promotes diacetyl production by allowing oxidative decarboxylation of 2-acetolactate [42, 43]. In unstirred cultures, the redox potential of the medium decreases rapidly at the start of fermentation. Only acetoin and 2-acetolactate areproduced. The authors also showed that controlled oxygenation of the Lactococcus lactis ssp. lactis culture medium favoured diacetyl production by increasing the activity of diacetyl synthase [44].
Neijssel et al. [40] showed that the distribution of carbon flux from pyruvate depended on the NADH / NAD+ ratio, intracellular redox potential or the concentration of metabolites and particularly that of pyruvate.Finally, the authors suggested adding air or oxygen to milk in order to increase the amount of diacetyl in cheese [45].
References [36] and [37] are the only articles that mention dimethyl sulphide as a compound having a significant impact on the flavour of yoghurt. The metabolic pathways involved in the synthesis of sulphur compounds are not well-known in yoghurt. However, the literature mentions these synthetic pathways in the development of cheese flavour.
In general, the majority of sulphur aromatic compounds come from methionine [46]. Methanethiol is easily oxidized to dimethyl disulphide and dimethyl trisulphide [47]. The appearance of these compounds is the direct result of the methanethiol content and is modulated by the low redox potential in Cheddar. Dimethyl sulphide is produced by a metabolic pathway that does not involve methanethiol, but that is different to that of dimethyl sulphide and trimethyl disulphide from methionine [48].
Studieshave also shown that when the redox potential decreases, methanethiol and hydrogen sulphide concentrations increase [45]. Moreover, the cheeses to which reducing compounds (dithiothreitol or glutathione) were added contained higher amounts of sulphur compounds and had better qualitative and quantitative flavour performances [45]. It therefore seems that a reducing environment is essential for the production of aroma compounds by bacteria. If a cheese is exposed to air, the redox increases and this leads to the oxidation of sulphur compounds, resulting in lower quality aromatics.
3.4.2. Impact on aroma biosynthesis by lactic acid bacteria
Studies on aroma biosynthesis by LAB usually take into account environmental factors such as pH and temperature. However, the Eh of the medium has not yet been considered, although it is supposed to affect bacterial metabolism [49, 50]. Martin et al.[51] determined to what extent Eh can affect the metabolic pathways involved in the production of aroma compounds in Lb. bulgaricus and S. thermophilus.Four aroma compounds (acetaldehyde, dimethyl sulphide, diacetyl and pentane-2,3-dione) were chosen as metabolic tracers of lactic acid bacteria metabolism. The same gaseous conditions as in the study ofthe effect of Eh on model acid skim milk gels and non-fat yoghurt were chosen. The amounts of each of the four aroma compounds extracted using a headspace solid-phase micro-extraction technique (HS-SPME) and analysed using gas chromatography coupled with mass spectrometry (GC-MS) during 28 days of storage are reported in Table 3.
Firstly, the authors focused on the impact of these different Eh conditions on the biosynthesis of these four aromas by bacteria after one day of storage [51]. In the standard yoghurt (made in ambient air), diacetylwas observed in the highest concentrations,and acetaldehyde the lowest. This result is contrary to the literature where the lowest concentrationswere reported for dimethyl sulphide (0.013-0.070 mg.kg-1; measured using dynamic and trapped headspace GC [37, 41]). In the same way, published concentrations were generally higher for acetaldehyde (0.7-15.9 mg.kg-1) than in our standard yoghurt (0.18 mg.kg-1). In the literature, the concentrations of diacetyl (0.31-17.3 mg.kg-1) and 2,3-pentanedione (0.02-4.5 mg.kg-1) were lower than in our standard yoghurt (162 mg.kg-1 and 115 mg.kg-1 respectively).An explanation for these differences can be put forward: the quantification technique used by Ott et al.[41] and Imhof et al.[37] was dynamic and trapped headspace GC. This technique requires Tenax® traps which may be saturated, as we showed in a preliminary experiment. Furthermore, in our study,to enable a more complete extractionof the aroma compounds, a saturated solution of NaCl was added to the yoghurt. Finally, we did not use the same speciesof LAB as Ott and Imhof, which may have resulted in different quantities of the various aroma compounds.
Yoghurts made with air bubbling had significantly higher concentrations of acetaldehyde and diacetyl compared to standard yoghurts. The concentration of dimethyl sulphide was significantly lower and that of pentane-2,3-dione was the same.
With N2bubbling, the concentration of acetaldehyde was similar to that in yoghurts made with air bubbling, whereas the concentration of dimethyl sulphide was lower. The concentration of diacetyl was the same as in standard yoghurts and the concentration of pentane-2,3-dione was not significantly different from that in yoghurts made in air (bubbling or not).
The authors also demonstrated that oxidative Eh conditions clearly increased the production of aroma compounds [51]. These results are consistent with the bibliography. Oxidative conditions stimulated the production of volatile sulphur compounds such as dimethyl sulphide, and aldehydes such as acetaldehyde [49]. In the presence of oxygen, the oxidative decarboxylation of 2-acetolactate and 2-aceto-hydroxybutyrate to diacetyl and pentane-2,3-dione respectively was also favoured[40, 42, 44, 52]. For diacetyl, our result can be explained by the fact that in anaerobic conditions lactic acid bacteria dehydrogenate the NADH produced during glycolysis via lactate dehydrogenase (LDH) activity. Boumerdassi et al.[44] confirmed that oxygen increases NADH oxidase activity [53], which causes NADH re-oxidation at the expense of LDH, butanediol dehydrogenase and acetoin dehydrogenase activity[54]. Then, excess pyruvate is partially eliminated through acetolactate production, which increases diacetylproduction [44].
Finally, bubbling with N2 – H2 (reducing conditions), the concentration of acetaldehyde and pentane-2,3-dione was the same as in standard yoghurts. The concentration of dimethyl sulphide was the same as in yoghurts made without oxygen and the concentration of diacetyl was significantly lower than under the other three Eh conditions.
Then, [51] kept the yoghurts in Hungate tubes at 4 °C for 28 days in order to prevent exposure of the contents to oxygen, and the gaseous conditions applied to the milk arethus assumed to be constant during storage.
Gaseous conditions and storage period (days)
Aroma compound (mg.kg)
ACH
DMS
DY
PTD
Ambient air
1
0.18a ± 0.02
10.16a ± 0.59
162.08a ± 13.49
115.25a ± 33.70
7
0.13ab ± 0.02
10.16a ± 0.99
115.55cb ± 5.13
84.33ab ± 1.86
14
0.10b ± 0.00
9.52a ± 0.42
91.63c ± 8.02
71.56ab ± 4.49
21
0.18a ± 0.00
13.06b ± 1.21
141.29ab ± 11.77
65.19b ± 5.49
28
0.16ab ± 0.01
11.82ab ± 0.48
112.66c ± 7.56
51.79b ± 2.95
Air bubbling
1
0.28a ± 0.00
5.27a ± 0.53
299.90a ± 18.37
123.47a ± 3.23
7
0.14b ± 0.01
6.34ab ± 0.30
127.58bc ± 3.93
83.98b ± 2.20
14
0.11b ± 0.01
6.85b ± 0.32
104.23b ± 4.66
78.10b ± 3.15
21
0.24a ± 0.02
9.33c ± 0.55
143.84c ± 6.69
67.89c ± 0.80
28
0.13b ± 0.02
6.78b ± 0.30
101.91b ± 3.03
54.36d ± 4.19
N2bubbling
1
0.35a ± 0.04
3.72a ± 0.22
147.79a ± 9.91
110.87a ±4 .49
7
0.22bc ± 0.02
5.68ab ± 0.34
103.13bc ± 6.50
75.67b ± 1.98
14
0.18c ± 0.01
6.16b ± 0.17
78.80c ± 4.60
58.16c ± 0.48
21
0.28ab ± 0.04
10.34c ± 1.37
122.27ab ± 8.94
51.95c ± 2.29
28
0.18c ± 0.00
7.16b ± 0.77
84.76c ± 9.92
38.72d ± 3.03
N2 – H2 bubbling
1
0.17ab ± 0.00
2.71a ± 0.57
102.73a ± 9.10
76.99a ± 5.90
7
0.13bc ± 0.02
5.49b ± 0.53
89.61ab ± 7.70
66.10ac ± 2.29
14
0.11c ± 0.01
6.07bc ± 0.43
74.35b ± 5.42
57.60bc ± 0.86
21
0.19a ± 0.01
7.48c ± 0.53
112.09a ± 7.82
52.10bd ± 0.59
28
0.12c ± 0.01
7.22c ± 0.63
78.36b ± 9.30
40.60d ± 7.93
Table 3.
Evolution of average amounts of aroma compounds (mg.kg-1) quantified in headspace of yoghurts made under different Eh conditions (ambient air, bubbling with air, bubbling with N2 and bubbling with N2 – H2) during 28 days of storage. ACH: Acetaldehyde (A); DMS: Dimethyl sulphide (B); DY: Diacetyl (C); PTD: pentane-2,3-dione (D). Values are means of experiments carried out in triplicate. Values in the same column should be compared.
During the 28 days of storage, for the standard yoghurt, the quantities of acetaldehyde and dimethyl sulphide produced were relatively stable, while diketone concentrations significantly decreased.
Foryoghurts made with air bubbling, the aroma profiles remained almost constant. During storage, the concentration of acetaldehyde decreased slightly whereas that of dimethyl sulphide increased slightly. The diketone concentration significantly decreased.
For yoghurts made without oxygen (bubbling with N2), the quantities of acetaldehyde, diacetyl and pentane-2,3-dione decreased during storage while that of dimethyl sulphide increased.
For yoghurts produced under reducing conditions (bubbling with N2 – H2), the aroma profiles during storage were the same as those made without oxygen. The concentration of acetaldehyde, diacetyl and pentane-2,3-dione decreased while that of dimethyl sulphide increased.
Furthermore, during storage, different profiles were observed for the four aromas depending on the Eh conditions [51]. Under oxidizing conditions (+170 to +245 mV), the concentration of acetaldehyde was relatively stable during storage, which is in accordance with the literature [9, 55, 56] and the concentration of dimethyl sulphide was also stable.On the contrary, under reducing conditions (-300 to -349 mV), the concentration of acetaldehyde decreased and that of dimethyl sulphide increased. The metabolic pathways involved in the biosynthesis of sulphur compounds are still unclear. Under reducing conditions, it seems that another pathway promotes the production of dimethyl sulphide and that acetaldehyde may be reduced to ethanol. For diketones, whatever the Eh conditions, the concentration decreasedduring storage. Diacetyl and pentane-2,3-dione can be reduced respectively to acetoin and pentane-2,3-diol [57].
4. Impact of Eh on other dairy products
4.1. Probiotic dairy products
The use of gas to modify Eh seems to be an interesting way of varying the organoleptic properties of dairy products as well as improving the survival of oxygen sensitive strains during storage in fermented dairy products containing probiotics. Indeed, these microorganisms are mainly anaerobes. Oxygen, which is a powerful oxidant, has a drastic effect on Eh values and the viability of probiotic bacteria during manufacturing and storage [58-60]. So, many studies modify the redox potential to protect probiotics from oxygen toxicity in dairy products [1, 61-65]. However, these techniques sometimes have deleterious effects on the organoleptic properties of fermented milk. An alternative to these methods could be the use of gases. Indeed, Ebel et al.[18] showed that fermented dairy products made from milk gassed with N2, and more particularly those made from milk gassed with N2– H2, were characterized by a significant increase in Bifidobacterium bifidum survival during storage (Figure 2).
Figure 2.
Evolution of a population of Bifidobacterium bifidum during fermentation and storage. Different gaseous conditions were applied to the milk: control (solid line), gassed with N2 (dashed line), or gassed with N2–H2 (dotted line).
After 28 days of storage, a difference in bacterial counts of 1.2 log and 1.5 log was observedbetween the control milk and after bubbling with N2 or N2– H2respectively. No differences were highlighted during the fermentation process. It is interesting to note that this technique was set up without affecting the fermentation kinetics and survival of S. thermophilus and Lb. bulgaricus.The use of gas is a possible way of improving probiotic survival during storage without affecting acidification properties of yoghurt strains and consequently organoleptic properties.
4.2. Cheese
Controlling Ehin cheese seems essential in governing aroma characteristics. Indeed, a reducing Ehisnecessary for the development of the characteristic flavour of certain fermented dairy products such as cheeses, notably through the production of thiol compounds [45, 66]. It has also been reported that Cheddar has a reducing Eh and is an indicator of the establishment of the conditions required for the formation of aroma compounds [67]. As shown previously, Eh can modify the metabolic pathways of aroma production by lactic bacteria [51]. Kieronczyk et al.[49] demonstrated that reducing Eh conditions can stimulate carboxylic acid production in cheese, while oxidative Ehconditions improve the production of volatile sulphur compounds and aldehydes. By ripening cheese under reducing Eh conditions, the production of volatile fatty acids increased [68]. Adjusting the Eh of the milk before cheese ripening could be a possible way of modifying the metabolism of lactic bacteria.
5. Conclusion
Pasteurdefinedfermentation as"life without air". In lactic acid bacteria, some exogenouselectron acceptorsmayinterfere significantly with thefermentative metabolismby acting ondifferentcellular activities. A better understanding of the adaptive mechanismstoextracellularredoxis still lacking, but the results inthe literature showthat lactic acid bacteriamay use passive or active mechanisms. A remarkablefeature in lactic acid bacteriais theirability to reduce theredoxenvironment to low Eh values.
With the prospect offood applications, changing Ehusingpure or a mixture ofgaseshas the advantage ofmaintainingproductsafety as opposed tothe use ofoxidizing or reducingmolecules. This chapter demonstrates the importance of Eh both on the physico-chemistry of milk gels and bacterial metabolism and viability. The use of gas to modify Eh seems to be an interesting way of varying the organoleptic properties of dairy products.
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Redox potential",level:"1"},{id:"sec_2_2",title:"2.1. Definition of Eh",level:"2"},{id:"sec_3_2",title:"2.2. Measurement of Eh",level:"2"},{id:"sec_4_2",title:"2.3. Use of gas to modify Eh",level:"2"},{id:"sec_6",title:"3. Effect of Eh on a fermented dairy product: Yoghurt",level:"1"},{id:"sec_6_2",title:"3.1. Reminder regarding the manufacture of yoghurt",level:"2"},{id:"sec_7_2",title:"3.2. Yoghurt strains: Lactobacillus delbrueckii ssp. bulgaricus and Streptococcus thermophilus",level:"2"},{id:"sec_8_2",title:"3.3. Texture",level:"2"},{id:"sec_8_3",title:"3.3.1. A look at yoghurt texture",level:"3"},{id:"sec_9_3",title:"Table 1.",level:"3"},{id:"sec_10_3",title:"Table 2.",level:"3"},{id:"sec_12_2",title:"3.4. Aroma compounds",level:"2"},{id:"sec_12_3",title:"3.4.1. A look at yoghurt aroma compounds",level:"3"},{id:"sec_13_3",title:"Table 3.",level:"3"},{id:"sec_16",title:"4. Impact of Eh on other dairy products",level:"1"},{id:"sec_16_2",title:"4.1. 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Appl.environ.microb. 59618931897'},{id:"B55",body:'GardiniF.LanciottiR.ElisabettaGuerzoni. M.TorrianiS.1999Evaluation of aroma production and survival of Streptococcus thermophilus, Lactobacillus delbrueckii subsp. bulgaricus and Lactobacillus acidophilus in fermented milks. Int.dairy j. 92125134'},{id:"B56",body:'ImhofR.BossetJ. O.1994Quantitative GC-MS analysis of volatile flavour compounds in pasteurized milk and fermented milk products applying a standard addition method. LWT- Food sci technol. 273265269'},{id:"B57",body:'OttA.GermondJ. E.ChaintreauA.2000Vicinal diketone formation in yogurt: 13C precursors and effect of branched-chain amino acids. J.agr food chem. 483724731'},{id:"B58",body:'StorzG.ImlayJ. A.1999Oxidative stress. Curr.opin.microbiol. 2218894'},{id:"B59",body:'TalwalkarA.KailasapathyK.2004A review of oxygen toxicity in probiotic yogurts: Influence on the survival of probiotic bacteria and protective techniques. Compr.rev. food sci.f. 33117124'},{id:"B60",body:'TalwalkarA.KailasapathyK.2004The role of oxygen in the viability of probiotic bacteria with reference to L. acidophilus and Bifidobacterium spp. Curr.issues intest.microbiol. 5118'},{id:"B61",body:'BolducM. P.BazinetL.LessardJ.ChapuzetJ. M.VuillemardJ. C.2006Electrochemical modification of the redox potential of pasteurized milk and its evolution during storage. J agric.food chem. 541346514657'},{id:"B62",body:'BolducM. P.RaymondY.FustierP.CPChampagneVuillemard. J. C.2006Sensitivity of bifidobacteria to oxygen and redox potential in non-fermented pasteurized milk. Int.dairy j. 16910381048'},{id:"B63",body:'Dave RI, Shah NP1997Effect of cysteine on the viability of yoghurt and probiotic bacteria in yoghurts made with commercial starter cultures. Int.dairy j. 78-9: 537 EOF546 EOF'},{id:"B64",body:'Lourens-HattinghA.ViljoenB. C.1 EOF17 EOF'},{id:"B65",body:'MortazavianA. M.EhsaniM. R.MousaviS. M.ReinheimerJ. A.EmamdjomehZ.SohrabvandiS.RezaeiK.2006Preliminary investigation of the combined effect of heat treatment and incubation temperature on the viability of the probiotic micro-organisms in freshly made yogurt. Int.j. dairy technol. 591811'},{id:"B66",body:'KristoffersenT.1985Development of flavor in cheese. Milchwissenschaft. 404197199'},{id:"B67",body:'UrbachG.1995Contribution of lactic acid bacteria to flavour compound formation in dairy products. Int. dairy j. 58877903'},{id:"B68",body:'LedonH.IbarraD.2006Method for modifying hygienic, physico-chemical and sensory properties of cheese by controlling the redox potential. US 2009/0214705 A1. L’Air Liquide, France.'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"F. Martin",address:null,affiliation:'
Unité Procédés Alimentaires et Microbiologiques, UMR A 02.102, AgroSup Dijon/Université de Bourgogne, 1 esplanade Erasme, Dijon, France
Unité Procédés Alimentaires et Microbiologiques, UMR A 02.102, AgroSup Dijon/Université de Bourgogne, 1 esplanade Erasme, Dijon, France
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1. Introduction
In statistical physics only a few problems can be solved exactly. For complex problems, numerical methods can give exact results for problems that could only be solved in an approximate way. Numerical simulation can be a way to test the theory. The numerical results can be compared to the experimental results. The numerical simulation is placed between the fundamental and the experimental treatment; it has a quasi-experimental character (numerical experience). For problems of statistical physics, the most widely used simulation methods are the Monte Carlo method and the molecular dynamics method.
The first Monte Carlo simulation (MCS) was proposed by Metropolis et al. in 1953 [1]. The second Monte Carlo simulation was proposed by Wood and Parker in 1957 [2]. The obtained results were in good agreement with the experimental results of Bridgman [3] and those of Michels et al. [4]. In this method we attribute a series of initial positions chosen randomly to a system of N particles interacting through a defined potential. A sequence of particle configurations is generated by giving successive displacements to particles; we only retain configurations to ensure that the probability density is that of the chosen.
Molecular dynamics simulation (MDS) has been first introduced to simulate the behavior of fluids and solids at the molecular or atomic level. MDS was used for the first time by Alder and Wainwright in the late 1950s [5, 6] to study the interactions of hard spheres. The principle is the resolution of equations of motion for a hard sphere system in a simulation cell. The basic algorithm is Verlet’s algorithm [7].
In this chapter, we will present techniques of numerical simulations using the Monte Carlo method. We will present an application on the gas phase during plasma-enhanced chemical vapor deposition (PECVD) of thin films. The application concerns collisions between particles. Particles are in Brownian motion. Collisions, elastic or inelastic, are considered to be binary. Non-elastic collisions result in effective chemical reactions.
In Section 2, we cite some MCS and MDS works on PECVD processes. Section 3 presents general rules on numerical simulation methods. Section 4 presents how to simulate a physical problem using MCS? We present the Metropolis algorithm as a scheme to trait random configurations and different modules related to elaborate an MCS code. In Section 5, we apply the MCS on SiH4/H2 gas mixture during a PECVD process. Finally the conclusion summarizes the contents of the chapter.
2. Simulation works on the PECVD using MCS and MDS
The PECVD is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells and for film transistors and electronic devices [8, 9]. Reactions during plasma deposition are complex and are not understood completely.
Gorbachev et al. [10, 11, 12] have developed a model that is based on chemical reactions and different processes in a PECVD reactor. The model takes into account the formation of SinHm oligomers (n ≤ 5). It presents a simulation of the growth of the films. Gorbachev et al. found that Si2H5 and Si3H7 strongly influence the growth of the film [11].
Valipa et al. [13] calculated the β reactivity of the SiH3 radical on a surface of a silicon lattice plane during the growth of a-Si:H using MDS. The mechanisms of physical and chemical interactions of low temperature plasmas with surfaces can be explored using MDS [14].
For a CH4/H2 mixture, Farouk et al. used the Monte Carlo method (PIC/MC); they calculated the ionization rate of the plasma and the deposition rate of the thin layer [15]. Rodgers et al. [16] have developed three-dimensional Monte Carlo simulations of diamond (100) surface CVD. Other works on MCS are in [17, 18, 19].
In our previous works [20, 21, 22, 23, 24], we were interested in the study of the gas phase and the interaction of plasmas with the surface, for SiH4/H2 and CH4/H2 gas mixtures during PECVD processes. The used numerical simulation techniques were MCS and MDS. To complete the studies, we used the fluid model [25].
3. General rules for numerical simulation methods
The starting point of numerical simulation is a physical phenomenon; its purpose is to obtain useful physical results. Between these two points, several steps can be identified. These steps are general and they are applicable for MCS. The steps can be summarized as follows:
3.1 Definition of the physical phenomenon and main hypothesis
The physical phenomenon must be defined by the description of the dominant domain of physics. The main assumptions and simplifying approximations are necessary to understand the physical phenomenon and the design of the first model.
3.2 Definition of the mathematical model
Mathematical model requires a mathematical formulation of the problem. It may be a problem of elements or discrete object or a problem of a continuous medium; it may be a spatiotemporal problem or frequency problem and may be a deterministic or probabilistic problem.
It would be interesting to know the mathematical equations that govern the phenomenon:
The forces between particles and elements
The potential interaction
The determination of a time scale
The determination of a length scale
Definition of constant magnitudes of motion and equilibrium magnitudes
Continuity equations, balance equations, transfer equations, etc.
3.3 Elaboration of simulation code
The MCS technique has been chosen for this work; knowing its basic algorithm is necessary for elaborating the simulation. This step requires some actions:
Validation of the model on simple cases
Simulation calculation on complex phenomena
4. Algorithms and techniques for MCS
The MCS is based on a probabilistic process with a random choice of configurations and samples of the situation of the physical system. The two pedagogical examples most cited in the literature are the integration of a single variable function and Ising’s model of spin. In the following subsection, we define the integration of a single variable function. We introduce the Ising model at the end of Section 4.2.2.
4.1 Integration of function of a single variable
Calculation of the definite integral for a function f(x) of a single variable x on domain {a, b} has been proposed (Figure 1):
Figure 1.
The integral of a function f(x).
Let:
I=∫abfxdxE1
Let xi and yi be real random numbers (i = 1, 2,…, N), and let H be a real number greater than the f(x) for x belonging to the domain {a, b} (or x ∈ {a, b}).
Let r1 and r2 be two random numbers belonging to the domain {0, 1} according to a uniform distribution law. Generators (e.g., Ran, RANDOM, RANDUM, or other IMSL mathematical libraries) of random numbers can be used:
xi=a+r1b−aandyi=0+r2H−0E2
where xi and yi are random numbers (xi ∈ {a, b} and yi ∈ {0, H}).
The Monte Carlo (MC) method is based on a probabilistic process. Let N be the total number of cases chosen (possible cases). It is necessary to count the number of favorable cases (or the number of points below the curve y = f(x)); let yi ≤ f(xi)). The number of favorable cases is Nfav. When N➔∞, the value I of the integral is [26]:
I=NfavNb−aH−0.0=NfavNb−aHE3
An example [26] is the calculation of the value π by calculating the integral I on a quarter circle of unit radius (R = 1.0). The pairs of random numbers (xi, yi) satisfying the condition: xi2 + yi2 ≤ 1. The function f(x) is equal to 1−x2.
We take a = 0.0, b = 1.0, and H = 1.0.
For different values of N, we show that the numerical solution tends to π = 4I.
Although this integral is simple, it shows the strength and simplicity of the method. The technique can be generalized for the integration of multivariate functions.
We note that integration by the MC method is based on:
The choice of random configurations according to a uniform distribution law
Each configuration chosen is either favorable or unfavorable (the “or” is exclusive).
For statistical physics problems, the probabilistic choice of configurations is not always deterministic; the favorable and unfavorable cases are not exclusive. According to the Metropolis algorithm [26, 27], the steps of the simulation are:
Choice of a simulation cell of adequate shape to the studied phenomena. The size of the simulation cell is related to a scale of length characteristic of the forces and interaction potential of the studied phenomenon. This cell may contain Npc particles (and/or elements).
Choice of an initial configuration that responds to some physical and thermodynamic properties. The total or internal energy of the system is Ei.
Infinitesimal random displacement of a particle (or element of the system) and calculation of the new internal energy of the system Ef. This displacement is related to the physical magnitudes: time scale and length scale. The physical system tends toward a minimization of the internal energy of the systemwith some fluctuation. Let ΔE = Ef-Ei the fluctuation.
If ΔE ≤ 0; the new configuration is retained (favorable) and the different averages can be obtained; go to step (c).
If ΔE > 0; a random number ε is chosen such that 0 < ε < 1. Let the probability Pr equal to: Pr = exp. (−ΔE/kBT) (where kB is the Boltzmann constant and T is the temperature).
If ε < Pr, accept the move and in any case go back to step (c) for a new choice of an infinitesimal displacement (new configuration). Note that if such a trial move is rejected, the old configuration is again counted in the averaging with probability Pr.
Figure 2 shows how to choose between the selected configurations. Let ε be a random number following a uniform law; If ε1 ≤ Pr the configuration is retained, and if ε2 > Pr the configuration is rejected.
Figure 2.
Configuration choice according to Metropolis scheme.
Numerical simulation using the MC method is a very important tool for the study of static properties. The basic algorithm is based on probability notions. Understanding of the distribution function and/or interaction potentials is the heart of the calculation.
4.2.2 Thermodynamic quantities at equilibrium
In equilibrium statistical physics, the system has a certain probability that can be in any states. The probability of being in a state μ with energy H(μ) is given by the Boltzmann distribution P(μ):
Pμ=exp−Hμ/kBTZE4
where T is the absolute temperature and kB is called Boltzmann’s constant. It is conventional to denote the quantity (kBT)−1 by the symbol β. The normalizing factor Z, or partition function, is given by:
Z=∑μexp−Hμ/kBT=∑μexp−βHμE5
The average of a quantity Q fora system in equilibrium is:
<Q>=∑μQμPμ=1Z∑μQμexp−βHμE6
The internal energy U, is given by:
U=1Z∑μHμexp−βHμE7
which can be written in terms of a derivative of the partition function:
U=1Z∂Z∂β=−∂logZ∂βE8
From thermodynamics we have expressions for the specific heat C, the entropy S, and the Helmholtz free energy F:
C=∂U∂T=−kBβ2∂U∂β=−kBβ2∂2logZ∂β2E9
or
C=T∂S∂T=−β∂S∂βE10
and
S=−kBβ∂logZ∂β+kBlogZE11
and
F=U−TS=−kBlogZE12
We can calculate other parameters affecting the system.
The Monte Carlo method is an excellent technique for estimating probabilities, and we can take advantage of this property in evaluating the results. The simplest and most popular model of a system of interacting variables in statistical physics is the Ising model. It consists of spins σi which are confined to the sites of a lattice and which may have only the values (+1) and (−1). These spins interact with their nearest neighbors on the lattice with interaction constant J; they can interact with an external magnetic field B coupling to the spins. The Hamiltonian H for this model is [26]:
H=−J∑i,jσiσj−B∑iσiE13
The Ising model has been studied in one and two dimensions to obtain results of thermal properties, phase transition, and magnetic properties [26, 27, 28]. For chosen values of J and/or B, different steps may be taken for the calculations (simulation cell, initialization, configurations, boundary conditions, calculation algorithms). For any configuration, each spin takes the two possible directions. The detail of the calculation procedure is not the purpose of this chapter.
4.2.3 MCS module designs
4.2.3.1 Simulation cell and initialization
We give a system of N particles (atoms, molecules, ions or particles) placed in a cell of fixed volume, generally of cubic form. The initial positions may, depending on the case, be distributed randomly according to a certain law (uniform or otherwise) or have a given symmetry. In a fluid, a gas, or a plasma, the particles may have random positions in general; in a solid or surface, with a crystal structure, the particles take ordered positions. The choice of random initial positions allows great freedom on the choice of the number of particles in the cell.
At the first step, the particles are given velocities that are generally selected to have a zero total momentum. If the system is in thermodynamic equilibrium, the initial velocities will be randomly chosen according to a Maxwell-Boltzmann law. In the general case, the velocity distribution is according to the problem dealt with. All other phase properties can be initialized to the particles; the main thing is the conservation of the total quantities of the system.
4.2.3.2 Potentials of interaction
The particles interact with each other according to chosen interaction potentials. Since the interaction potentials are specific for each “numerical experiment,” the main part of the work consists in calculating the interaction energies for each proposed configuration.
The choice of interaction potentials is directly related to the mathematical formulation of the problem according to the state of the medium: fluid, gas, plasma, or solid. It can be Lennard-Jones potential, Coulomb potential, Debye potential, Morse potential, Stillinger-Weber potential, Born-Mayer potential, Moliere potential, or others.
4.2.3.3 Boundary conditions
In general, two main boundary conditions are used: periodic boundary conditions (PBC) and minimum image convention (MIC) [29].
To minimize the surface effect, periodic boundary conditions (PBC) [30] are invariably imposed. The simulation cell is reproduced throughout the space to form an infinite mesh. We can simulate the properties of an infinite system. The particles that we follow are in the central cell; if a particle crosses a wall with a certain velocity, its image returns with the same velocity by the opposite wall. Under these conditions, the number of particles in the central cell, and consequently the density, is constant. These conditions also allow the conservation of the energy and the momentum of the system and do not introduce periodic effects (because of the interaction between particles).
According to the hypotheses and according to the geometry of the problem, other boundary conditions are proposed [26]. For example, in order to model thin films, the simulation cells are longitudinal and parallel to the film; one uses PBC in the directions parallel to the film. In the direction normal to the film, free edge boundary conditions can be used. In such cases, it may be appropriate to also include surface fields and surface interactions. In this way, one can study phenomena such as wetting, interface localization-delocalization transitions, surface-induced ordering and disordering, etc.
The core of the program includes calculating the potential energies of particle configuration and particle collisions. The interactions and collisions between particles can be elastic or inelastic; they can be binary or collective. For computation, the interaction energy of a particle with its neighbors is carried out by refocusing a base cell on the particle. This particle only interacts with particles in this region. This is called the “minimal image convention” (MIC) [1].
4.2.3.4 Sampling of random data
Generally, a RANDOM generator of real random numbers ri belonging to the domain {0, 1} (or ri ∈ {0, 1} is available. This distribution law is uniform.
To have a real random number xi belonging to the domain {a, b} (or xi∈ab) according to a law of uniform distribution, we have:
xi=a+rib−aE14
To have a real random number xi belonging to the domain {a, b} (or xi ∈ {a,b}) according to a formula (or law) of nonuniform distribution f(x), a histogram technique is used. Let Nm be the number of intervals. If the mesh is regular (Figure 3):
Figure 3.
Random number selection according to f (x) distribution.
Δx=b−a/NmE15
We define:
fi=fxifori=0,….,mand:xi=a+i.ΔxE16
We define the sequence:
S0=0and:Si+1=Si+Δxfxi+fxi−1/2E17
and the sequence:
rx0=0etrxi=Si/SmE18
Hence each real random number ri belongs to the domain {0, 1} (where ri ∈ {0, 1}) (according to the uniform law); this number belongs to the domain {rxj-1, rxj}. It corresponds to a random value xran of the domain {xj-1, xj}; this number satisfies the formula (or the law) of nonuniform distribution f(x).
This technique can be generalized for a nonuniform distribution law f(x) with an irregular mesh Δxi, or with tabular data f(xi) with i = 1,…, m.
The technique can be generalized, too, for a discrete distribution law f(i) with i = 1,…, m.
In the literature, the reader can find simple algorithms for the choice of random numbers of some simple functions (Gaussian, etc.).
4.2.3.5 Control of the evolution of the physical system
It is necessary to find some parameters allowing the control of the smooth course of the evolution of the system. We must look for the constants of movement. For example for an isolated system, we have the conservation of the total energy and the quantity of matter.
4.2.3.6 Statistical calculations
By using the numerical simulation, it is possible to calculate many spatiotemporal quantities F(r,t). These quantities can be positions, speeds, kinetic moments, particle energies, concentrations, transport coefficients, etc. It would then be possible to calculate all other quantities related to F(r,t).
For the calculation of the averages, one can note the quantities on the space, on the time or on both. The histogram methods can be used. Static or dynamic distribution functions and spatial or temporal correlation functions can be calculated. It should be noted that the SMC is much more adequate for static properties because of the probabilistic choice of configurations.
Any calculated function or parameter F(r,t) can be used for another application in another calculation program.
4.3 Other large methods of Monte Carlo simulation
In the MCS model discussed extensively in this chapter, it’s more about collisions between particles. It’s particle-particle MCS or PP-MCS. In many problems of physics, the general idea is the same, but the applications and proposed models are numerous.
Other MCS models, named particle-in-cell MCS (PIC-MCS), are based on particle-cell interactions. In these last models, we also use a probabilistic choice of configurations and small variations in the state of the system (following the Metropolis algorithm); the interaction is between the particle with a cell, a mesh, or a drop. The parameters and variables of the cell, although local and instantaneous, are macroscopic. These parameters and variables can be thermodynamic, fluid, or electromagnetic. An example of the model based on PIC-MCS is described by Mattei et al. [31] for simulation of electromagnetic particle-in-cell collision in inductively coupled plasmas. Several works can be found in the literature on this same line of work. Other MCS models using particles may be considered. [32].
For statistical physics problem solving (such as thin film deposition problems), MCS models use experimental, numerical, or theoretical data from other methods and models. Models can be improved to hybrid models. In the hybrid models, connections between two modules can be realized. The first module is MCS; the second module is fluid, electromagnetic, or other. An example of a three-module hybrid model is presented by Mao and Bogaerts [33] to study gas mixtures in PECVD system. The three modules are MCS, fluid, and electromagnetic. The first module EM calculates the electromagnetic fields by solving Maxwell equations. These fields are used as inputs in the module MCS, where the electron density, electron temperature, electron energy distribution function, and electron impact reaction rates can be computed with a Monte Carlo procedure. Subsequently, the module fluid calculates densities and fluxes of the various plasma species (i.e., heavy particles and electrons) with continuity equations and the electrostatic field with Poisson’s equation. This electrostatic field is used as input again in the EM. This cycle is iterated until convergence. The schematic of the hybrid model is given in Figure 4.
Figure 4.
Schematic of a hybrid model of three modules used to study gas mixtures in the PECVD [33].
To solve statistical physics problems with evolutions as a function of time, kinetic models of MCS (kMCS) are used. Using kMCS, Battaile and Srolovitz [17] described kinetic phenomena of the diffusive motion of a single interstitial atom in a close-packed metal crystal. The motion of the interstitial atom is usually limited to two types: vibration of the atom around the center of the interstitial hole in which it resides and hops to nearest-neighbor interstitial sites. The atom can hop into any of the nearest-neighbor interstitial sites; it executes a random walk. In an MC simulation of this diffusion process, the new position of the interstitial atom is chosen at random from a list of the adjacent interstitial sites.
Other CVD and PECVD works on MCS are presented in Ref.s [15, 34, 35, 36, 37, 38]. They show how MCS methods can study properties of gas mixtures and properties of the growth of thin films.
5. Example of application: Monte Carlo simulation of a gas mixture in the PECVD
In this section, we present an example of PP-MCS of collisions and reactions in gas phase of SiH4/H2 mixture used in PECVD process. Some paragraphs have been treated in previous works [21, 24].
5.1 Description of the physical phenomenon
We use a MCS to study collisions and chemical reactions in gas phase of SiH4/H2 mixture used in the PECVD process. In this phase, important reactions have been identified that contribute to the production and the consumption of hydrogen (H), silylene (SiH2), and silyl (SiH3). The hydrogen consumption reactions SiH4 + H → SiH3 + H2 and SiH3 + H → SiH2 + H2 are found to play a central role in deciding the distribution of hydrogen [39].The plasma chemistry indicates that H atoms and SiH3 radicals play an important role in the a-Si:H deposition process [40]. Experimentally, it is generally accepted that SiH3 radicals dominate a-Si:H and μc-Si film growth from SiH4 plasmas in the PECVD; it is the key precursor of a-Si:H deposition [41]. The proposed MCS allowed to get the ratio SiH2/SiH3 and mean value of densities of species. It provides information on SiH4 dissociation and on the production of SiH3, H, SiH2, and Si2H6 and other important parameters.
The plasma in the PECVD reactor is weakly ionized. For our study, the mixture gas contains 22% of SiH4 and 78% of H2; the pressure is 100 mtorr, the temperature of the gas ranges from 373 to 723 K, the electron temperature is about 2.5 eV, and the electron density is 3. 108 cm−3. The process is considered to be stationary. We take into account electrons and eight neutral species (SiH4, SiH3, SiH2, H, H2, Si2H6, Si2H5, SiH). Reactions taken into account include seven electron-neutral and 14 neutral-neutral reactions. Table 1 shows the 21 reactions and rate constants Kreac. At low temperature, the neutrals interact occasionally with each other and move under the effect of thermal agitation; their velocity distribution function is Maxwell-Boltzmann distribution. Electrons have the mean velocity with kinetic energy Te.
List of gas phase reactions and corresponding rate constants [24].
Let Kreaccons and Kreacprod be the rate constants of the consumption and the production of species A. The chemical reaction for the consumption of A is as:
a·A+b·B→Kreacconsc·C+d·D
And chemical reaction for the production of A is as:
a\'·A\'+b\'·B\'→Kreacprodc\'·A+d\'·D\'
Rate production and consumption for any species A are taken as:
5.2 Description of Monte Carlo simulation technique
5.2.1 Simulation cell and phase coordinates
The MCS is based on binary collisions at the microscopic level. Elastic collisions are between all particles, and inelastic collisions (or effective collisions) are those that result in a chemical reaction. A chemical reaction needs a collision involving at least two particles (atoms, ions, electrons, or molecules). According to kinetic theory, gases consist of particles in random motion. These particles are uniformly distributed in a cell which has a parallelepiped form of sizes Lx, Ly, and Lz (Figure 5). These particles move in a straight line until they collide with other particles or the walls of their container. Dimensions and volume of Monte Carlo cell must take into consideration the mean free path of species.
Figure 5.
Form of the simulation cell.
Let ni be the density of neutral spice i (i = 1,…, 8). The first particle i is randomly chosen according to a probability of neutral species Prsp,I (nonuniform discrete distribution) given by:
Prsp,i=ni∑j=18njE20
The chosen particle takes randomly three components of space in cell ri(xi, yi, zi) according to the normal distribution (nonuniform distribution). It takes also randomly three components of velocity vi (vxi, vyi, vzi) according to Maxwell-Boltzmann distribution.
5.2.2 Treatment of elastic and inelastic collisions
Let ni and nj be the densities of species i and j in the gas and Vij the relative velocity between the two species i and j.
According to the kinetic theory of gases, we have for an incident particle i on a target particle j the average collision frequency νij as:
υij=Vijnj<σij>E21
where <sij> is the cross section of the particle j.
The mean free path <λι> of species i is:
<λi>=1nj<σij>E22
The time between two collisions τij is then:
τij=<λi>Vij=1υijE23
For chemical effective reactions (inelastic collisions) between two reactive species i and j giving products i’ and j’, the rate constant reaction verifies [45]:
kij=<σijVij·Vij>E24
General rules of collision theory are applied:
The new velocities of the colliding particles are calculated using conservation of energy and momentum for elastic collisions.
Conservation of total energy as isolated system.
Movement of the center of mass and relative motion around the center of mass.
The reader can refer to some fundamental physics books that deal with general notions of collisions and corresponding parameters [45, 46, 47, 48].
The plasma in the PECVD reactor is weakly ionized. At low temperature, particles interact occasionally with each other and move under the effect of thermal agitation. In reality, only a small fraction of collisions are effective (result in a chemical reaction) [21].
In our MCS, after traveling a random walk given by a Gaussian distribution, the first chosen particle collides with a second particle (molecule, atom, radical, or electron). The last particle j is randomly chosen according to a (i-j) collision probability Prcol,j (nonuniform discrete distribution) given by:
Prcol,j=νij∑k=19νikE25
where νij is the neutral-neutral or electron-neutral collisional frequency. The collision theory indicates that the collision between molecules can provide the energy needed to break the necessary bonds so that new bonds can be formed [49]. Particles must have sufficient energy to initiate the reaction (activation energy), so the two chosen particles must have kinetic energy equal to or greater than the barrier energy (Ea) of a gas phase reaction. The difference between the kinetic energy of the two particles and the activation energy define the kind of collision (effective or not effective).
The activation energy is given by:
Ea=−kBTlnKreac/νijE26
where the pre-exponential factor is assumed to be the collision frequency factor and Kreac is the rate constant of the gas phase reaction.
The two colliding particles (e.g., the electron and SiH4 molecule) can interact by several reactions (R1, R2, R3, and R4 in Table 1); we choose randomly one of gas phase reactions occurring according to a, nonuniform discrete distribution reaction probability Prreac (i,j):
Prreacij=Kreacij∑KreacijE27
where ∑Kreacij is the sum of all rate constants of possible reactions between i and j.
All chemical systems go naturally toward states of minimum Gibbs free energy [21, 24]. A chemical reaction tends to occur in the direction of lower Gibbs free energy. To determine the direction of the reaction that is taking place, we use the old and new values of Kreac and the equilibrium constant with reactants and product concentrations. Each set of binary collisions can be related or converted into time. As cited in section (a), Table 1 gives gas phase reactions and corresponding rate constants used in this MCS.
To continue the simulation, after the elastic collision, particle i takes new values of components velocity and new mean free path; mean free path is taken from a normal (nonuniform) distribution (Gaussian distribution). If the collision is inelastic, we have to take a new particle.
From Metropolis algorithm, the scheme of this MCS is as follows:
Choices of particle of spice i with random position, velocity, and mean free path; periodic boundary conditions are used to keep particles in the elementary cell.
Choices of random collision with a spice j.
Study of collision type (elastic, inelastic). If the collision is elastic the particle i move with a new velocity and mean free path, and we return to step (b). If the collision is inelastic particles i and j give new particles i’ and j’, according to Metropolis scheme, and we return to step (a) or (b). Periodic boundary conditions are used to keep particles in the elementary cell.
At each step, we can note the different statistics.
5.2.3 The choice of simulation parameters
Once the species are selected for the simulation model, an estimate of species densities should be made. Following the model of interaction and collisions between particles (binary, collective, etc.), a first choice of the minimum number Ni of particles of each species is made. A first estimate of the sizes (Lx, Ly, Lz) of the elementary cell is made.
The study of the types of interaction potentials and the calculation of the approximate values of the force ranges, the kinetic energies, the internal energies, and the energies of activation make it possible to correct the minimal numbers Ni of particles and the sizes (Lx, Ly, Lz) of the elementary cell.
Let kp be the number of a species, kp = 1,…, 9. The minimal numbers Qnp(kp) and the sizes (Lx, Ly, Lz) have to be discussed for statistical calculations.
For numerical programming, according to the programming language used and according to the size (or the computational capacity) of the computer, it is necessary to find a judicious choice of the tables of integer or real values and which values would be useful to save all during simulation. Let Ncol,m be the maximum number of elastic collisions per particle, and let Ncycle be the number of cycles to average the simulation calculations.
For this MCS, the numerical chosen values are in Table 2.
Cell dimensions and steps for collisions
Number of species Kp
Initial number of particles in cell
Lx (m)
4.68 10−6
1
Qnp(SiH4)
Qnp1
Ly (m)
4.68 10−6
2
Qnp(SiH3)
10
Lz (m)
20.0 10−3
3
Qnp(SiH2)
10
4
Qnp(H)
10
Ncol,m
500
5
Qnp(H2)
Qnp5
Ncycle internal cycle
2000
6
Qnp(Si2H6)
10
Ncycle external cycle
200,000
7
Qnp(SiH)
10
8
Qnp(Si2H5)
10
9
Qnp(e)
Qnp9
Table 2.
Used quantities and parameters in calculations for the gas temperature Tg = 520 K.
For radicals (e.g., SiH3), particle numbers Qnp(k) are very small; we take Qnp(k) = 10. These numbers cannot take value 1 or 0, even if a species k is in trace form in the gas. The value 0 for a species k means that any other species k’ does not make a collision with the species k; and the value 1 means that we have no collisions between particles of the same species in the cell.
Qnp1, Qnp5, and Qnp9 are calculated from the volume of cell, the pressure, the temperature, and the total number of particles in the cell (Qnp1 = 0.81187824 * 109; Qnp5 = 0.20296956 * 109; Qnp9 = 131).
5.2.4 Calculation of statistical properties and some results of the calculations
As we have chosen a stationary regime, we must reach the values and properties at equilibrium. The results of the simulation show this trend. In MCS, averaged values, distribution functions, autocorrelation functions, and correlation functions can be calculated. To ensure rapid convergence of calculations, it would be useful to look for statistically symmetric (or stationary or unsteady) parameters [26, 50].
As an example for our MCS calculation, we have:
The number of Si2H6, SiH, and Si2H5 particles reaching the surface is negligible.
Let Ns,i and Ns, H2 be the densities of a species i and H2 reaching the surface. The ratios Ns,i/Ns, H2 are too small (Table 3).
Let Ns,i be the density of a species i reaching the surface and Nv,i the density of same species i in volume. The ratios Ns,i/Nv,i are too small (Table 4); the surface effect is negligible.
The reactions begin with the dissociation (consumption) of H2 and SiH4 by R5, R1, and R2 reactions.
The production of SiH3 is done by R8, and then there is production of SiH2 by R12.
The reaction R2: SiH4 + e → SiH2 + 2H + e plays the central role in SiH4 dissociation by electron impact [24]. This result is compatible with [39].
The second important chemical reaction in the SiH4 dissociation is R1: SiH4 + e → SiH3 + H + e [24]. This result is compatible with that of Perkins et al. [51] and that of Doyle et al. [52].
Type
H2
SiH4
H
SiH3
SiH2
Ns,i/Ns, H2
1
0.23
1.67 10−4
8.60 10−5
9.86 10−6
Table 3.
Ratios Ns,i/Ns, H2 of particles reaching the surface compared to H2.
Type
SiH4
SiH3
SiH2
v, j
6.695 10−6
7.965 10−6
775 10−6
Table 4.
Ratios Ns,i/Nv,i of particles reaching the surface compared to volume.
6. Conclusions
MCS is a widely used method in statistical physics to study thermodynamic, structural, or phase properties. It is based on random and probabilistic processes. The purpose of this chapter is to present the technique for general use in physics for the study of thin film deposition problems. The technique can be generalized to other fields of science: biology, economics, transportation, and social sciences.
We started by presenting general rules for numerical simulation methods. Metropolis algorithm has been considered as the basic algorithm. After, we presented the different steps for the realization of a MCS code. We chose the particle-particle model MCS (PP-MCS) to explain the different steps and procedures to be applied in the deposition of thin layers by PECVD processes. We have shown that this technique can be generalized to the particle-in-cell MCS (PIC-MCS) case or kinetic MCS (kMCS), as it can be joined with other modules to give hybrid models. It is important to know how to choose random configurations from the laws or probability distributions in the system.
A numerical application is presented for collisions in a SiH4/H2 gas mixture in the PECVD process. A preliminary work of determination of the chemical reactions between molecules and radicals is made. A choice of the simulation cell is made, and the definition of the probabilities of the collisions between peers is made. The Metropolis algorithm makes it possible to follow the various elastic and inelastic collisions; it also makes it possible to make the statistics of the interactions with the surface. The results are compatible with [39, 51, 52].
Other questions may be asked to account for molecular ions, surface and volume kinetics, or thin film formation. The techniques and different models of the MCS (PP-MCS, MCS-PIC, kMCS) allow taking care of these questions.
The interconnection of the MCS with other models (MDS, hybrid model, fluid model, electromagnetic model, etc.) would allow answering more questions. The methods can be applied to other specialties than the physical sciences.
\n',keywords:"MCS, potential, reaction rates, collisions, thin film deposition",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/68593.pdf",chapterXML:"https://mts.intechopen.com/source/xml/68593.xml",downloadPdfUrl:"/chapter/pdf-download/68593",previewPdfUrl:"/chapter/pdf-preview/68593",totalDownloads:561,totalViews:0,totalCrossrefCites:0,dateSubmitted:"March 25th 2019",dateReviewed:"July 11th 2019",datePrePublished:"August 19th 2019",datePublished:"December 18th 2019",dateFinished:null,readingETA:"0",abstract:"Many physical phenomena can be modeled using Monte Carlo simulation (MCS) because it is a powerful tool to study thermodynamic properties. MCS can be used to simulate interactions between several particles or bodies in the presence of local or external fields. The main idea is to create a high number of different random configurations; statistics can be taken according to appropriate algorithms (Metropolis algorithm). In this chapter, we present basic techniques of MCS as the choice of potential, reaction rates, simulation cell, random configurations, and algorithms. We present some principal ideas of MCS used to study particle-particle collisions in the gas and in plasmas. Other MCS techniques are presented briefly. A numerical application is presented for collisions in gas phase during thin film deposition by plasma-enhanced chemical vapor deposition (PECVD) processes. Parameters and results of the simulation are studied according to a chosen reactor and mixture.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/68593",risUrl:"/chapter/ris/68593",signatures:"Fethi Khelfaoui and Oumelkheir Babahani",book:{id:"8190",title:"Theory, Application, and Implementation of Monte Carlo Method in Science and Technology",subtitle:null,fullTitle:"Theory, Application, and Implementation of Monte Carlo Method in Science and Technology",slug:"theory-application-and-implementation-of-monte-carlo-method-in-science-and-technology",publishedDate:"December 18th 2019",bookSignature:"Pooneh Saidi Bidokhti",coverURL:"https://cdn.intechopen.com/books/images_new/8190.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"22336",title:"Dr.",name:"Pooneh",middleName:null,surname:"Saidi",slug:"pooneh-saidi",fullName:"Pooneh Saidi"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"299501",title:"Prof.",name:"Fethi",middleName:null,surname:"Khelfaoui",fullName:"Fethi Khelfaoui",slug:"fethi-khelfaoui",email:"fethi.khelfaoui@gmail.com",position:null,institution:{name:"Université Kasdi Merbah Ouargla",institutionURL:null,country:{name:"Algeria"}}},{id:"300166",title:"Dr.",name:"Oumelkheir",middleName:null,surname:"Babahani",fullName:"Oumelkheir Babahani",slug:"oumelkheir-babahani",email:"babahaniok@hotmail.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Simulation works on the PECVD using MCS and MDS",level:"1"},{id:"sec_3",title:"3. General rules for numerical simulation methods",level:"1"},{id:"sec_3_2",title:"3.1 Definition of the physical phenomenon and main hypothesis",level:"2"},{id:"sec_4_2",title:"3.2 Definition of the mathematical model",level:"2"},{id:"sec_5_2",title:"3.3 Elaboration of simulation code",level:"2"},{id:"sec_7",title:"4. Algorithms and techniques for MCS",level:"1"},{id:"sec_7_2",title:"4.1 Integration of function of a single variable",level:"2"},{id:"sec_8_2",title:"4.2 Principle of the MCS model",level:"2"},{id:"sec_8_3",title:"4.2.1 Calculation algorithm (Metropolis algorithm)",level:"3"},{id:"sec_9_3",title:"4.2.2 Thermodynamic quantities at equilibrium",level:"3"},{id:"sec_10_3",title:"4.2.3 MCS module designs",level:"3"},{id:"sec_10_4",title:"4.2.3.1 Simulation cell and initialization",level:"4"},{id:"sec_11_4",title:"4.2.3.2 Potentials of interaction",level:"4"},{id:"sec_12_4",title:"4.2.3.3 Boundary conditions",level:"4"},{id:"sec_13_4",title:"4.2.3.4 Sampling of random data",level:"4"},{id:"sec_14_4",title:"4.2.3.5 Control of the evolution of the physical system",level:"4"},{id:"sec_15_4",title:"4.2.3.6 Statistical calculations",level:"4"},{id:"sec_18_2",title:"4.3 Other large methods of Monte Carlo simulation",level:"2"},{id:"sec_20",title:"5. Example of application: Monte Carlo simulation of a gas mixture in the PECVD",level:"1"},{id:"sec_20_2",title:"5.1 Description of the physical phenomenon",level:"2"},{id:"sec_21_2",title:"5.2 Description of Monte Carlo simulation technique",level:"2"},{id:"sec_21_3",title:"5.2.1 Simulation cell and phase coordinates",level:"3"},{id:"sec_22_3",title:"5.2.2 Treatment of elastic and inelastic collisions",level:"3"},{id:"sec_23_3",title:"Table 2.",level:"3"},{id:"sec_24_3",title:"Table 3.",level:"3"},{id:"sec_27",title:"6. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equation of state calculations by fast computing machines. The Journal of Chemical Physics. 1953;21:1087-1092. DOI: 10.1063/1.1699114'},{id:"B2",body:'Wood WW, Parker FR. Monte Carlo equation of state of molecules interacting with the Lennard-Jones potential. The Journal of Chemical Physics. 1957;27:720-733. 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DOI: 10.1103/PhysRev.159.98'},{id:"B8",body:'Wong J, Kherani NP, Zukotynski S. Monte Carlo modeling of the dc saddle field plasma: Discharge characteristics of N2 and SiH4. Journal of Applied Physics. 2007;101:013308-013314. DOI: 10.1063/1.2409566'},{id:"B9",body:'Matsuda A, Nomoto K, Takeuchi Y, Suzuki A, Yuuki A, Perrin J. Temperature dependence of the sticking and loss probabilities of silyl radicals on hydrogenated amorphous silicon. Surface Science. 1990;227:50-56. DOI: 10.1016/0039-6028(90)90390-T'},{id:"B10",body:'Gorbachev YE, Zetevakhin MA, Krzhizhanovskaya VV, Shveïgert VA. Special features of the growth of hydrogenated amorphous silicon in PECVD reactors. Journal of Technical Physics. 2000;45:1032-1041. DOI: 10.1134/1.1307013'},{id:"B11",body:'Gorbachev YE. Effect of oligomers on the growth of amorphous silicon films in a PECVD reactor. Technical Physics. 2006;51:733-739. DOI: 10.1134/S1063784206060089'},{id:"B12",body:'Gorbachev YE, Zetevakhin MA, Kaganovich ID. Simulation of the growth of hydrogenated amorphous silicon films from an RF discharge plasma. Journal of Technical Physics. 1996;41:1247-1258'},{id:"B13",body:'Valipa MS, Aydil ES, Maroudas D. Atomistic calculation of the SiH3 surface reactivity during plasma deposition of amorphous silicon thin films. Surface Science. 2004;572:L339-L347. DOI: 10.1016/j.susc.2004.08.029'},{id:"B14",body:'Graves DB, Brault P. Molecular dynamics for low temperature plasma-surface interaction studies. Journal of Physics D. 2009;42:1-27. DOI: 10.1088/0022-3727/42/19/194011'},{id:"B15",body:'Pandey SC, Singh T, Maroudas D. Kinetic Monte Carlo simulations of surface growth during plasma deposition of silicon thin films. The Journal of Chemical Physics. 2009;131:1-12. DOI: 10.1063/1.3152846'},{id:"B16",body:'Rodgers WJ, May PW, Allan NL, Harvey JN. Three-dimensional kinetic Monte Carlo simulations of diamond chemical vapor deposition. The Journal of Chemical Physics. 2015;142:214707. DOI: 10.1063/1.4921540'},{id:"B17",body:'Battaile CC, Srolovitz DJ. Kinetic Monte Carlo simulation of chemical vapor deposition. Annual Review of Materials Research. 2002;32:297-319. DOI: 10.1146/annurev.matsci.32.012102.110247'},{id:"B18",body:'YangY G, ZhouX W, Johnson RA, Wadlty HNG. Monte Carlo simulation of hyperthermal physical vapor deposition. Acta Materialia. 2001;49:3321-3332. DOI: 10.1016/S1359-6454(01)00139-2'},{id:"B19",body:'Chen Z-Y, Zhu Y, Chen S-H, Qiu Z-R, Jiang S-J. The kinetic process of non-smooth substrate thin film growth via parallel Monte Carlo method. Applied Surface Science. 2011;257:6102-6106. DOI: 10.1016/j.apsusc.2011.02.004'},{id:"B20",body:'Babahani O, Khelfaoui F, Meftah MT. Analytical calculation of site and surface reaction probabilities of SiHx radicals in PECVD process. The European Physical Journal Applied Physics. 2013;62:10301-10307. DOI: 10.1051/epjap/2013120345'},{id:"B21",body:'Babahani O. 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Physikalishce Zeitschrift. 1912;13:297-309'},{id:"B31",body:'Mattei S, Nishida K, Onai M, Lettry J, Tran MQ, Hatayama A. A fully-implicit particle-In-cell Monte Carlo collision code for the simulation of inductively coupled plasmas. Journal of Computational Physics. 2017;350:891-906. DOI: 10.1016/j.jcp.2017.09.015'},{id:"B32",body:'Hockney RW, Eastwood JW. Computer Simulation Using Particles. IOP Publishing Ltd; 1988'},{id:"B33",body:'Mao M, Bogaerts A. Investigating the plasma chemistry for the synthesis of carbon nanotubes/nanofibers in an inductively coupled plasma enhanced CVD system: Effect of different gas mixtures. Journal of Physics D: Applied Physics. 2010;43:205201. DOI: 10.1088/0022-3727/43/20/205201'},{id:"B34",body:'Battaile CC, Srolovitz DJ. A kinetic Monte Carlo method for the atomic-scale simulation of chemical vapor deposition: Application to diamond. Journal of Applied Physics. 1997;82:6293. DOI: 10.1063/1.366532'},{id:"B35",body:'Lothar K, Kuhn Frank M, Olaf D. Kinetic Monte Carlo simulations of surface reactions on supported nanoparticles: A novel approach and computer code. The Journal of Chemical Physics. 2015;143:044108. DOI: 10.1063/1.4926924'},{id:"B36",body:'May PW, Harvey JN, Allan NL, Richley JC, Mankelevich Yu A. Simulations of chemical vapor deposition diamond film growth using a kinetic Monte Carlo model and two dimensional models of microwave plasma and hot filament chemical vapor deposition reactors. Journal of Applied Physics. 2010;108:114909. DOI: 10.1063/1.3516498'},{id:"B37",body:'Harris SJ. Mechanism for diamond growth from methyl radicals. Applied Physics Letters. 1990;56:2298. DOI: 10.1063/1.102946'},{id:"B38",body:'May PW, Harvey JN, Allan NL, Richley JC, Mankelevich Yu A. Simulations of chemical vapor deposition diamond film growth using a kinetic Monte Carlo model. Journal of Applied Physics. 2010;108:014905. DOI: 10.1063/1.3437647'},{id:"B39",body:'Aman-ur-Rehman, Kwon HC, Park WT, Lee JK. A study of the role of various reactions on the density distribution of hydrogen, silylene, and silyl in SiH4/H2 plasma discharges. Physics of Plasmas. 2011;18:093502. DOI: 10.1063/1.3630933'},{id:"B40",body:'Moravej M, Babayan SE, Nowling GR, Yang X, Hicks RF. Plasma enhanced chemical vapour deposition of hydrogenated amorphous silicon at atmospheric pressure. Science and Technology. 2004;13:8-14'},{id:"B41",body:'Hoefnagels JPM, Barrell Y, Kessels WMM, Van de Sanden MCM. Inflow and shock formation in supersonic, rarefied plasma expansions. Journal of Applied Physics. 2004;96:4094'},{id:"B42",body:'Gorbachev YE, Zatevakhin MA, Krzhizhanovskaya VV, Shveigert VA. Special features of the growth of hydrogenated amorphous silicon in PECVD reactors. Technical Physics. 2000;45:1032-1041. DOI: 10.1134/1.1307013'},{id:"B43",body:'Perrin J, Leroy O, Bordage MC. Cross-sections, rate constants and transport coefficients in silane plasma chemistry. Contributions to Plasma Physics. 1996;36:3-49. DOI: 10.1002/ctpp.2150360102'},{id:"B44",body:'Amanatides E, Stamou S, Mataras D. Gas phase and surface kinetics in plasma enhanced chemical vapor deposition of microcrystalline silicon: The combined effect of RF power and hydrogen dilution. Journal of Applied Physics. 2001;90:5786-5798. DOI: 10.1063/1.1413241'},{id:"B45",body:'Moison M, Pelletier J. Physique Des Plasmas Collisionnels: Application Aux décharges Haute fréquence. France: EDP Sciences; 2006'},{id:"B46",body:'Delcroix J-L, Bers A. Physique Des Plasmas 1. Paris: Inter Editions/CNRS Editions; 1994'},{id:"B47",body:'Atkins PW, de Paula J. Chimie Physique. 4th ed. De Boeck; 2015. 973 p. ISBN-10: 2804166511'},{id:"B48",body:'Atkins PW. Eléments de Chimie Physique. De Boeck Université; 1998. 512 p. ISBN-10: 2744500100'},{id:"B49",body:'Moore JT, Hren C, Mikulecky PJ. U Can: Chemistry I for Dummies. Wiley; 2015. 456 p. ISBN: 978-1-119-07940-8'},{id:"B50",body:'Allen MP, Tildesley DJ. Computer Simulation of Liquids. Oxford: Clarendon Press; 1987'},{id:"B51",body:'Perkins GGA, Austin ER, Lampe FW. The 147-nm photolysis of monosilane. Journal of the American Chemical Society. 1979;101:1109-1115'},{id:"B52",body:'Doyle JR, Doughty DA, Gallagher A. Silane dissociation products in deposition discharges. Journal of Applied Physics. 1990;68:4375'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Fethi Khelfaoui",address:"fethi.khelfaoui@gmail.com;, khelfaoui.fe@univ-ouargla.dz",affiliation:'
Physics Department, RPPS Laboratory, Faculty of Mathematics and Matter Sciences, Kasdi Merbah Ouargla University, Algeria
Physics Department, RPPS Laboratory, Faculty of Mathematics and Matter Sciences, Kasdi Merbah Ouargla University, Algeria
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However, subunit vaccines are weak immunogens and thus have limited capacity in eliciting the humoral and cellular immunity against pathogens. Recently, nanoparticles (NPs) formed with certain small molecules through self-assembly have been employed as an effective carrier for subunit vaccines to play roles of adjuvant, delivery and stabilization of antigens, thus engendering a vaccine adjuvant-delivery system (VADS), which shows promises to overcome the hurdles in developing subunit vaccines. In particular, the small molecule-self-assembled NPs as a VADS can not only deliver vaccine ingredients to immune cells but also influence the immunoresponse toward a Th1 (type 1 T helper cell) and Th2 balanced pathway to establish both humoral and cellular immunity. 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He has worked extensively for health systems strengthening contributing to health policies formulation, decentralization, public private partnership, strengthening information system, building capacity of the health managers, establishing community health revolving fund, and introducing community governance in health system. He has worked with projects funded by bilateral and multilateral donors such as Global Health Canada, USAID, World Bank, JSI, KfW, DFID, France, Italy and Norway etc.\nHe has secured research grants and fellowships from World Health Organization, USAID, Aga Khan Foundation, Liverpool School of Tropical Medicine, David & Lucile Packard Foundation, and Higher Education Commission of Pakistan. His flagship work on health seeking behaviors, social determinants and health services utilization has got a cutting edge in the field. 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