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Nanomaterials 2020, 10, 555 9 of 12 Nanomaterials 2020, 10, 555 10 of 13 Figure 6. Absorbance over a treatment time of t = 120 s for stock solution S3 and resulting determination Figure 6. Absorbance over a treatment time of t = 120 s for stock solution S3 and resulting of the critical time t determination of the critical time tcrit for plasma treatment. obtained by [52] c Ag0 − c Ag0 1 max t crit 3.4. Reaction Rate Coefficient 3.4. Reaction Rate Coefficient for plasma treatment. A parameter of the reaction kinetics is the reaction rate coefficient k of the silver nanoparticle synthesis, which can be determined by in situ UV/VIS spectrometry. For this purpose, the following A parameter of the reaction kinetics is the reaction rate coefficient k of the silver nanoparticle simplifications have to be applied. The reduction of silver ions is mainly affected directly by electrons, synthesis, which can be determined by in situ UV/VIS spectrometry. For this purpose, the following according to Equation (1). The plasma provides a large amount of electrons for the reduction of silver simplificiaotnisoantsthhe ainvterfatoce betwaepenpliqeudid. aTnhdeplraesmdua,cwtihoinch iosfthseilrveaesroniownhsy tihse rmeaacitniolnycoarfrfeespctoends dtoiraectly by electrons, according to Equation (1). The plasma provides a large amount of electrons for the pseudo-first order: This allows the reaction to be determined by +0 Ag →Ag. (3) reduction of silver ions at the interface between liquid and plasma, which is the reason why the reaction corresponds to a pseudo-first order: + + +0−kt cAgA=gc→AAgg·e., (4) (3) + Thiswahlelroewk sistherreeaactciotinornateocobeffidceietnetr,mc (iAnged) ibsythe silver ion concentration at a treatment time t, and t0 t c (Ag+) is the initial silver ion concentration before treatment. The reaction rate coefficient k can be 0 obtained by [52] 𝑐 Ag+ = 𝑐 Ag+ ∙ e-kt, (4) + + ctAg 1 where k is the reaction rate coefficient, ct(Ag ) is the silver ion concentration at a treatment time t, and k=−ln · , (5) c Ag+ t + c0(Ag ) is the initial silver ion concentration befor0e treatment. The reaction rate coefficient k can be k=−ln ·. + (6) 𝑐Ag 1 cAg0 t 𝑘=-ln ∙ , 𝑐 Ag+ 𝑡 (5) ∙ . (6) max Assuming that the silver ion concentration is dependent on and, hence, approximately proportional to the absorbance A of the Lambert–Beer law (Equation (2)), k results in 𝑐 Ag0-𝑐Ag0 1 𝑡 𝑘=-ln max t k=−lnA −A0·1, (7) with A for the maximum absorbance and A as absorbance at a treatment time t. However, it should proportional to the absorbance A of the Lambert–Beer law (Equation (2)), k results in of silver ions from the liquid volume to its surface. It is, thus, an idealized approach for the description 𝑐 A A g t max Assumingmaxthat the silver ion concentrtation is dependent on and, hence, approximately be mentioned that the applied model does not consider all contributing phenomena such as diffusion of the process. 𝑘 = -ln 𝐴 − 𝐴 ∙ 1, (7) 𝐴𝑡 The slope of the linear regression taken from the Arrhenius plot in Equation (6) over the plasma treatment time t to tcrit results in the reaction rate coefficient k, summarized for the various stock with Amax for the maximum absorbance and At as absorbance at a treatment time t. However, it solutions in Table 1. The reaction rate k in the linear synthesis range increases more strongly if the should bseilvmerenitiroatneecdontcheantrtahtieonaopfpthliesdtomckosdoleultidonoeisvneoryt hciognhsainddevriacellvceorsnat. ributing phenomena such as diffusion of silver ions from the liquid volume to its surface. It is, thus, an idealized approach for the description of the process. The slope of the linear regression taken from the Arrhenius plot in Equation (6) over the plasma treatment time t to tcrit results in the reaction rate coefficient k, summarized for the various stock solutions in Table 1. The reaction rate k in the linear synthesis range increases more strongly if thePDF Image | Formation Kinematics of Plasma-Generated Silver Nanoparticles
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