Looking At Modeling Fluorescence Quenching Biology Essay

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Florescence technique can be used to obtain insights into the environment structure and variability of organic matter. One important, technique is fluorescence quenching which involves a decrease in organic matter fluorescence emission intensity by externally added quenching agent (Szarka et al., 1994). The resulting decrease in fluorescence emission intensity can be measured and related directly to the quenching agent concentration via different quenching models. Previous work in biological science has been using fluorescence quenching technique to determine halide and metal ion concentrations (Lakowicz, 1999; Badugu et al., 2004; Brege et al, 2007) due to both the sensitivity of fluorescence measurements and the simplicity of the quenching reaction method employed by the Stern-Volmer relationship. However the complexity of steady state fluorescence quenching mechanism generates difficulties in its interpretation, and the quenching data do not follow the standard linear Stern Volmer expression due to the incidence of other processes beside dynamic quenching causing deviations and nonlinearity in the data behavior ( full details will be presented in litreature ). Therefore, there is a need to perform fluorescence quenching models in a systematic way to overcome some of the problems that generates from various data behavior in order build a baseline knowledge on the impact of the treatment process (i.e. disinfection via chlorination) on the organic matter fluorescence intensity of potable water, the nature of the residual fluorescence signal, and thus the suitability of fluorescence quenched technique as a monitoring tool in water treatment works.

Modeling fluorescence quenched data can be classified by the model used and by the purpose of the analysis. The most common model used is the standard linear Stern Volmer equation and a modified form of the equation is used when either positive or negative deviation from linearity occur on the quenched data. In addition, the behavior of the fluorescence quenched data gives an indication of the efficiency of fluorescence quenched and the potential formation of non fluorescence complexes during reaction time. Examples of the methods used for fluorescence quenching models found in the literature (section xxx).

The mechanism of chlorine quenching organic matter in aqueous solutions is not well understood (Korshin, 1999; Giri, 2003; Beggs et al., 2009) during chlorination, disinfection by products (DBP's) form when organic matter reacts with an oxidant/ disinfectant (i.e. chlorine) the varying levels of DBP's (such as THM's ) are formed depending on the characteristics of organic matter, chlorine dose, pH, temperature and reaction time(Liang and Singer 2003; Roccaro et al; 2008; Miller et al., 2009) leading to have an affect on the fluorescence signature of quenched data. This chapter, aims to explore the fluorescence quenching models linking experiments that have different mixture of quenching decay to the steady state standard Stern Volmer equation and investigate how fluorescence quenching models can be used to track changes in organic matter characteristic and the potential formation of DBP's during chlorination.

7.2. The Ksv value concept and the Stern Volmer Equation

Knowledge of the value Stern Volmer constant is of interest, enabling the study of changes in the chemical structure of organic matter and therefore its fluorescence properties. Quenching reactions can be generally classified as either static or dynamic processes or a combination of both. Static quenching can be attributed to the formation of non fluorescent ground state complex compounds where the fluorophore can form a stable complex with another molecule. Whereas, dynamic quenching occurs when the excited fluorophore experiences contact with an atom or molecule that can facilitate non-radiative transitions to the ground state without the formation of complex (Lakowicz, 1999).The interpretation of a change in the quenchability (i.e. the decrease or increase in fluorescence intensity ) can be expressed by changes in quenching constant value the standard Stern Volmer relationship which is consistent with either static or dynamic quenching mechanism is used to present the fluorescence quenching data as plots of ( Fo/F ) versus [Q] (Lakowicz, 1999).

……………………………………………………………………………………(1)

Where, Fo and F are the fluorescence intensity in the absence and presence of quencher, respectively. Q is the concentration of the quencher, in this case it represents chlorine consumed (), and is the Stern -Volmer quenching constant. Figure (1-a,b,c and d) shows a typical Stern Volmer plot, Fo/F fluorescence intensity in the absence and presence of quencher versus [Q] chlorine consumed for the 4 WTW's, Initial chorine concentrations (2.1, 1.7, 1.3, 1, 0.5 mg/l), over 2 hours reaction period. Quenching data are expected to have a linear relationship, a linear stern Volmer plots indicate that all fluorophores are equally accessible to the quencher. In order to calculate the Stern Volmer constant for the same data presented in Figure (1-a,b,c and d) linear regression (least square fit method) was applied to all the fluorescence quenched data, Figure 2 shows an example of applying least square fit method for data of Draycote WTW's the results of value and correlation coefficient are summarized in Table 1-a,b,c and d. Generally the results indicate that a decrease in initial chlorine concentration leads to a decrease in . The R2 value is relatively good, however, its interesting to notice that R2 explore the low values at high and low initial chlorine ranges i.e. for 2.1 and 0.5 mg/l. of the 5 water treatment works, Strensham fluorescence quenched data can be seen to have the most high value range between ( 0.99+/- 0.0004 for 2.1 mg/l and 0.82 +/- 0.0021 for 0.5 mg/l) , this is likely to be due to the type of water having an intermediate organic matter character with low measured TOC 4.24 mg/l and consequently low amount of chlorine consumed. Whitacre fluorescence quenched data exhibited value between (0.96+/- 0.0081for 1.7 mg/l - 0.66 +/-0.0029 for 0.5 mg/l) this is due to the character of organic matter having high microbial organic matter , high chlorine consumed and high measured TOC 4.98 mg/l in comparison to Strensham WTW. For Melbourne fluorescence quenching data the range of value was between (0.88+/-0.007 for 2.1 mg/l - 0.42 +/- 0.0019 for 0.5 mg/l) having high measured TOC 7.33 mg/l. for Draycote fluorescence quenched data the nature of organic matter structure (hydrophilic ) with high measured TOC 8.09 mg/l result in a large amount of chlorine consumed, consequently lowering the range ( 0.58+/-0.0009 for 2.1 mg/l - 0.325 +/- 0.0026 mg/l). Interestingly, Bamford fluorescence quenching data did not exhibit any change in fluorescence ratio during the 2 hours reaction, Once chlorinated a rapid decrease in fluorescence intensity occurred and the Fo/F ratio stabilized during 2 hours of reaction therefore, it was not able to obtain values for this site. This is likely to be due to the type of water being (hydrophobic rich ) and a less reactive organic matter yield to a slow chlorine consumed(Beroza, 2009). Overall, the values of the quenching constants appears to follow a trend depending on initial chlorine concentration and organic matter character therefore, at 2.1>1.7>1.3>1>0.5 mg/l. In addition the values of quenching constant elucidate the reaction type between the organic molecule and the quencher (i.e. high values of quenching constant reveal that fluorescence intensity data is efficiently more quenched at high chlorine concentration, meanwhile low quenching constant indicate that not all the organic molecules interacted with the quencher due to low initial chlorine concentration and rapid decay of chlorine (Cl< OM) this explains the high values of calculated experimental error of calculated standard error range +/- 0.0021 -0.0029 for 0.5 mg/l low chlorine concentration, whereas a reduce in experimental error occurs at high initial chlorine concentration 2.1 mg/l, calculated standard error range +/- 0.0004- 0.0009, see appendix (x) for deriving the error analysis equation and Table A shows an example of calculating the experimental error for Draycote WTW.

Recent studies have began to evaluate how fluorescence spectroscopy may be used to assess organic matter reactivity and simulate DBP's formation during organic matter chlorination studies such as peak intensity excitation -emission pairs (Marhaba and Kochar, 200; Chen and Valentin, 2007) as well as the emission wavelength that corresponds to half the maximum fluorescence intensity 0.5 (Fabbricino and Korshin, 2004) and correlated theses measure to DBP formation. Likewise (Rocaro et al., 2009) utilize transformation in fluorescence intensity at specific wavelength during chlorination to predict DBP formation. A potential limitation of these methods, show that chlorine breaks down the active aromatic structure in humic molecules into smaller compounds shifting the location of desired intensity readings and possibly increasing intensity in some readings (Fabbricino and Korshin, 2004) giving incorrect indication of fluorescence quenching mechanism ( this will be explained more in chapter investigating quenching mechanism). Moreover, the characteristics of organic matter which can be divided into fractions of hydrophobic and hydrophilic. Hydrophobic fraction consist of preliminary humic and fulvic acids with high molecular weight, being less reactive which yield to low chlorine consumed. Whereas, hydrophilic have low molecular weight (proteins and amine acids ) which were found to be more likely to react with chlorine resulting in high DBP formation(Gang et al., 2002; Miller et al., 2009). It was shown that by applying the standard Stren Volmer relationship and the determination a significant information can be obtain on the changes in organic matter structure through different ranges of chlorination. Also an increase in value can be correlated to a decrease in DBP's formation; this is in agreement with observations from laboratory test runned on the same set of quenched data indicating the fact that during chlorination organic matter experience two kinds of quenching mechanism both (static and dynamic). Strensham WTW had the high values (0.99 - 0.89) with a low average of THM (24.37 - 9.25ug/l for 2.1 and 0.5 respectively. Whereas Draycote WTW data had the lowest range of value with high THM average (40.37- 32.55) for 2.1 and 0.5 respectively (further work on relationship between quenching and THM formation will be discussed in chapter x).

7.3. Predictive Equations

7.3.1. Modified Stern Volmer equation

As noted earlier, the value of can be determined by measuring the fluorescence intensity at different quencher concentrations using standard linear Stern Volmer equation. However, the steady state fluorescence quenching data do not follow the standard linear Stern Volmer expression. This is likely due to chlorine consumption, formation of non fluorescence complexes and some errors accrue within the analysis (see appendix for error analysis determination). Consequently the gradient of best fit line for the correlation of Stern Volmer equation does not passes through the intercept one on the y-axis, which one would expect as (the fluorescence intensity in the absence of quencher / fluorescence intensity in the presence of quencher is equal to one)when chlorine consumption is zero. Therefore, an approach has been developed to the use of Stern Volmer application in order to overcome some of the problems and allow straight forward application with relatively good accuracy during the use of fluorescence quenching technique on different sources of water treatment works. The developed model will imply constraining the correlation such that the line of best fit passes through the intercept one, Figure (3-a, b, c and d) can be seen in for Draycote WTW for range of chlorine concentration2.1, 1.3, 1. and 0.5 mg/l, shows the best fit lines with one line not fitted through intercept one, and the other fitted through intercept one. The method will only have a slightly effect on value of the gradient line and in some cases a slightly change in the correlation coefficients R2 e.g. for chlorine concentration 2.1mg/l the exhibited a slightly decrease in value from 0.58 to 0.56 for lines (not fitted and fitted through the intercept 1) respectively, with the correlation coefficient being the same R2 0.94 Figure 3-a. While, for chlorine concentration 0.5 mg/l slightly increase in values from 0.325 to 0.330 for lines (not fitted and fitted through the intercept 1) respectively Figure (3-d). Although the developed method had a slightly effect on the values of . The overall correlation of with initial chlorine concentration had similar trends to the observed correlation when applying the standard liner Stern Volmer equation (not fitted through the intercept) for each of the 5 WTW's with different magnitude indicating that this developed method does don't deteriorate the standard Stern Volmer relationship, and fits for the purpose.

7.3.2. Sphere of action quenching model

In previous section fluorescence quenching of organic matter by various chlorine range and Ksv value has been investigated by steady state linear Volmer relationship. However in some cases, it has been observed that experimental data show a deviation (either positive or negative) from linearity (Lakowicz, 1999). The positive deviation (upward curvature) is attributed to various processes such as formation of non fluorescence complex and intersystem crossing, whereas negative deviation (down curvature) occur when the fluorophores are not equally accessible to the quencher i.e. one being accessible to quencher and the other inaccessible to quencher and a modified Stern Volmer equation was used to gain information about the most accessible fluorophore residue (Laws and Contino, 1992), a different theory suggested that chlorine consumed over course of reaction, and many of the carbon atoms in OM will not properly participate in redox reaction specially if the chlorine concentration was low and decay rapidly, which reasonably explains the negative curve toward the x-axis in the observed data as the fluorescence intensity starts to recover after a period of time when low chlorine concentration decay (Korshin et al., 2000) (a more detailed explanation will be in chapter quenching mechanism). In Figure (1-a,b,c and d) of 4 WTW's there appear to have a non linearity deviation upward curvature plot for high chlorine concentration 2.1 and 1.7 mg/l and a downward curvature plot at low chlorine concentration 0.5 mg/l, this gives an indication of the presence of parallel quenching process taking place beside dynamic quenching mechanism (Thipperudrappa et al., 2007). Such deviation has been observed by researchers (Knutson, 1992; Laws and Contino, 1992; Szarka et al., 1995; Lakowicz, 1999; Geddes, 2001, Giri, 2003, Thipperudrappa, 2006) suggesting that in case the steady state fluorescence quenching data do not follow the stander linear SternVolmer relationship, a modified Stern Volmer equation for the nonlinear deviation can be applied in order to gain more information on the insight reactions between the quencher and organic matter. For fluorescence quenched data exhibiting an upward curvature plot the sphere of action static quenching model (Lakowicz, 1999) will be applied to the experimental data

…………………………………………………………… …………..(2)

Where W is a function of quencher concentration Q. According to this model, static quenching occurs if the quencher molecule is very close or in contact with the fluorescent molecule at the exact excitation moment, and this was interpreted by the fact that only a certain fraction (e.g. W), of the excited state molecules are actually quenched by collisinoal mechanism. However, some molecules in the excited state which is (1-W) are deactivated almost after being formed because of the randomly positioned quencher which interact strongly with the excited state molecules forming dark complex compounds.

The additional fraction W is expressed as;

(3)

Where V is the static quenching constant, and represents an active volume element surrounding the fluorophore in its excited state.

Frank and Wavilow, 1931 suggest that static quenching mechanism occurs in a randomly distributed system, when a quencher happens to reside within a sphere of action surrounding the fluorophore upon its excitation state. The probability of the quencher being within this volume at time of excitation depends on the volume and quencher concentration. Assuming that the quencher is randomly distributed in solution, then the probability of static quenching is given by Poisson distribution. W is a function of quencher concentration Q, therefore depends on the quencher concentration. For high quenching efficiency the stern Volmer plot generally will deviate from its linearity consequently Equation (2) can be expressed in the following,

………………………………… ………… (4)

In case when VQ <=1 ; W ≈(1-VQ)

……………………………………………… (5)

W=1-[V*Q ]…………………………… ……………………………… …… ……..(6)

Figure (4) shows an example for plot of versus for chlorine concentration 2.1mg/l Draycote WTW. From the linear regression method the values of the slope) and the intercept (V) has been determined for the initial chlorine concentrations Table 2-a, b, c, and d summarized the results of for all the 4 WTW's. It's interesting to mention that a general comparison between the calculated values of using both the standard linear and modified Stern Volmer equation will not be applicable as the value in the modified Stern Volmer equation will involve the value of quenching constant with respect to dynamic quenching constant in this case the value of W ( Szarka et al., 1994), while value in the standard Stern Volmer equation will represent the association constant of the complex formation by meaning the presence of parallel quenching process both static and dynamic (Thipperudrappa et al., 2006). Finally for the negative Stern Volmer deviation which occur for low chlorine concentration, <= 0.5 mg/l as stated a modified Stern Volmer equation was used to gain information about the most accessible fluorophore residue. On a study by Wyatt et al., (1987) an experiment was conducted on three halide sensors quenching tryptophan residues in protein to gain information about the most accessible residues using a modified Stern Volmer equation. however, Lakowicz, (1999) revealed that the use of the modified Stern Volmer method for negative curvature will provide a arbitrary results throughout applying the method on a data for (Lehrer, 1978) and calculating the assumed classes of tryptophan residues quenched by iodide. Consequently, for the purpose of this study only standard linear Stern Volmer equation will be applied for fluorescence quenched data of initial chlorine concentration <= 0.5 mg/l.

7.4. Performance of predictive quenching models

To provide a better understanding of the best fit model to represent the fluorescence quenched data, the three models (model 1standard linear Stern Volmer, model 2 the modified standard linear Stern Volmer (fitted through the intercept1) and model 3Sphere of Action) were tested through applying the calculated Ksv value to determine the predicted Fo/F and a comparison between the calculated (Fo/F) values and the experimental data was taken place based on Root Mean Square Error (RMSE) method which imply selecting the most fit model depending on lower RMSE value. Table 4 and Figure 5-a, b, c and d, show an example of plotting the calculated predicted values of Fo/F for models1, 2 and 3 among the experimental data for Draycote WTW, Table 5 . From the graphics, and the calculated values of RMSE of the 5 initial chlorine concentrations for each water treatment work Table 3-a,b, c and d. Results showed that for high chlorine concentration 2.1 and 1.7 mg/l, model 3 Sphere of Action is more likely to represent the quenched data having RMSE 0.028 less than RMSE (0.052and 0.047) for both model 1 and 2 respectively within a difference of (46% ) suggesting that for high initial chlorine concentration the Sphere of Action model 3 will be more consistent when calculating the predicted values and quenching constant this is in agreement with (Thipperudrappa et al., 2007) suggesting the at high quencher concentrations positive deviation would observe and experimental data is preferably to be analysed by using Sphere of Action static quenching model. For chlorine concentrations 1.3, 1 and 0.5 mg/l, the value of RMSE for model 1 and 2 is less than RMSE for model 3 for Strensham, Whitacre and Melbourne and Draycote. Overall, it can be seen that model 2 will be more consistent when calculating the predicted values and quenching constants for 1.3, 1 and 0.5 mg/l, this indicates the theory of the presence of static quenching even in the absence of a curvature plot (Lakos et al., 1995) which explains why RMSE of model 3 in some sites e.g. in Draycote RMSE value, is either equal or slightly more than value of RMSE model 2 confirming the hypothesis of the model 2 ability to predicted the changes in organic matter structure during chlorination.

7.5. Conclusions

A basic understanding of fluorescence quenching models for chlorinated potable water is a prerequisite to develop baseline knowledge on the changes in organic matter character during chlorination. Furthermore, the possibility of developing a straightforward model representing conditions of fluorescence quenching. Thus, in chapter 7 the effect of different quenching models in representing the fluorescence quenched data was investigated. It was shown that the constant quenching value Ksv yield a significant information on quantitative and qualitative changes in organic matter structure through different chlorination conditions and water types. Ksv value for 2.1 >1.7>1.3>1>0.5 mg/l chlorine concentration, for different type of water Ksv value varies depending on water quality source as for Strensham WTW the Ksv value high ranges (0.99-0.82) due to its intermediate organic matter character, low TOC and low chlorine consumption, while Draycote WTW's exhibited the lower range of Ksv (0.58- 0.325) due to water source relatively hydrophilic, high measured TOC concentration and high chlorine demand. Whitacre and Melbourne were in between exhibiting Ksv ranges (0.96-0.66) and (0.88-0.42) respectively. Interestingly Bamford WTW showed a different approach the Ksv value was not calculated as the fluorescence organic matter exhibited rapid quenching once chlorinated afterwards the Fo/F ratio remains constant during 2 hours of reaction. This is likely to be due to the type of water (which is hydrophobic rich) and less reactive organic matter which yield to a slow chlorine consumption. Also it was found that Ksv values can be used as preliminary indicator of THM formation and to compare between different sites potential THM formation ability e.g. Draycote WTW with low range of Ksv value exhibited high averages of measured THM and for Strensham WTW with high range of Ksv values, low averages of measured THM. Furthermore, the ability of three quenching modeling methods (standard liner Stern Volmer equation, the modified standard liner Stern Volmer equation line fitted through the intercept 1 and Sphere of action ) to determine the Ksv value and predict the Fo/F was tested.

Overall, the modified standard liner Stern Volmer (equation line fitted through the intercept 1) and Sphere of Action model provided the best analysis in predicting changes in fluorescence properties during chlorination. Although the standard linear Stern Volmer model has been reported to characterize changes in fluorescence quenched data for different applications, here it was found to be less robust. And the developed model 2 is more consistent when calculating the predicted values and quenching constant.

Figure 1.a: Typical Stern Volmer plot, peak C fluorescence intensity in the absence and presence of quencher versus chlorine consumed. For Draycote post GAC water samples Initial chorine concentrations (2.1, 1.7, 1.3, 1, 0.5 mg/l), over 2 hours of reaction at time intervals (5, 15, 30, 45, 60, 120 minutes).

Figure 1.b: Typical Stern Volmer plot, peak C fluorescence intensity in the absence and presence of quencher versus chlorine consumed. For Strensham post GAC water samples Initial chorine concentrations (2.1, 1.7, 1.3, 1, 0.5 mg/l), over 2 hours of reaction at time intervals (5, 15, 30, 45, 60, 120 minutes).

Figure 1.c: Typical Stern Volmer plot, peak C fluorescence intensity in the absence and presence of quencher versus chlorine consumed. For Whitacre post GAC water samples Initial chorine concentrations (2.1, 1.7, 1.3, 1, 0.5 mg/l), over 2 hours of reaction at time intervals (5, 15, 30, 45, 60, 120 minutes).

Figure 1.e: Typical Stern Volmer plot, peak C fluorescence intensity in the absence and presence of quencher versus chlorine consumed. For Melbourne post GAC water samples Initial chorine concentrations (2.1, 1.7, 1.3, 1, 0.5 mg/l), over 2 hours of reaction at time intervals (5, 15, 30, 45, 60, 120 minutes).

Figure 2; A typical Stern Volmer plot, Fo/F for humic like fluorescence intensity in the absence and presence of quencher (free chlorine consumed) of Draycote WTW applying the least square fit method. Initial concentrations (2.1, 1.7, 1.3, 1, 0.5 mg/l), over 2 hours of reaction at time intervals (5, 15, 30, 45, 60, 120 minutes).

Figure 3.a; A typical Stern Volmer plot, Fo/F by applying model 1 (not fitted through the intercept) and Model 2 (linear trend line fitted through 1) for 2.1 mg/l , Draycote WTW.

Figure 3.b ;A typical Stern Volmer plot, Fo/F by applying model 1 (not fitted through the intercept) and Model 2 (linear trend line fitted through 1) for 1.3 mg/l , Draycote WTW.

Figure 3.c ;A typical Stern Volmer plot, Fo/F by applying model 1 (not fitted through the intercept) and Model 2 (linear trend line fitted through 1) for 1 mg/l , Draycote WTW.

Figure 3.d; A typical Stern Volmer plot, Fo/F by applying model 1 (not fitted through the intercept) and Model 2 (linear trend line fitted through 1) for 0.5 mg/l , Draycote WTW.

Figure 4 ;the relationship between [1-(F/Fo)]/[C] vs F/Fo for initial chlorine concentration 2.1 for Draycote WTW.

Figure 5.a; A comparison between the experimental data (observed data) and model 1 standard Stern Volmer equation, model 2 modified Stern Volmer equation and model 3 Sphere of Action model. Initial chlorine concentration 2.1 mg/l over two hours reaction period, Draycote WTW.

Figure 5.b; A comparison between the experimental data (observed data) and model 1 standard Stern Volmer equation, model 2 modified Stern Volmer equation and model 3 Sphere of Action model. Initial chlorine concentration 1.3 mg/l over two hours reaction period, Draycote WTW.

Figure 5.c; A comparison between the experimental data (observed data) and model 1 standard Stern Volmer equation, model 2 modified Stern Volmer equation and model 3 Sphere of Action model. Initial chlorine concentration 1 mg/l over two hours reaction period, Draycote WTW.

Figure 5.d; A comparison between the experimental data (observed data) and model 1 standard Stern Volmer equation and model 2 modified Stern Volmer equation. Initial chlorine concentration 0.5 mg/l over two hours reaction period, Draycote WTW.

Table 1.a: the values of Ksv Stern Volmer quenching constant by applying the standard equation and the correlation coefficients. for the initial chlorine concentrations(2.1, 1.3, 1 and 0.5 mg/l ) for Draycote WTW.

Cl (mg/l)

Ksv

R2

S.E

2.1

0.58

0.94

0.0009

1.3

0.402

0.97

0.0014

1

0.392

0.98

0.0021

0.5

0.325

0.90

0.0026

Ksv quenching constant; Ksv.SE =Ksv * {(error Fluorescence (0.05/ F ) + error chlorine consumed (0.02/ Q)}

Table 1.b: the values of Ksv Stern Volmer quenching constant by applying the standard equation and the correlation coefficients. for the initial chlorine concentrations(2.1, 1.3, 1 and 0.5 mg/l ) for Strensham WTW.

Cl (mg/l)

Ksv

R2

S.E

2.10

0.99

0.95

0.0004

1.70

0.92

0.97

0.0006

1.30

0.91

0.97

0.0008

1.00

0.87

0.99

0.0009

0.50

0.82

0.74

0.0021

Table 1.c: the values of Ksv Stern Volmer quenching constant by applying the standard equation and the correlation coefficients. for the initial chlorine concentrations(2.1, 1.3, 1 and 0.5 mg/l ) for Whitacre WTW.

Cl (mg/l)

Ksv

R2

S.E

1.70

0.96

0.94

0.0081

1.30

0.86

0.92

0.0009

1.00

0.81

0.91

0.0009

0.50

0.66

0.77

0.0029

Table 1.d: the values of Ksv Stern Volmer quenching constant by applying the standard equation and the correlation coefficients. for the initial chlorine concentrations(2.1, 1.3, 1 and 0.5 mg/l ) for Melbourne WTW.

Cl (mg/l)

Ksv

R2

S.E

2.10

0.88

0.95

0.0007

1.70

0.87

0.93

0.0015

1.30

0.49

0.98

0.0006

1.00

0.48

0.85

0.0017

0.50

0.42

0.64

0.0019

Table 2.a; Calculated values of quenching constant (Ksv ) and static quenching constant (V ) of initial chlorine concentration (2.1, 1.3 and 1 mg/l) Draycote WTW.

Cl (mg/l)

Ksv

V

2.1

-0.178

0.495

1.3

0.6583

-0.194

1

-1.429

1.514

Table 2.b; Calculated values of quenching constant (Ksv ) and static quenching constant (V ) of initial chlorine concentration (2.1, 1.7, 1.3 and 1 mg/l) Strensham WTW.

Cl (mg/l)

Ksv

V

2.10

-0.405

0.792

1.70

0.089

0.468

1.30

0.082

0.505

1.00

0.231

0.418

Table 2.c; Calculated values of quenching constant (Ksv ) and static quenching constant (V ) of initial chlorine concentration (1.7, 1.3 and 1 mg/l) Whitacre WTW

Cl (mg/l)

Ksv

V

1.70

-0.119

0.659

1.30

-0.217

0.185

1.00

-0.559

-0.941

Table 2.d; Calculated values of quenching constant (Ksv ) and static quenching constant (V ) of initial chlorine concentration (1.7, 1.3 and 1 mg/l) Whitacre WTW

Cl (mg/l)

Ksv

V

2.10

-0.337

0.735

1.70

0.451

0.304

1.30

-0.133

0.450

1.00

0.751

-0.146

Table 3.a ; The RMSE for model 1 the standard Stern Volmer equation , model 2 the modified Stern Volmer equation and model 3 sphere of action for Draycote WTW.

Cl

model 1

model 2

model 3

Cl 2.1

0.0516

0.0468

0.0283

Cl1.3

0.0169

0.0169

0.0170

Cl 1

0.0129

0.0126

0.0116

Cl0.5

0.0146

0.0145

Table 3.b; The RMSE for model 1 the standard Stern Volmer equation , model 2 the modified Stern Volmer equation and model 3 sphere of action for Strensham WTW.

 

model 1

model 2

model 3

Cl 2.1

0.0730

0.0816

0.0526

Cl 1.7

0.0510

0.0428

0.0286

Cl1.3

0.0456

0.0416

0.0478

Cl 1

0.0718

0.0612

 0.0149

Cl0.5

0.0718

0.0612

 

Table 3.c; The RMSE for model 1 the standard Stern Volmer equation , model 2 the modified Stern Volmer equation and model 3 sphere of action for Whitacre WTW.

model 1

model 2

model 3

Cl 2.1

0.0831

0.0805

0.0277

Cl 1.7

0.0669

0.0568

0.0474

Cl1.3

0.0742

0.0641

0.211

Cl 1

0.0527

0.0514

0.0734

Cl 0.5

0.0629

0.0573

Table 3.d; The RMSE for model 1 the standard Stern Volmer equation , model 2 the modified Stern Volmer equation and model 3 sphere of action for Melbourne WTW.

model 1

model 2

model 3

Cl 2.1

0.0592

0.0533

0.0212

Cl 1.7

0.0465

0.0461

0.0503

Cl1.3

0.0182

0.0179

0.0193

Cl 1

0.0441

0.0361

0.0351

Cl 0.5

0.0469

0.0383

Table 4 ; The observed and calculated values of Fo/F for model 1,2 and 3 for chlorine concentrations 2.1, 1.3, 1, 0.5 mg/l Draycote WTW.

Chlorine concentration

2.1

time (minutes)

Cl consumed

observed

model 1

model 2

model 3

0

0.00

1.00

1.00

1.00

1

5

0.64

1.33

1.19

1.18

1.3

15

0.75

1.37

1.23

1.22

1.38

30

0.81

1.42

1.26

1.25

1.43

45

0.89

1.46

1.34

1.33

1.5

60

0.92

1.52

1.37

1.36

1.54

120

0.97

1.64

1.41

1.39

1.59

Chlorine concentration

 1.3

time (minutes)

Cl consumed

observed

model 1

model 2

model 3

0

0

1.00

1.00

1.00

1.00

5

0.4

1.18

1.16

1.16

1.16

15

0.51

1.20

1.21

1.21

1.21

30

0.55

1.22

1.22

1.22

1.22

45

0.69

1.25

1.28

1.28

1.28

60

0.7

1.28

1.28

1.28

1.28

120

0.74

1.33

1.30

1.30

1.30

Chlorine concentration

 1 

time (minutes)

Cl consumed

observed

model 1

model 2

model 3

0

0.00

1.00

1.00

1.00

1.00

5

0.32

1.12

1.13

1.12

1.12

15

0.39

1.15

1.15

1.15

1.15

30

0.45

1.18

1.18

1.17

1.17

45

0.59

1.20

1.23

1.23

1.23

60

0.64

1.25

1.25

1.25

1.25

120

0.70

1.29

1.27

1.27

1.28

Chlorine concentration

0.5

time (minutes)

Cl consumed

observed

model 1

model 2

model 3

0

0.00

1.00

1.00

1.00

 

5

0.22

1.07

1.07

1.07

 

15

0.23

1.08

1.07

1.08

 

30

0.35

1.13

1.11

1.12

 

45

0.39

1.15

1.13

1.13

 

60

0.41

1.13

1.13

1.14

 

120

0.43

1.12

1.14

1.14

 

Appendix A;

Error analysis calculation

But Fo = F

i.e., the error in KSV = error in F + error in Q

= () + ()

The error determining chlorine is 0.02 , thus =0.02. The error in determining fluorescence is known to be 0.05 nm , thus = 0.05 . The Ksv is the quenching constant for each initial chlorine concentration. using the equation of calculated error in Ksv ; = Ksv * [ ( + () ] , error would apply for each point , Ksv +/- average of Ksv

Table A ; the calculation of standard error analysis and values for chlorine concentration 2.1, 1.3, 1 and 0.5 mg/l for Draycote WTW.

2.10

Q

0.02/Q

F

Fo/F

0.05/F

§Ksv=(Ksv*(0.02/F+0.05/F)

§Ksv*100

§Ksv*100/KSV

 

0.00

#DIV/0!

82.00

1.00

0.00

 

 

 

 

0.64

0.03

61.54

1.33

0.00

0.0186

1.86

3.21

 

0.75

0.03

60.00

1.37

0.00

0.0160

1.60

2.75

 

0.81

0.02

57.69

1.42

0.00

0.0148

1.48

2.56

 

0.89

0.02

56.15

1.46

0.00

0.0136

1.36

2.34

 

0.92

0.02

53.85

1.52

0.00

0.0131

1.31

2.27

 

0.97

0.02

50.00

1.64

0.00

0.0125

1.25

2.16

 

 

 

 

 

 

 

1.48

2.55

 

 

 

 

 

SD

0.0022

0.22

0.39

 

 

 

 

 

SE

0.0009

0.09

0.16

1.30

0.00

#DIV/0!

81.54

1.00

0.00

 

 

 

 

0.40

0.05

69.23

1.18

0.00

0.0201

2.01

5.07

 

0.51

0.04

67.69

1.20

0.00

0.0159

1.59

4.00

 

0.55

0.04

66.92

1.22

0.00

0.0147

1.47

3.71

 

0.69

0.03

65.38

1.25

0.00

0.0118

1.18

2.98

 

0.70

0.03

63.85

1.28

0.00

0.0117

1.17

2.94

 

0.74

0.03

61.54

1.33

0.00

0.0111

1.11

2.78

 

 

 

 

 

SD

0.0035

0.35

0.88

 

 

 

 

 

SE

0.0014

0.14

0.36

1.00

0.00

#DIV/0!

81.54

1.00

0.00

 

 

 

 

0.32

0.06

73.08

1.12

0.00

0.0248

2.48

6.32

 

0.39

0.05

70.77

1.15

0.00

0.0204

2.04

5.20

 

0.45

0.04

69.23

1.18

0.00

0.0177

1.77

4.52

 

0.59

0.03

67.69

1.20

0.00

0.0136

1.36

3.46

 

0.64

0.03

65.38

1.25

0.00

0.0125

1.25

3.20

 

0.70

0.03

63.08

1.29

0.00

0.0115

1.15

2.94

 

 

 

 

 

SD

0.0052

0.52

1.32

 

 

 

 

 

SE

0.0021

0.21

0.54

0.50

0.00

#DIV/0!

81.54

1.00

0.00

 

 

 

 

0.22

0.09

76.15

1.07

0.00

0.0298

2.98

9.16

 

0.23

0.09

75.38

1.08

0.00

0.0285

2.85

8.76

 

0.35

0.06

72.31

1.13

0.00

0.0188

1.88

5.78

 

0.39

0.05

70.77

1.15

0.00

0.0169

1.69

5.20

 

0.41

0.05

72.31

1.13

0.00

0.0161

1.61

4.95

 

0.43

0.05

73.08

1.12

0.00

0.0153

1.53

4.72

 

 

 

 

 

SD

0.0065

0.65

2.00

 

 

 

 

 

SE

0.0026

0.26

0.82

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