Characterization of ZnO nanoparticle The XRD graph shown in Figs. 1, 2, 3, and Table 3 present a detailed characterization of ZnO nanoparticles. Distinctive 2θ values (31.94, 34.64, 36.42, 47.83, 56.85, 62.93, and 68.2) in Fig. 1, corresponding to zinc oxide diffraction (100, 002, 101, 102, 110, 103, 112), authenticate the crystalline structure22. Employing the Debye-Scherrer equation, the average grain size23 was determined at 42.64 nm (± 3) (Table 3), further verification by scanning electron microscopy (SEM), revealed the spherical morphology of ZnO nanoparticle, providing further confirmation of their size being less than 100 nm (Fig. 2 (a)). Additionally, transmission electron microscopic (TEM) analysis in Fig. 2(b) confirmed a particle size range of 50–100 nm.
For this experiment, a sample of Ghaf seeds weighing ten grams, equivalent to approximately (350 ± 6) seeds in triplicates, was used. Following the imbibition process, significant alterations were observed in the shape, weight, and color of the Ghaf seeds. The primary response parameter studied is the percentage of responded seeds. The numbers of responded seeds are counted in each run to calculate the percentage of responded seeds.
Identification of optimum factors and their levels
The experimental design, structured in accordance with the Taguchi orthogonal array (L16), was executed to investigate the impact of varied physico-chemical parameters on seed germination. Table 2 encapsulates the response values for mean responded seed and S/N ratio, with all experimental trials meticulously conducted in triplicates to ensure result accuracy and reliability. Observations across the experimental runs revealed notable fluctuations in responded seed percentages. Specifically, experimental run 16 (C4T4t1A2) exhibited the minimum responded seed percentage, while conversely, experimental run 10 (C3T2t4A2) demonstrated the highest percentage at 88% (Table 4). These findings underscore the discernible influence of combined physico-chemical parameters during incubation on the percentage of responded seeds and subsequent seed germination. The analysis of these outcomes provides valuable insights into the nuanced effects of experimental conditions on critical response variables. Concentration consistently stood out as the most favorable at Level 3, showcasing the highest S/N ratio in the main effect plot (Fig. 3). Similarly, temperature displayed optimal performance at Level 3, emphasizing its significance, while time peaked at Level 2, and Agitation at Level 1.
The main effect plot and response table for S/N ratio provide a focused assessment of the optimization study outcomes24, specifically examining concentration, time, temperature, and agitation. In the S/N ratio table, where larger values are preferable, each factor is evaluated at four levels (1 to 4), presenting the corresponding signal-to-noise ratio. The Delta values represent the difference between the maximum and minimum S/N ratio for each factor, indicating the degree of improvement across levels25. Concentration emerges as the top performer with a Delta of 2.00 Table 5, showcasing the most significant improvement among factors. Temperature follows with notable improvement, while time and agitation show marginal changes.
These response tables emphasize concentration's pronounced influence on the optimization study, seen in both S/N ratio and mean response values. The findings offer valuable guidance for prioritizing and refining optimization parameters, with concentration identified as a key driver of improvement.
Table 6 presents the results of the Analysis of Variance (ANOVA) for the optimization study, offering a breakdown of the contributions of different factors to the observed variability in the response variable. The Regression analysis, comprising concentration, time, temperature, and agitation, is statistically significant (p ≤ 0.014) and accounts for 98.86% of the total variability. Concentration stands out as the primary influencer, demonstrating substantial significance (p ≤ 0.002) and contributing 91.88% to the model's explanatory power. This underscores concentration's pivotal role in the optimization process. On the other hand, time, temperature, and agitation exhibit comparatively lower impacts. Temperature contributes significantly to the model, explaining 6.12% of the variability (p ≤ 0.100), while time and agitation show minimal influence. The ANOVA table validates the statistical significance of the regression model, with concentration emerging as the major driver, emphasizing its crucial role in explaining the observed variability in the response variable within the optimization study.
Analysis of interelation between the factors
The analysis of the contour plot (Fig. 4) reveals that concentration exhibits a lack of interaction with other parameters, such as temperature, time, and agitation. The contour lines corresponding to concentration remain consistently parallel, indicating that changes in concentration do not significantly impact the response variable differently at various levels of temperature, time, or agitation. On the contrary, a robust interaction is evident between the factors of time, temperature, and agitation. The contour lines associated with the combinations of these variables intersect and exhibit non-parallel patterns. This indicates that alterations in one of these factors have a varying impact on the response depending on the levels of the other two factors26. The observed strong interaction among time, temperature, and agitation underscores the complexity of their combined effects and emphasizes the need for a comprehensive understanding of their interplay in optimizing the system. Optimizing seed germination outcomes, thereby enhancing the precision and efficacy of our experimental approach.
Predicting the best factor for increased % of responded Ghaf seeds
The regression model, with a low standard error (S = 1.79699) and a high R-squared value (98.86%), effectively explains nearly 99% of the variability in responded seeds based on concentration, time, temperature, and agitation
The regression analysis reveals a predictive model for the number of responded seeds based on the factors of concentration, time, temperature, and agitation. The regression Eq. (4)
Responded seeds
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=
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64.56 + 0.0 concetration_125 + 6.00 concetration_250 + 17.50 concetration_500 + 0.75 concetration_1000 + 0.0 Time_2 + 1.50 Time_4 + 0.25 Time_8 + 0.50 Time_16 + 0.0 Temperature_25 + 1.75 Temperature_30 + 4.00 Temperature_35 + 4.50 Temperature_40 + 0.0 Agiation_0 + 0.50 Agiation_50–0.50 Agiation_100 + 0.25 Agiation_150…………………………………………………………………………………(4)
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The regression equation represents the relationship between the responded seeds and the specified levels of concentration (125, 250, 500, and 1000) ng/mL, time (2, 4, 8, and 16) hrs., temperature (25, 30, 35, and 40) ͦ C, and agitation (0, 50, 100, and 150) RPM. Each coefficient indicates the contribution of the corresponding factor level to the number of responded seeds.
Regression equations were used to compute the anticipated percentages of responded seeds for each trial run and predict the impact of alterations in parameters on the dependent variables. The corresponding predicted values for the percentage of responded seeds in certain experimental runs are detailed in Table 5. An alternative approach for forecasting the dependent variables involves the formulation of equations through the Taguchi method. Consequently, the Taguchi-predicted values for multiple Signal-to-Noise (SN) ratios at the optimal factor level (ε0) were also determined using Eq. (5).
ϵ0=ϵm+∑i = 1j(ϵi−ϵm)……………………………………………………………….. (5)
Here, ε0 represents the prediction, εm denotes the total mean S/N ratio, εi signifies the mean S/N ratio at the optimal level, and j corresponds to the number of input process parameters27.
Validation of the predicted equations and confirmatory analysis
Verification of the proposed experimental design's validity is crucial to substantiate the expected enhancement in the process response through the optimal parameters identified by the matrix test. Five runs (1, 4, 8, 12 & 16) were randomly selected from the L16 Taguchi Orthogonal Array (OA), in addition to a run utilizing the optimized levels of incubation parameters (C3t2T4a2), for the purpose of validating both the regression and Taguchi models. The predicted values from both Taguchi and regression analyses are same, demonstrating consistency in their predictions. Each experimental run was conducted in triplicate, and the average percentage of responded seeds was compared with the predicted values. Table 7 presents the comparative data between actual experimental values and predicted values for particle size and PDI, as determined by the Taguchi method and regression prediction equation. The minimal error observed (less than 6% of responded seeds) in the comparison between experimental and predicted values underscores the efficacy of mathematical modeling in forecasting optimal incubation parameters for enhanced seed germination. A confirmatory analysis given in Fig. 5(a) illustrates the emergence of responded seeds following treatment with the optimized parameter combination of 500 ng/ml concentration, 40°C temperature, 4 hours duration, and 50 RPM agitation (C3t2T4a2). In contrast, Fig. 5(b) portrays the seeds treated with a water control.