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<p>In this work, <i>Micrococcus luteus</i> was used to investigate the microbial synthesis of lead sulfide (PbS) nanoparticles. The influence of system variables, particularly pH and incubation time, on bacterial cell growth and PbS nanoparticle yield has been investigated. A successful synthesis was carried out to obtain spherical, highly pure cubic PbS nanoparticles with a direct band gap of 2.32&#xa0;eV and an average diameter of approximately 85&#xa0;nm. Microbial growth kinetics and the evolution of hydrogen sulfide (H₂S), an essential phase in nanoparticle synthesis, were statistically analyzed and linked. In this work, we proposed a novel theoretical framework, hereafter referred to as the PH model (Prajakta-Hemant Model) a breakpoint model to describe the critical power of hydrogen (pH) dependent behaviour impacting H₂S production and nanoparticle formation. Compared to Lorentzian fitting and Response Surface Methodology (RSM), this model showed greater precision in replicating the nonlinear physiological responses under changing pH and time circumstances. In addition, simulated 3D graphs illustrating the occupied volume of bacterial cells per millilitre in growth medium within a set of pH and incubation time were created using Python programming, offering a quantitative and visual representation of bacterial kinematics. With numerous implications for applications in green nanotechnology, the combination of statistical and biological modelling techniques described here provides an alternative route for regulating and enhancing the microbial synthesis of semiconductor nanomaterials.</p> Graphical abstract <p></p>

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Statistical modelling of micrococcus luteus growth kinetics in microbial lead sulphide (PbS) nanoparticle synthesis via PH-breakpoint and lorentzian models

  • 期刊论文

  • 发表日期：

    2026年7月13日

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  • Prajakta Bhoi,
  • Hemant Tarkas

摘要

In this work, Micrococcus luteus was used to investigate the microbial synthesis of lead sulfide (PbS) nanoparticles. The influence of system variables, particularly pH and incubation time, on bacterial cell growth and PbS nanoparticle yield has been investigated. A successful synthesis was carried out to obtain spherical, highly pure cubic PbS nanoparticles with a direct band gap of 2.32 eV and an average diameter of approximately 85 nm. Microbial growth kinetics and the evolution of hydrogen sulfide (H₂S), an essential phase in nanoparticle synthesis, were statistically analyzed and linked. In this work, we proposed a novel theoretical framework, hereafter referred to as the PH model (Prajakta-Hemant Model) a breakpoint model to describe the critical power of hydrogen (pH) dependent behaviour impacting H₂S production and nanoparticle formation. Compared to Lorentzian fitting and Response Surface Methodology (RSM), this model showed greater precision in replicating the nonlinear physiological responses under changing pH and time circumstances. In addition, simulated 3D graphs illustrating the occupied volume of bacterial cells per millilitre in growth medium within a set of pH and incubation time were created using Python programming, offering a quantitative and visual representation of bacterial kinematics. With numerous implications for applications in green nanotechnology, the combination of statistical and biological modelling techniques described here provides an alternative route for regulating and enhancing the microbial synthesis of semiconductor nanomaterials.

Graphical abstract