A modified Boltzmann sigmoidal model for the phase transition of smart gels

Abstract

Smart gels are soft polymeric systems that exhibit a reversible phase transition when exposed to environmental stimuli. A modified Boltzmann sigmoidal equation is proposed to model the phase transition behavior of smart gels. The equation can be solved through nonlinear conventional mathematical techniques by determining the hydrogel volume as a function of a particular stimulus. The theoretical results are in good agreement with the experimental data and are similar to those obtained from multiphysical mathematical models. Moreover, for all of the adjusted parameters, error probabilities approaching zero were obtained.

Tailored setting times with high compressive strengths in bassanite calcium sulfoaluminate eco-cements

“…Many authors have used a Boltzmann sigmoidal model to describe viscous fluids undergoing a setting reaction including starch, photopolymerizable acrylates and gels [46,47,48]. In our case, the Boltzmann sigmoidal model represents successfully the dynamics of the hydration of the three pastes with R 2 correlation factors higher than 0.999.…”

Physicochemical and sensory properties of purple Brazilian cherry (Eugenia uniflora, L.) foams

“…The curve-fitting computations with drying time were done using thinlayer drying models, that is, Newton, Henderson and Pabis, logarithmic, two-term, two-term exponential and Wang and Singh models (Kadam & Balasubramanian, 2011). Boltzmann model (Trzcinski et al, 2012) produces a sigmoidal curve and it has been used in a series of transport phenomena modelling (Skrdla & Robertson, 2005;Navajas et al, 2007;Navarro-Verdugo et al, 2011;Oleksy & Hansen, 2011) although literature describing its use in food engineering and food science studies could not be found.…”

Methodological Framework for Estimating the Correlation Dimension in HRV Signals

“…A modified Boltzmann sigmoid curve was used by Navarro-Verdugo et al [22] as a model for the phase transition of smart gels: $\begin{array}{c}f\left(x\right)=A_{\mathrm{2}}-\frac{\left(A_{\mathrm{2}}-A_{\mathrm{1}}\right)}{B+e^{\left(-x+x_o\right)/\alpha }},\end{array}$ where A 1 , A 2 , x o , and B are the parameter designed. The first derivative of f ( x ) is $\begin{array}{c}\frac{df\left(x\right)}{dx}=-\frac{\left(A_{\mathrm{2}}-A_{\mathrm{1}}\right)e^{\left(-x+x_o\right)/\alpha }}{\left[\alpha {\left(B+e^{\left(-x+x_o\right)/\alpha }\right)}^{\mathrm{2}}\right]}.\end{array}$ …”