New advances in the determination of energetic surface properties and transition temperatures of poly(methyl methacrylate) adsorbed on alumina

Abstract This study investigates the surface thermodynamic properties of α-alumina, poly(methyl methacrylate) (PMMA), and PMMA adsorbed on alumina as functions of temperature (303–473 K) and recovery fraction $$\theta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>θ</mml:mi> </mml:math> . The analysis is performed using inverse gas chromatography at infinite dilution within a thermodynamic framework based on the Hamieh thermal model and the London dispersion interaction equation. The methodology enables the determination of the London dispersive surface energy (LDSE), the dispersive and polar free energies of adsorption, the Lewis acid–base surface energy components, and the total surface energy. The results show that $${\gamma}_{\text{s}}^{\text{d}}(T,\theta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mtext>s</mml:mtext> </mml:mrow> <mml:mtext>d</mml:mtext> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> exhibits a nonlinear dependence on temperature, with characteristic maxima associated with transition phenomena. At the liquid–liquid transition, $${\gamma}_{\text{s}}^{\text{d}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mtext>s</mml:mtext> </mml:mrow> <mml:mtext>d</mml:mtext> </mml:msubsup> </mml:math> reaches nearly constant values of approximately 26 mJ m⁻ 2 , indicating a polymer-dominated interfacial state. A significant dependence of surface energetic parameters on recovery fraction is observed, including a characteristic maximum around $$\theta \approx 0.38$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>0.38</mml:mn> </mml:mrow> </mml:math> . The glass transition temperature $${T}_{\text{g}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>g</mml:mtext> </mml:msub> </mml:math> shows a systematic shift with $$\theta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>θ</mml:mi> </mml:math> , whereas the β-relaxation temperature remains essentially constant. The analysis also reveals that polar (acid–base) interactions are more sensitive to $$\theta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>θ</mml:mi> </mml:math> than dispersive interactions, reflecting their localized and specific nature. The temperature and coverage dependence of interfacial properties is interpreted through the evolution of the intermolecular separation distance $$H(T,\theta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , which follows a bilinear behavior with sharp variations near transition temperatures. These results demonstrate that interfacial thermodynamics are governed by coupled effects of temperature, polymer mobility, and surface coverage. Overall, this work provides a consistent thermodynamic description of polymer–oxide interfaces, highlighting the importance of considering both temperature and surface coverage in the analysis of surface energetics and interfacial transitions.