Bubble growth in a confined heated polymer: the example of safety glass

TL;DR

The paper addresses bubble formation in laminated safety glass by integrating experiments and a multi-physics diffusion–thermo–rheology model for two gases in a viscoelastic PVB interlayer. The approach couples gas diffusion with temperature dependent solubility and a time temperature dependent Maxwell rheology to predict bubble growth and pressure dynamics, including a metastable tendency for bubbles to form post lamination. Key findings show that bubble growth requires a pre existing nucleus above a critical size and that either water driven diffusion or anomalous air oversaturation can dominate depending on processing conditions, sometimes producing rapid frost like instabilities under confinement. The work provides a generalizable framework applicable to Maxwell type polymers and other viscoelastic materials, with implications for quality control in safety glass and related multi layer polymer systems.

Abstract

Laminated safety glass (LSG) is a composite assembly of glass and polyvinyl butyral (PVB), a viscoelastic polymer. LSG can be found in building facades, important landmarks around the world, and every major form of transportation. Yet, the assembly suffers from unwanted bubbles which are anathema to one of the most important features of glass: optical transparency. In here, we present an in-depth study of the reasons behind these bubbles, either during high-temperature quality control tests or normal glass operating conditions. We provide a physical model for bubble growth that deals with two gases, thermal effects on gas solubility and diffusivity, and a time-temperature dependent rheology. The model can be extended to n-component bubbles or other materials beyond PVB. By combining experiments and theory, we show that two gases are at play: air trapped in interfacial bubbles in the assembly during lamination and water initially dissolved in the polymer bulk. Both gases work in tandem to induce bubble growth in finished assemblies of LSG provided that (i) the original bubble nucleus has a critical size and (ii) the polymer relaxes (softens) sufficiently enough, especially at elevated temperatures. The latter constraints are relaxed in a condition we termed anomalous air oversaturation that may even trigger a catastrophic, yet beautiful ice flower instability.

Figures (8)

• Figure 1: Photographs of bubbles in laminated safety glass at A the LIPhy laboratory in Grenoble (courtesy of C. Schune, Saint-Gobain), B Technical University of Denmark (DTU) (C. Arauz-Moreno), C Jussieu Campus, Sorbonne University in Paris (E. Lorenceau), and D window frost failure in building façade (K. Piroird). See $\S$\ref{['sec:phys_desc']}-\ref{['sec:air_main']} for a thorough discussion on the physical mechanism behind these bubbles.
• Figure 2: A-C Glass lamination: stacking, calendering, and autoclaving. Red dots represent air molecules that become trapped in the polymer roughness $e$ at the polymer/glass interfaces. Across the steps, the nuanced shades of grey of the PVB polymer are meant to convey transparency transformations. D-F Images of laboratory-scale samples against a dark background that highlight how transparency evolves during the lamination process. The size of the samples is 10x10 cm. G-I Mass flux in the glass assembly. The size of the red arrows illustrates the relative speed with which gases can flow in or out of the sample. Fluxes in the z-direction are forbidden by the glass slides. G In the stacking step, gases can rapidly flow, inwardly or outwardly, because the edges of the assembly are open and the polymer roughness forms a percolating network. The vertical distance between the glass and polymer layers has been exaggerated for artistic purposes. H, I After calendering and autoclaving, gases slowly diffuse through the polymer bulk since the edges are sealed. J, K Bake test protocol and criteria for failure($\color{red}{\times}$)/success(✓).
• Figure 3: A Example of bubble dynamics in a pre-press (RB41) during a toy autoclave schedule which included a heating ramp without overpressure. $\circ$ Interfacial bubble ratio $A/A_o$ (bubble area/initial bubble area) inside the target area in the sample. Two PVB humidity conditioning levels were tested, standard ($\color{blue}a=0.25$) and reduced humidity ($\color{red}a=0.05$). $\diamond$ PVB relaxation modulus using eq. \ref{['eq:Gen_Maxwell_TTS']} for RB41 at standard humidity conditions only. The inset is the temperature schedule (color-matched to the main figure), , . See figure S4 in the supplementary material for the experimental set-up details. B Sketch of gaseous exchanges that take place in a pre-press when heated: water escapes from the bulk towards the non-spherical bubbles seeking to inflate them, while air does the opposite. Each gas has a distinct heat of solution $\Delta H_s$ sign which leads them to follow distinct thermodynamic paths with temperature, solubility ($H$) wise, in the PVB polymer. For completeness, the sketch also depicts the gaseous exchanges that take place between the PVB polymer and the surrounding amtosphere via the exposed edges of the polymer. Air enters while water leaves.
• Figure 4: A The PVB polymer is thought of as entangled chains separated by a plasticizer molecule (circles). The corresponding physical description is a Generalized Maxwell model which includes a plurality of parallel branches of Newtonian dashpots of viscosity $\eta_i$ and Hookean springs with elasticity $G_i$ to model the simultaneous viscous and elastic behavior of the polymer. Both features are compactly captured via a shear relaxation $G(t,T)$ that is time-temperature dependent. B Sketch of PVB relaxation with time and temperature in the log(t) space. The curves are self-similar with temperature and differ only via a shift factor $a_T$. The overall relaxation G(t) includes three distinct polymer states: glassy (cold temperatures/short timescales), rubbery (mid temperatures/mid timescales), and viscous melt (high temperatures/long timescales).
• Figure 5: Gas nuclei before (row i) and after (row ii) bake testing at 100°C for 16hrs.