Elsevier

Physics Letters A

Volume 327, Issue 1, 21 June 2004, Pages 61-66
Physics Letters A

A study of bubble inflation in polymers and its applications

https://doi.org/10.1016/j.physleta.2004.04.061Get rights and content

Abstract

This study described a method of dispersing nanogranules in HDPE utilizing the stretching, compression, and shearing effects induced by bubble inflation and oscillation in a polymer melt undergoing foaming. Theoretical calculations show that the bubble inflation is so fast (about 10−6–10−7 s), similar to the explosion of dynamite, that a complex composite stress field is exerted on the polymer melt around the inflating bubble. The calculations also predict an oscillation of the bubble radius under appropriate conditions. The successful dispersion of nanogranules in a polymer melt by bubble inflation has been shown by experiment, and a method, which we call In-Situ Bubble Stretching (ISBS), has been proposed. Comparison of our theoretical predictions of the dispersion with scanning electron micrographs of polymer composite supports our model.

Introduction

When nanoparticles are added to a polymer, the properties of the resulting polymer composites may be enhanced. And this research field has attracted significant attention in recent years. The nanoparticles in the polymer must be well dispersed, otherwise the beneficial effects of adding the nanomaterial to the polymer are greatly reduced. The dispersion process for nanoparticles is quite different from that for micron-particles owing their extensive tendency to aggregate in a polymer melt. However, employing conventional mixing and dispersion techniques cannot produce sufficient shearing or stretching stress to prevent aggregation of nanogranules. To date the problem of dispersing nanomaterials has mainly been solved by pretreating the nanomaterials with coupling or dispersing agents, then the surface energy of the nanoparticles is lowered by adding such agents. As a result the nanoscale effect of the nanogranules are eliminated or at least weakened. Another method of dispersion is relevant to those particles, which have a layered structure, such as clays in situ polymerization. When the pre-intercalated monomers between the layers of the granules are polymerized, an expanding interaction in a direction perpendicular to the layers of the clay may occur as a result of the volume increase which accompanies polymerization. This can be effective in dispersing the layered granules. This method is only suitable for dispersion of materials having a layered structure (such as montmorillonite, hydrotalcite, etc.), and is ineffective in dispersing nonlayered materials (such as CaCO3, ZnO, etc.) [1], [2], [3]. Therefore, for different nanomaterials of different structures no generally useful method exists to realize the dispersion of nanomaterials so far. But from our foaming experiments, we found that nanomaterials could well be dispersed with the quick inflation of the bubbles.

From literature, we know that the question of bubble growth in polymer melt was first referred by Han and Yoo, who built a Newtonian model to describe the growth of a single bubble in an infinite amount of polymer during mold filling [4]. And in another paper, Yoo and Han further investigated the oscillatory behavior of a gas bubble growing in viscoelastic liquids, and found that the diffusivity of a gas has a profound influence on the occurrence of oscillatory behavior, the elastic property of the suspending medium would also enhance the oscillatory behavior [5]. Amon and Denson once developed a cell model to describe the diffusion-induced growth of closely spaced single bubbles, by considering the effects of heat transfer, solidification, and the bulk flow of the foam in the mold cavity, they made their results of prediction coincide well with their experiments, although there still existed some quantitative differences between the two [6], [7]. Based on the investigation of Patel [8], Ramesh et al. made some modifications to the original Newtonian model to account for the non-Newtonian effects by modeling the polymer as a power law fluid, and compared the prediction results with other models such as the Newtonian model and the viscoelastic cell model [9]. More recently, Allen and Roy studied the nonlinear oscillations of spherical gas bubbles in linear and nonlinear viscoelastic fluids [10], [11]. From the above investigations, we can see that only micro-seconds are needed for the bubbles to grow from the nucleus to its near steady state, and the frequencies of bubble oscillation are of the order of magnitude of megahertz.

In this Letter, according to the models of bubble growth proposed in the literature, a theoretical calculation based on the In-Situ Bubble Stretching (ISBS) method was made, and the nanomaterial dispersion experiments using ISBS method was also reported. In addition to the stretching process, shearing, compression, oscillation of the bubble, as well as the evaluation of the forces and power exerted to the nanogranules, induced by bubble inflation are also analyzed [12], [13].

Section snippets

Preparation of the samples

Foaming is induced by addition of azodicarbonamide to high density polyethylene (HDPE) powder. In order to investigate the dispersion effect of the ISBS method on nanoscale granules, CaCO3 bioblast granules with size of 20–40 nm (the nanomaterial had not been treated with any surfactant, therefore the grain size of the added material is actually micrometer scale) were mixed with HDPE. A mixture composed of 100 phr HDPE powder and 7 phr of CaCO3 was stirred for 3 min in a high-speed stirrer and

Theoretical calculations of the inflation and oscillations in the ISBS method

From our experimental results, it can be seen that the ISBS method can be used to effectively disperse nanogranules in polymers. We used MathCAD to consider the process of bubble inflation and the results are reported in the following parts of this Letter.

For convenience of calculation we consider a spherical gas bubble growing in a large body of viscoelastic liquid. For the purpose of establishing a mathematical model of the ISBS method, an incompressible viscoelastic liquid is assumed, and a

Discussion and conclusions

It is clear from Fig. 1, Fig. 2, Fig. 3 that the aggregated nanogranules around the bubbles were fragmented and well dispersed in the polymer as result of the ISBS method. The dimension of aggregated nanogranules is about 2 μm and the dimension of dispersed nanogranules around the bubble is only 60 nm (measured with the help of the Photoshop 5.0 software).

If the bubble inflation process is assumed to be isothermal and bubble expansion is as fast as about 10−6 s (proved by theoretical

Acknowledgements

The study is supported by the Science & Technology investigation project of Ministry of Education in China under Grant No. 104025, as well as Nature Science Foundation of Beijing City under Grant No. 203001.

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