Elsevier

Polymer

Volume 254, 21 July 2022, 125059
Polymer

Analysis of nanocellular foaming with nucleating agents based on coarse-grained molecular dynamics simulations

https://doi.org/10.1016/j.polymer.2022.125059Get rights and content

Highlights

  • Nanocellular foaming with nucleating agents was simulated using coarse-grained model.

  • Nucleation, growth, and coalescence of nano foams can be reproduced by simulations.

  • Foaming mechanism was changed by interactions between polymers and nucleating agents.

  • There are two mechanisms: Foaming from nucleating agents and foaming within matrix.

Abstract

Nanoscale foaming using nucleating agents was modeled based on coarse-grained molecular dynamics simulations to analyze the nucleation and growth of nanocellular foams. Interactions between the polymer chains and nucleating agents, the blowing rate, and the number of nucleating agents were varied, and foam formation was analyzed. Snapshots of the simulated foamed structures were obtained and characteristic parameters—such as the number of foams and the size distribution of the foams—were estimated. In the case of weak attractive interactions between the polymers and nucleating agents, foams formed first at the interfaces of the polymers and nucleating agents, then formed in the polymer matrix. In the case of strong attractive interactions, foams originated only in the polymer matrix. These nucleation-type foams depended on the number and size of the foams, and on their growth and coalescence. Our simulations indicate that the foamed structures can be modulated by the following parameters: interactions between the polymer chains and nucleating agents, the blowing rate, and the number of nucleating agents.

Introduction

Many industrial products—such as cars, airplanes, houses, and other buildings—make use of foamed materials. Foamed materials are lightweight, provide high-quality insulation, and have low heat conduction; these functions contribute to energy savings and life convenience. In housing, foamed materials are used as thermal insulants. Many studies have focused on foamed structures, structural formation, and how to control structure; these studies have been reviewed in numerous papers [[1], [2], [3], [4], [5], [6], [8], [9]]. Many studies have focused on making small foams (from the micron-to nanoscale) and uniform foams. Foam structure is closely related to corresponding foam functions; techniques to control foam structures have been studied. Recently, high-functioning materials have been requested by users; one such function is transparency [10,11]. To modulate the transparency, fine control of the foamed structure is needed, although it is difficult to precisely control the structure of foams. The transparency is considerably affected by the characteristic sizes, such as the size of the foam and the thickness of the shell of the foam. For example, such considerations pertain to the white turbidity of materials that exhibit phase separation.

Analyses of both the foam structure and the formation of a given structure are needed to understand foamed materials; theories and simulations have contributed to these analyses. Classical nucleation theory can explain the critical radius of foam formation, in which one can separate the states of nucleation and growth of a single foam. Several simulation studies based on classical nucleation theory with statistical thermodynamics theory have been performed, and clear data on the sizes of foams and their dynamics have been obtained [[12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]. Kim et al. reported that nanocellular formation cannot be explained completely by classical nucleation theory [16]. This is because the structure and dynamics of polymer chains are necessary for a description of the physics of the interfaces of foams on the nanoscale, which cannot be included in classical nucleation theory. Studies of foaming, including the structure and dynamics of the polymer chains, are needed. Several detailed analyses of foam structures have been reported. Ma et al. studied both two- and three-dimensional foamed structures using confocal laser scanning microscopy, and revealed the relationship between the section structure and the corresponding three-dimensional (3D) structures in terms of cell size and cell density [27]. Yang et al. reported a model based on classical nucleation theory, and verified that their model changed in accordance with the foaming agent content and shot size [28]. They obtained the number density of a nucleated bubble in accordance with the kinetics results of their model, which were in good agreement with their experimental results.

Several techniques to make fine foams that exhibit a finely controlled structure have been reported; such as using a supercritical fluid under high pressure [29,30] and using nucleating agents [[31], [32], [33]]. Using these techniques, foamed materials that exhibit controlled structures and properties have been produced in batches or by continuous manufacturing. In the present study, the focus was on foaming using a supercritical fluid with nucleating agents. The foams were derived from the nucleating agents, and the control of the structures was examined by nucleation theory. In the initial state, the raw materials were under high pressure. Once the pressure was rapidly decreased, the dissolved gas initiated nucleation and foam growth. To control the foamed structure, several parameters can be considered. The pressure before foaming is affected by the quench depth, which contributes to the dynamics of the phase transition over the course of foaming; in previous studies the pressure drop rate was also a control parameter [21,22,34,35]. The affinity of the nucleating agent for the matrix polymer is also important for structure control. Although the importance of these control parameters is evident, the detailed mechanism of the polymer chain dynamics is not thoroughly understood. Several groups have studied the effect of nucleating agents. Goren et al. studied foam from a poly(methyl methacrylate)/silica nanocomposite that contained various sizes of silica particles and exhibited various surface modifications [31]. They concluded that heterogeneous nucleation was influenced by both the size of the silica particles and the surface chemistry. Small particles provided many nucleation centers; and particles with a small surface free energy—such as silica nanoparticles with surface fluoroalkanes—reduced the critical nucleus radius. Leung et al. studied the critical nucleation radius in accordance with the surface affinity [32]. They concluded that the difference between the wetting angle and the conical cavity angle determined foam growth. McClurg reported four guidelines for identifying an ideal nucleating agent. One of the guidelines is favorable interactions between the polymer matrix and the nucleating agent, from energetics and kinetics standpoints [33]. The kinetics are strongly related to the polymer dynamics.

In the present study, coarse-grained molecular dynamics (CGMD) simulations were performed to study foam formation. The nucleating agents were modeled as single spherical particles, which were mixed into the bulk matrix polymers. Using this system, blowing model simulations were performed to study foamed materials. Our series of simulations revealed that foaming with nucleating agents may be affected by the interactions between the nucleating agents and the polymers, and the foaming mechanism may be related to the interaction potentials. In a previous study of the fracture of filler-filled polymeric materials using CGMD simulations, the fracture voids were formed by various mechanism involving the attractive and repulsive interactions between the filler and the polymer [36]. The interfacial effect of the filler or nucleating agent can only be studied using CGMD simulations. Section 2 presents an overview of the simulations. Section 3 presents and discusses the results of the CGMD simulations in foam formation. Section 4 presents the conclusions.

Section snippets

Simulation model and methods

To simulate the foaming process, we modeled it using bead-spring (BS) chains according to the method described by Kremer and Grest [37]. The details of the simulation method, the parameters used in the Langevin equation, and the Gaussian white noise were the same as those described by Kremer and Grest. [37], and the following parameter set was used: k=30.0ε/σ2, R0=1.5σ, and Γ=0.5τ1 where τ is the unit of time. The unit of temperature was T0=kB/ε. To perform the foaming process simulation using

Parameter study and types of foam formation

The foaming simulation was performed in accordance with the parameters ε = 2.0, 5.0, 10.0, 20.0, and 50.0; and v = 5.0 × 10−5, 1.0 × 10−4, 5.0 × 10−4, 1.0 × 10−3, and 5.0 × 10−3 [1/τ]. The number of nucleating agents was initially fixed at 64. Fig. 3 shows a snapshot of each simulation when the volume was 2.12 × larger than the initial system. In Fig. 3, the nucleating agents are represented by blue spheres, the polymer chains are represented in red, and the interface in which the polymer

Conclusions

Foaming was studied using CGMD simulations. The nucleation, growth, and coalescence of foams depend on several parameters: interactions between the polymer chain and the nucleating agent, the blowing rate, and the number of nucleating agents. The number of nucleating agents and the interaction potential are parameters that modulate the size and number of foams. Regarding strongly attractive interactions, the foams only originated in the polymer matrix; a simple nucleation and growth mechanism

CRediT authorship contribution statement

Hiroshi Morita: Conceptualization, Methodology, Data curation, Writing – review & editing. Satoshi Yoda: Conceptualization, Validation, from experimental side. Takumi Ono: Validation, from experimental side, Writing – original draft, Writing – Part of Original Draft. Kouhei Tazumi: Validation, from experimental side. Takeshi Furuya: Conceptualization, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is based on results obtained from a project (JPNP16010) commissioned by the New Energy and Industrial Technology Development Organization (NEDO), Japan.

References (39)

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