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Kinetics of Formation of Microstructure in Polyurethane Foams Infused With Micro and Nanosized Carbonaceous Fillers.


Cellular materials such as foams have excellent application prospects in civil, aerospace and mechanical engineering. As a type of lightweight material, polyurethane (PU) foams have good heat insulation and mechanical properties. There are a variety of methods to improve the properties of these foams among which the adding micro- or nanoparticles to the foaming system is an important innovation to enhance the mechanical and thermal properties of new PU foams [1]. The properties of PU foams depend on their morphology--density, size of cells and their size distribution, anisotropy of cells, thickness of walls, and so on. Thus, it is very important to investigate the foaming process to be able to create foam with desirable properties. PU foams are created by the so-called reaction foaming, during which the polymerization and the foam expansion take place simultaneously. The reaction kinetics is usually simplified in terms of two overall reactions that is, the gelling reaction and the blowing reaction [2]. Many theoretical model exist which describe the evolution of the PU foam morphology. The evolution of the bubble size can be calculated by one of the two main approaches. The first uses the assumption that the process is entirely controlled by the chemical reaction. The concentration of the dissolved blowing agent (carbon dioxide) is assumed to be always equal to the equilibrium concentration and the rest of the blowing agent is immediately evaporated into bubbles. The second more general bubble-shell model [3]. also includes the effect of diffusion limitation. Recently, Karimi and Marchisio [4] proposed a model, which can predict the evolution of the foam density, temperature, and bubble size distribution using the population balance equation and successfully coupled it with bubble-shell model of Ferkl et al. [5]. However, even this model neglects the additional important aspects of the foam morphology, such as the thickness of walls and the content of polymer in struts. This information is critical for determining mechanical [6] and heat insulating [7] properties of the final foam.

The goal of this work is to study the kinetics of reaction foaming of PU in the presence of different fillers (macro- and nanosized), and the evolution of the bubble size distribution in the process of this synthesis. This process can be described with the aid of the kinetic model of reversible aggregation developed by Kilian et al. [8]. The model can help to explain the formation of a complex morphology in liquid-like systems, that was applied to many polymer systems [9]. A similar approach, we assumed, could be successfully applied to the formation of PU foams reinforced with fillers [10]. Previously studies using such statistical method for describing the evolution of the bubble size distribution used Dirac delta functions centered on nodes of a quadrature approximation [4]. All previous studies neglected additional important aspects of the foam morphology that is, that the bubbles are not spherical but have any anisotropy. The production of PU foams with anisotropic cellular structures could be important for applications in which, for instance, different mechanical properties depending on the load direction are required. This is because the cells are elongated. Shape anisotropy of the cells can be defined as the ratio between the maximum and the minimum length of the cell. Polymer foams usually present anisotropy ratios of about 0.9 [11]. Hence, the important part of our study is an investigation of the evolution of the shape anisotropy of the foam bubbles with time, and its dependence on the presence of different fillers.



The isocyanate used in this study was a oligomeric aromatic isocyanate based on 4,4'-diisocyanate diphenylmethane (MDI) (PM200, from Yantai Wanhua Co. [PR China]). As a chain extender methylene-bis-(2-chloroaniline) (cuamine M) from Ihara Chemical Ind. (Japan) was used. As the main polyol VORANOL 4711 polyether polyol from Dow Chemical Co. (USA) was used. Other polyols were VORANOL RA-640 polyether polyol from Dow Chemical Co. (USA) and PDA-800 from Kazan SK (Russia) (polyester of adipic acid and polyethylene glycol. As catalyst we used 2,2'-dimorpholinodiethylether from Hunstman AG (Switzerland).

As fillers were used carbon nanotubes, thermoexpanded graphite (TEG) and carbon fibers (CFs).

As carbon nanotubes are used agglomerates of multi-wall carbon nanotubes (MWCNTs) from Bayer AG (Germany) with next properties: inner mean diameter ~4 nm, outer mean diameter ~ 13 nm, length > 1 [micro]m. Before using agglomerates of MWCNT have been mill on mill grinder to produce MWCNT with mean length ~200 nm.

TEG was supplied from OOO Novamet-Sealur (Perm, Russia). TEG has an anisotropic structure and consists of 0.66 [+ or -] 0.07 [micro]m thick 2D graphite layers, 0.20 [+ or -] 0.02 [micro]m of which are filled with deformed weakly interacting sheets with a thickness of 0.01 mm consisting of separate crystallites oriented in the sheet plane.

CFs (Trade mark Ural T-l) were supplied from OJSC SvetlogorskKhimvolokno (Novopolotsk, Belorussia). CF has diameter 6-10 [micro]m and length 50-100 [micro]m. The fillers are used in amount of 1 wt%.

Synthesis of PU Foams Samples

PM200 and the polyol were dehydrated under vacuum overnight at room temperature and 60[degrees]C respectively. All samples were prepared using the prepolymer technique [12]. For the isocyanate prepolymer a mixture of 63.9 wt% of PM 200 and 35.1 wt % of VORANOL 4711 was used. For the polyol a mixture of 58 wt% of PDA-800, 38 wt% of Cuamine M and 4 wt% of VORANOL RA-640 was used. We used this mixture of polyols for preparation of the PU foams because we had optimized it previously. The use of an individual polyol led to soft or to hard foams.[10] The ratio of NCO to (OH plus N[H.sub.2]) groups was 1:1. The calculated amount of filler was added to the polyol and then magnetically stirred for at least 24 h (Scheme 1).

Optical Microscopy

An optical microscope, a Micromed Met 400 (Micromed Met Co., Russia) with magnification up to 400 was used to analyze the surfaces of the PU foams in the process of synthesis between two glass with dimension 2 cm x 2 cm. The thickness of samples was controlling by glass fiber with diameter of 1 mm. For analysis was used at least 20 images from different places of the samples.

Fourier-Transform Infrared Spectroscopy

The polyols with fillers and calculated amount of Cuamine M was mixed to full dissolution and 0.02 wt% of catalyst (Metatine 712E) was added. After that to this mixture was added MDI and the mixture was casted onto KBr windows for recording IR-spectra. The infrared spectra were acquired using the Vertex Bruker Fourier-transform infrared spectrometer. A spectral resolution of 2 [cm.sup.-1] was maintained, and 32 scans were co-added for acceptable signal-to-noise ratio. For each kinetic measurement was used at least four experiments. Statistical deviation in kinetic data was <0.5%.

The Images Analysis

The optical images were analyzed as described in our previous paper [10].


The process of synthesis of PU foams includes two global reactions, which are often called "gelling" and "blowing". The gelling reaction between isocyanate and polyol, which creates urethane bonds, can be written as:
[R.sub.1] - NCO + [R.sub.2] - OH [right arrow] - NH - CO - O -
isocyanate      [R.sub.1]                        [R.sub.2]
                polyol                           urethane bond

The blowing reaction between isocyanate and water, which creates urea bonds, can be written as:
2[R.sub.1] - NCo + [H.sub.2]O [right arrow] [R.sub.1] - NH - CO - NH -
             isocyanate                     [R.sub.1] + C[O.sub.2]
                                                             urea bond

Baser and Khakhar [13,14] showed that the gelling reaction is of the second order and the blowing reaction is of the first order. However, our investigation of the kinetics of catalyzed by dibutyltin dilaurate reaction of PU-polyurea synthesis [15] showed that both reactions are zero-order. The complication of the process in our case is connected with concern in reaction amine (N[H.sub.2]) from the chain extender. The intensity of the absorption band for NCO stretching was calculated by taking an integral of the band at 2,275 [cm.sup.-1] and subtracting the integral value under the baseline in the same region by using Opus Software (Bruker). The resultant intensity values were divided by the intensity of the absorption band at 2,930 [cm.sup.-1] for the CH stretching, which remained practically unaffected throughout both the gelling and blowing reactions, to ensure that the quantitative results are independent of the thickness of the sample film. The examined system (polymerization in a thin layer between two glasses) is almost isothermal. But real foaming (in a cup with a rising foam) is highly non-isothermal. We understand this difference from foaming at real industrial process conditions; however, as model approach this way can be used.

Figure 1 shows the IR spectra taken in the course of the PU foams formation. A closer look at the spectra in the spectral region of 2,400-1,600 [cm.sup.-1] reveals that the absorption band for NCO stretching at 2,275 [cm.sup.-1] gradually decreases as the reaction proceeds, and ultimately disappears upon completion of the reaction. A new absorption feature grows in at 1,740-1,650 [cm.sup.-1] upon urethane and urea bond formation. The first step in the kinetic studies of reactions is to determine the order of reactions. The graph of natural logarithm of NCO absorbance vs. time exhibits a linear decay (Figs. 2 and 3). Hence, the reaction under study is of first order at all amounts and types of fillers. Typically, noncatalyzed NCO - OH reactions follow second-order kinetics (first order with respect to NCO and OH) [16]. However, the use of a catalyst decreases the reaction order [17]. at that more effective catalyst has more pronounced effect on decrease the reaction order [18]. Hence, the catalyst we selected (dibutyltin dilaurate) is very effective for PU foams synthesis. The reaction rate constant was determined by measuring the slope of the kinetic curve (Fig. 2).

The kinetics of the gelling and blowing reactions can be separated by studying the IR spectra using the part of carbonyl groups in urethane and urea bonds [19] in the C=O (1,750-1,600 [cm.sup.-1]) region. The graph of the natural logarithm CO absorbance for urethane and urea bonds vs. time are linear (Figs. 4 and 5) only at the first stage. Hence, the gelling and blowing reactions have two stages: in the first stage the reactions are first-order, and in the second stage they are second-order. The viscosity of the reacting mixture is not constant during the PU foaming process. It decreases with increasing temperature, increases with the conversion of the polyols and approaches infinity when the gel point is reached [20]. Hence, the progress of the PU foaming process leads to an increase of diffusion limitation and change the order reactions.

The main objective of this study is to investigate the evolution of bubble size during foaming. It is well accepted that the bubble size distribution represents one of the most important properties of the final PU foam. In case of the PU foaming, the initial reaction mixture is vigorously mixed for several seconds. This results in small air bubbles being whipped into the liquid. Thus, the system never reaches large enough supersaturation, which would lead to nucleation of additional bubbles. The bubble growth can be mathematically described through a Schulze-Flory delta functions [8].

The PU foams were analyzed by optical microscopy in order to determine their morphology relative to the filler used (Fig. 6). The purpose of the optical microscopy analysis was to determine the size of the bubbles and their size distribution, both of which undoubtedly affect the performance of the resulting PU foams. The optical images obtained were segmented and subjected to digital analysis to elucidate the statistical size distributions of the bubbles. To analyze the resulting histograms we used the model of reversible aggregation [10].

The area of each bubble was converted into the bubble diameter for a circle with the area equivalent to the bubble area. Two processes determine the mean bubble size during a PU foaming process: primary growth and coalescence. Figure 6 shows also the histograms that resulted from the statistical analysis of the optical images of the PU foams formed at loading different fillers. The histograms were obtained by using a bimodal version of the model reversible aggregation [10]. In Fig. 6, the two lower lines represent the individual distributions, whereas the upper line represents the sum over the two ensembles forming at primary growth and coalescence. We suggest that the cells involved in the first statistical ensemble (i.e., small bubbles, distribution no. 1) were formed during the primary growth steps of the PU foam synthesis whereas the bubbles involved in the second statistical ensemble (large bubbles, distribution no. 2) resulted from the coalescence. The mean bubble area of each statistical ensemble as a function of the PU foam compositions are given in Table 1. The mean bubble size of each statistical ensemble can be assumed as a basic value when the influence of additives on the PU foam morphology is analyzed. Therefore, the blowing reaction, which leads to the diffusion of the gas molecules towards and into the bubbles, results in the bubble growth, whereas by sliding onto each other, bubble coalescence within the PU foam also occurs. This scheme of the bubble growth was supported by our data on the mean size of primary bubbles for the PU foam formation when loaded with different fillers (Fig. 7).

The mean sizes of primary bubbles are in good correspondence with the kinetics of isocyanate group disappearance. Similar, the mean size of primary bubbles correlate with rate constant of isocyanate groups disappearance. The mean size of the primary bubbles of the PU foams follows the same order as the rate constants of isocyanate group disappearance (MWCNT, neat, TEG, and CF). For large bubbles formed through coalescence, a similar dependence is observed (Fig. 8), because their sizes are directly related to those of primary bubbles.

Therefore, the growth of the bubbles of PU foams and their size distribution are governed by the hydrolysis reaction of the isocyanate groups. The kinetics of phase formations is a fundamental subject in material and interfacial science that has a broad impact in material manufacturing and use. Three important kinetic phenomena associated with phase formation, are microstructure, growth rate, and shape evolution. The growth processes associated with the phase formation vary depending on driving forces. The analytical description of the kinetics of bubble growth was performed through the use of the universal law of cluster growth in the form [21]:

<d> = [ct.sup.n] (1)

For this purpose, the experimental results were presented in logarithmic coordinates (Fig. 9). The analysis of the data makes it possible to distinguish two stages of bubble growth. At the first stage, the power index is n [approximately equal to] 1, while at the second stage, n [approximately equal to] 1/2. The first stage (1-7 min, Fig. 9a) corresponds the fast growth of bubbles as result the admission of carbon dioxide without diffusion limitation. The second stage (after 8 min, Fig. 9b) corresponds to the diffusion mechanism of coalescence [21].

As can see, at both stages the dominant effect of chemical kinetics is that the maximum of bubble size is observed for the PU foams filled with MWCNT. However, the presence of the fillers decreases the coalescence, as can see from relative contribution of the two statistical ensembles (Table 1). As a result, the mean size of bubbles of neat PU foam is close to that of PU foam filled with MWCNT. The dimensions of fillers also influence on bubble growth. Thus, the use of 2D fillers (TEG) leads to formation of smaller bubbles in PU foams, which is important for their isolation properties.

The production of foams with anisotropic cellular structures could be important for applications in which, for instance, different mechanical properties depending on the load direction are required. This is because the bubbles are elongated. In order to examine the single bubbles deformation we used a shape factor F determined as F = 4[pi]A/[P.sup.2] were A is the area and P the perimeter of the particle's cross section [11]. For an un-deformed particle, F = 1 (sphere) and for the maximum deformation F = 0 (ultra-thin fiber of a vanishing diameter). Polymer foams usually present anisotropy ratios of about 0.9 [11].

Figure 10 shows quantitatively the evolution of anisotropy of the bubbles with time of foaming. The most interesting finding here is the maximum anisotropy of the PU foam bubbles filled with MWCNT. This finding correlates with the mean bubble size. The anisotropy is minimum at loading with TEG, where the mean bubble area is also a minimum. Hence, the deformability of bubbles is predetermined by their size rather than other condition.


In this work, at study of the growth of bubbles of PU foams infused with 1 wt% of micro (TEG and CF) and nanosized (MWCNT) carbonaceous fillers with different dimensionality (ID and 2D) has been presented. Kinetics of the gelling and blowing reactions was studied by IR spectroscopy. It was shown that independently on filler used, the reactions is in two stages, first the stage being of first order, and next one of the second order. It has been observed that nanosized fillers (MWCNT) accelerate the reaction of disappearance of isocyanate groups.

The main objective of this study was to investigate the evolution of bubble size during foaming. The optical images obtained during foaming were analyzed using the model of reversible aggregation to elucidate the statistical size distributions of the bubbles. It was shown that the process of foaming also proceeds in two stages, and consists of two overlapping processes of bubble growth and their coalescence. The mean sizes of bubbles determined by the rate of generation of carbon dioxide, depend on the filler used. The presence of 2D fillers (TEG) leads to formation of bubbles with the smallest mean size diameter. The presence of fillers leads to suppression of bubble coalescence and narrower size distributions.


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Dmitry V. Pikhurov (iD), (1) Vjacheslav V. Zuev (iD) (1,2)

(1) ITWO University, Sankt Petersburg, 197101, Russian Federation

(2) Institute of Macromolecular Compounds of the Russian Academy of Sciences, Sankt Petersburg, 199004, Russian Federation

Correspondence to: V.V. Zuev; e-mail:

DOI 10.1002/pen.25040

Caption: SCH 1. Foaming process.

Caption: FIG. 1. IR SDectrum of PU foam filled with 1 wt% of MWCNT.

Caption: FIG. 2. The evolution of absorbance of C=0 groups of PU foam filled with 1 wt% of MWCNT with foaming time. [Color figure can be viewed at]

Caption: FIG. 3. Evolution of the natural logarithm of NCO groups at foaming. ([??]--neat PU foam, x --PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). [Color figure can be viewed at]

Caption: FIG. 4. Evolution of the natural logarithm intensity of CO urethane groups at foaming. ([??]--neat PU foam, X -PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). [Color figure can be viewed at]

Caption: FIG. 5. Evolution of the natural logarithm intensity of CO urea groups at foaming. ([??]--neat PU foam, x--PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). [Color figure can be viewed at]

Caption: FIG. 6. Optical images of PU foams at foaming (1) after 1 and (2) after 11 min; a--neat PU foam, b--PU foam with CF, c--PU foam with TEG, d--PU foam with MWCNT) and corresponding statistical distributions of bubble areas. Lines 1 and 2 are distributions for first and second statistical ensembles. [Color figure can be viewed at]

Caption: FIG. 7. Evolution of mean diameter of bubbles of first statistical ensemble at foaming ([??]--neat PU foam, x--PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). [Color figure can be viewed at]

Caption: FIG. 8. Evolution of mean diameter of bubbles of second statistical ensemble at foaming ([??]--neat PU foam, x--PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). [Color figure can be viewed at]

Caption: FIG. 9. (a) Dependence of the natural logarithm of the mean diameter of bubbles vs the natural logarithm of the foaming time at first stage of foaming ([??]--neat PU foam, X--PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). (b) Dependence of mean diameter of bubbles vs square root of foaming time at second stage of foaming ([??]--neat PU foam, x--PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). [Color figure can be viewed at]

Caption: FIG. 10. Evolution of bubble anisotropy with foaming ([??]--neat PU foam, X--PU foam with CF, [??]--PU foam with TEG, [??]--PU foam with MWCNT). [Color figure can be viewed at]
TABLE 1. Summary of kinetic parameters.

                             First order
                                 rate         First order
                               constant           rate
           Rate constant       creation         constant
           disappearance        of CO         creation of
               of NCO          urethane         CO urea
              groups,          groups,          groups,
Loading,   [min.sup.-1] x   [min.sup.-1] x   [min.sup.-1] x
1 wt%        [10.sup.4]       [10.sup.3]       [10.sup.3]

Neat             30               16               25
MWCNT            46               17               23
TEG              22               6                17
CF               16               17               25

              Second order
             rate constant         Second order
              creation of         rate constant
              CO urethane          creation of
                groups,              CO urea         Part of first
           1 x [Mol.sup.-1] x   1 x [Mol.sup.-1] x    ensemble in
Loading,     [min.sup.-1] x       [min.sup.-1] x      full volume
1 wt%          [10.sup.3]           [10.sup.3]

Neat               4                    7                0.551
MWCNT              5                    8                0.641
TEG                2                    7                0.608
CF                 4                    7                0.568
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Author:Pikhurov, Dmitry V.; Zuev, Vjacheslav V.
Publication:Polymer Engineering and Science
Article Type:Report
Date:May 1, 2019
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