# How increasing amounts of trimerization catalyst impact the formation, isocyanurate content and microstructure of poly(urethane-isocyanurate) rigid foams

Joël Reignier, Françoise Méchin, Alexandru Sarbu

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Joël Reignier, Françoise Méchin, Alexandru Sarbu. How increasing amounts of trimerization catalyst impact the formation, isocyanurate content and microstructure of poly(urethane-isocyanurate) rigid foams. Industrial and engineering chemistry research, 2024, 63 (48), pp.20824-20839. 10.1021/acs.iecr.4c02965 . hal-04768993

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How increasing amounts of trimerization catalyst impact the
formation, isocyanurate content and microstructure of
poly(urethane-isocyanurate) rigid foams

<table><tr><td>Journal:</td><td>Industrial & Engineering Chemistry Research</td></tr><tr><td>Manuscript ID</td><td>ie-2024-02965m.R2</td></tr><tr><td>Manuscript Type:</td><td>Article</td></tr><tr><td>Date Submitted by the Author:</td><td>n/a</td></tr><tr><td>Complete List of Authors:</td><td>Reignier, Joël; INSA Lyon, CNRS UMR 5223<br>MECHIN, Françoise; Institut National des Sciences Appliquees de Lyon, IMP<br>Sarbu, Alexandru; Soprema SAS</td></tr></table>
<figure><img src="image_2.png" /><figcaption>Graphical Abstract</figcaption></figure>

213x77mm (149 x 149 DPI)
# How increasing amounts of trimerization catalyst impact the formation, isocyanurate content and microstructure of poly(urethane-isocyanurate) rigid foams

Joël REIGNIER<fnref n="1" />,<fnref n="2" />, Françoise MECHIN<fnref n="1" />, Alexandru SARBU<fnref n="3" />

## Abstract

This study investigates the effect of trimerization catalyst (mainly composed of potassium ethyl hexanoate) content (0.5 to 6 pphp) on the kinetics, chemical properties and cellular morphology of poly(urethane-isocyanurate) rigid (PIR) foams. Increasing the trimerization catalyst content was found to accelerate the foaming process since all its characteristic times (cream time, gel time and tack-free time) were found to decrease (Δt_gel ~ -85%). Increasing the trimerization catalyst content was also found to significantly increase the maximum temperature reached during foaming, from 122°C to 162°C. ATR-FTIR spectroscopy analysis of the foam samples demonstrated that increasing the

<footnote n="1">¹ Université de Lyon, CNRS, Université Claude Bernard Lyon 1, INSA Lyon, Université Jean Monnet, CNRS
UMR 5223, Ingénierie des Matériaux Polymères F-69621 Villeurbanne Cédex, France</footnote>

<footnote n="2">² Author to whom correspondence should be addressed. E-mail: joel.reignier@polymtl.ca</footnote>

<footnote n="3">³ SOPREMA, 67025, Strasbourg, France</footnote>
trimerization catalyst level significantly increased the isocyanurate content of the PIR matrix, which corroborated the reduction of non-reacted isocyanate. Accelerating the chemical reactions was also found to decrease the foam density and the cell height significantly ($Δρ_f$ ~ -31% and $Δh$ ~ -47%, respectively), thus increasing the cell population density by more than a factor x15 through the reduction of cell coarsening and Oswald ripening. Open cell content was maintained very low with a value under 4% for all catalyst contents.

### Keywords

Polyurethane, polyisocyanurate, poly(urethane-isocyanurate), foam, infrared spectroscopy, catalyst, kinetics, cellular microstructure

## 1. Introduction

Poly(urethane-isocyanurate) rigid foams (PIR) are widely used for insulation in construction as they offer high insulation capabilities as well as higher fire resistance with respect to their polyurethane counterparts. Conceptually, urethane-modified polyisocyanurate foams are made of a copolymer of polyurethane and polyisocyanurate. Urethane bond is formed by the reaction of isocyanate and polyol, while isocyanurate bond (trimer) is formed by the cyclotrimerization of three isocyanate groups (gelling reactions). However, it is well known in the field of PIR formulations that their chemistry is very complex, and the precise description of the whole system is almost impossible because of the various possible side reactions (Figure 1). Determination of the concentrations of main functional groups in real PIR foam (isocyanate index=350) revealed that the proportion of urea and allophanate are not negligible in terms of NCO consumption with about 16wt.% and 5wt.%, respectively [1]. In model systems, direct cyclotrimerization of isocyanate through uretidinedione (dimer) was found to be favored in the absence of polyol [2] while isocyanurate formation is more prone to occur through urethane and allophanate formation (followed by ring closure) in presence of alcohol [3]. Computational study revealed that the cyclotrimerization of methyl isocyanate proceeds directly to
the isocyanurate (i.e. without uretidinedione) in presence of the right catalyst [4]. Isocyanurate (trimer) can also be generated through urea and biuret intermediate products when water (usually added as co-blowing agent to generate CO₂) reacts with excess of isocyanate (Figure 1). In parallel, physical blowing agents (often composed of pentane isomers and/or cyclopentane) are used as the major source of expansion of air bubbles entrapped during mixing but, as their name indicates, are not involved in the chemical reactions [5]. The trick of the formulation consists in balancing the blowing and gelling reactions in order to get a low-density foam product together with a low open-cell content to ensure a low thermal conductivity.

<figure><img src="image_3.png" /><figcaption>**Figure 1:** Schematic of competing reactions in the synthesis of poly(urethane-isocyanurate) foams.</figcaption></figure>

Obviously, one of the most important properties for PIR foam insulation panels used in the building sector is thermal conductivity (often called “lambda” or just noted “λ”) and it is accordingly the major preoccupation of manufacturers. Reducing λ can be accomplished by using the physical blowing agent (BA) with the lowest intrinsic thermal conductivity (mixtures of BA are often used) and/or by
decreasing the cell size. The latter is generally accomplished by adding small proportions of a
perfluorinated liquid compound [6,7] such as perfluoro(4-methyl-2-pentene). The mechanism behind
the cell size reduction of PUR/PIR foams in presence of organofluorine additives (OFAs) has never been
elucidated, but recent advances in the area of aqueous foams demonstrated that the phenomenon
should be related to the formation of a mixed fluorocarbon/surfactant layer at the interface between
the gas and water, not only preventing coarsening but also hindering coalescence [8]. A more recent
study seems to indicate that the reduction of pore size associated with the presence of
perfluorocarbons is not related to its impact on foam aging (coalescence and diffusional coarsening
were found to be negligible in their study) but it would mainly act by facilitating the entrainment of air
bubbles in the reactive mixture which will later become the cells of the foam [9].

Several researchers also reported the decrease in cell size upon addition of various fillers in PUR/PIR foams [10-14]. It is often claimed in the literature that the lower cell size is caused by an increase in the nucleation efficiency, according to the heterogeneous nucleation theory [13,15]. One can be surprised, however, by the extremely low nucleation efficiency of the filler with only one cell generated for about 10⁸ particles in the case of PUR-carbon nanofibers [16] or 10¹⁰-10¹¹particles for PUR-Cloisite® 30B composite systems [13].

In parallel, a number of studies have reported that the partial or complete substitution of standard petroleum-based polyols with biobased polyols could lead to a significant decrease in cell size [17-22]. Arguments based on the higher viscosity of the biobased polyol are often used, since increasing the medium viscosity should increase the number of air bubbles entrapped during mixing and limit cell coalescence [18,22]. Interestingly, some authors [20,23,24] argued that the cell size reduction was the result of the faster foaming and gelling reactions attributed to the presence of primary hydroxyl groups on the backbone of the bio-based polyol, reacting three times faster than secondary hydroxyls in polyurethane reactions [25].
Recent works in the area of nucleation of PUR/PIR foams aimed at comparing the competitive mechanism of aeration (entrapment of air bubble during intense mixing) and “real” nucleation (formation of stable nuclei from a supersaturated liquid/gas solution). In a general way, it has been established that the cellular morphology is mainly controlled by the number of air bubbles entrapped during mixing [5,26,27], even in the presence of fillers [28]. As a result, any factor that will impact the size distribution of air bubbles (viscosity of the phases including the addition of fillers, mixing device, speed of mixing, air pressure over the mixture, etc.) may potentially affect the final morphology of the foam and its thermal insulating properties. However, changes in the reaction kinetics of the foam formation are often neglected to interpret the results and rarely discussed. It also seems that studies dedicated to the effect of trimerization catalyst on the properties of PIR foams are rather scarce [29-31] perhaps because catalysis in PIR foams is much more complex that in PUR systems [32].

It is therefore the purpose of this study to determine how the change in reaction kinetics through an optimized catalysis may affect the chemistry of the solid phase or the cellular morphology of the PIR foams. To do so, the trimerization catalyst concentration was modified over a large range (much wider than what is normally used on a production line) in order to emphasize its influence on the PIR foam characteristics. The paper is structured as follows. First, the change in foaming kinetics was analysed using the foam qualification system FOAMAT in parallel to the measurement of characteristic times. The second part was dedicated to the resulting change in chemistry of the PIR matrix as determined by FTIR measurements. Eventually, the change in cellular morphology was analysed and discussed in detail. This study will be followed by another showing how the change in reaction kinetics impacted the thermal conductivity of PIR foams.
## 2. Experimental details

### 2.1. Materials

A modified phthalic anhydride-based aromatic polyester polyol (PS-2412, provided by STEPANPOL®) having a hydroxyl value of 240 mg KOH/g and an average functionality f~2 was used. The physical blowing agent, 2-methylbutane (Isopentane, boiling point 27.8°C) with molar mass of 72.15 g/mol was kindly supplied by Inventec. Tap water was used as a co-blowing agent. A complex tertiary amine (Niax catalyst PM-20 PLUS from Momentive) was used as both PUR and PIR catalysts in combination with potassium ethyl hexanoate (provided with a diluent, tradename Niax catalyst K-Zero 3000 from Momentive; 15 wt.% K atoms) known for its ability to enhance the trimerization of isocyanate. Unlike other potassium ethyl hexanoate catalysts which can be found on the market, it is worth noting that K-Zero 3000 does not contain any alcohol or glycol as solvent and as a result should not affect the amount of isocyanate consumed by the catalyst itself. However, it may contain about 3wt.% of water according to the supplier. The concentration of K-Zero 3000 (referred as "K-Oct" in this work) was varied from 0.5 to 6.0 parts per 100 parts polyol (pphp), which corresponds to 1.06x10⁻³ to 12.65x10⁻³ K atom per NCO group. Tegostab B 84501, a polysiloxane-ether copolymer used as a surfactant was supplied by Evonik. Tris(1-chloro-2-propyl) phosphate (TCPP) from Shekoy was used as a flame retardant and as a thinning agent for the liquid mixture. The polymeric 4,4'-diphenylmethane diisocyanate (pMDI), Desmodur 44V70L (NCO content 31.2 wt%, isocyanate equivalent weight M<sub>NCO</sub>=134.7 g/mol<sup>-1</sup>, functionality 2.7<f<3.0) was provided by Covestro. The amount of pMDI required for the reaction with polyester polyol and water was calculated in order to obtain an initial NCO/OH ratio of 3.37 (isocyanate index 337). However, it should be pointed out that this value only corresponds to a maximum since tiny quantities of water molecules may contaminate the various components such as polyol or catalyst. In our case, only the amount of K-Oct varies and a simple calculation indicates in the worst case (6 pphp K-Oct) that the water content may increase by 0.18 pphp (=3wt.% of H₂O in 6 parts of K-Oct) thus decreasing the isocyanate index from 337 to 325. This should have a very limited impact on the theoretical amount of isocyanurate trimer since it should only decrease from 43.34% to
42.64% based on the total mass of the formulation. This reduction can be considered as negligible when compared to the amount of residual isocyanate (unreacted) usually detected at the end of the foaming process (see section 3.4). Note that all chemicals were used as received without further purification.

## 2.2. Foaming Process and Kinetics

All formulations were aimed for a calculated Index of 337. Given the experimental conditions a potential 1.5% variation can be recorded for the Index value. A two-step procedure is used for the preparation of the PIR foams: First, a premix (Part A) was prepared from polyol and all the different additives. After the addition of each component (in the order: fire retardant, surfactant, chemical blowing agent, catalysts and finally physical blowing agent), the mixture was stirred for 5 seconds using an IKA rotating mixer fitted with a LENART disc (VOLLRATH GmbH - ø=60 mm) at a speed of 2500 RPM. The temperature of the polyol premix and pMDI was controlled to about 20±0.5°C. Foams were then prepared by adding (via a weighed syringe) the exact amount of pMDI (Part B) and immediately mixed at 4500 RPM for 5 s before being poured into the cylindrical mold (180 mm height, 150 mm in diameter) of the Foamat® apparatus (Model 281 from Lesstechnik GmbH, Germany) [33]. The inner side of the cylindrical wall was tightly covered with a facing sheet similar to those typically used for the panel production. The temperature of the expanding mixture was measured using a thin wire type J thermocouple inserted laterally through a hole in the cardboard cylinder at 5 cm from the bottom and in the center of the foam bun. According to the supplier, placing the thermocouple in the lower third of the cylinder should give the maximum core temperature. The height (H) of the rising PIR foams was constantly monitored as a function of time by an ultrasound sensor placed a dozen centimetres above the top of the cardboard cylinder. The dielectric polarization (DP) of the foam extreme bottom surface was measured during foaming through the polarization sensor (also called the cure-monitoring device or CMD) placed at the bottom of the foam bun. DP is mainly controlled by free chain-like molecules
with a large dipole moment (presence of polar ends such as OH and/or NCO groups) and should therefore regularly decrease during curing. It is interesting to note that the FOAMAT® apparatus also includes a gauge (Foam Pressure Measurement) that measures the force exerted by the foam during its downwards expansion once the growing polymer matrix reaches a sufficient rigidity. Even if the analysis of pressure (P) curves was found to yield valuable information regarding PUR formulations, it appeared to be biased in the case of PIR foams (P<500 Pa). This was tentatively attributed to some slipping of the foam on the lateral faces of the expansion container because trimerization reactions (reticulation) are strongly prevented at the cold surface (internal work not published). All data provided by the FOAMAT (height, temperature, pressure and dielectric polarization) are reported in Figure S1 as a function of time and for the various catalyst concentrations. Finally, each foam cylinder was removed from the mold after 15 min and conditioned at room temperature for 7 days before being cut and analyzed. In a general way, all samples used for foam characterization were taken in the center region of the foam because both temperature and foam density were found to be relatively uniform there, with the exception of outer edges [34]. The precise moment when the isocyanate was added to the premix was considered as the starting time. Details of the formulations are reported in Table 1.

<table><caption>**Table 1** : Compositions of the PIR foam formulations.</caption><thead><tr><th>Components (wt parts)</th><th>Content (pphp)</th></tr></thead><tbody><tr><td>Polyester polyol</td><td>100</td></tr><tr><td>TCPP (flame retardant)</td><td>16</td></tr><tr><td>B84501 (Silicone surfactant)</td><td>2.5</td></tr><tr><td>PM-20 PLUS (PUR and PIR catalysts)</td><td>1.33</td></tr><tr><td><strong>K-Oct (PIR catalyst)</strong></td><td><strong>0.5 – 6<sup>a</sup></strong></td></tr><tr><td>water</td><td>1.0</td></tr><tr><td>Isopentane</td><td>25.4</td></tr><tr><td>pMDI based isocyanate</td><td>244.55</td></tr></tbody></table>

<footnote>a i.e. 1.06x10⁻³ to 12.65x10⁻³ K atom per NCO group, or 948 to 79 NCO per K atom</footnote>
In parallel to the use of the Foamat® apparatus, the main characteristic reaction times of the various PIR foams were estimated: The cream time ($t_{cream}$) corresponds to the start of foam rise (start of expansion) which occurs simultaneously with slight color changes of the liquid mixture. The gel time ($t_{gel}$) marks the start of stable network formation and, practically, corresponds to the time when a wooden applicator stick (150 mm x 18 mm x 1.5 mm) encounters resistance when pushed vertically into the upper part of the rising foam bun. At the tack-free time ($t_{tack-free}$), the outer surface of the foam loses its stickiness (the flat part of the wooden stick is used for that purpose), which marks the end of the macroscopic phenomena. In a general manner, the experimental error on the characteristic times is about ± 1, 3 and 5 s for the cream, gel and tack-free times, respectively.

## 2.3. Foam Characterizations

### 2.3.1. ATR-FTIR Spectroscopy

Fourier Transform Infrared Spectroscopy (FTIR) was used in attenuated total reflectance mode (ATR) to characterize the evolution of the chemical structure of the various foams as a function of K-Oct content. For each sample, 32 scans were recorded in the range of 4000-600 cm⁻¹ at a resolution of 4 cm⁻¹. Note that an atmospheric background was collected before sample analysis. A thin slice (approximately 5 mm thick) was first sawed in the cylindrical foam bun at about 6 cm from the bottom. Each square base foam sample (around 2 cm x 2 cm) was then cut in the center of the disc and pressed with a constant clamping force over 6.89x10⁷ Pa through a flat tip (to ensure tight contact between the sample and the prism in the ATR) against the diamond crystal. This pressure exerted on each sample was found to be high enough to crush the foam sample, leading to an almost bulk film with a thickness of around 0.5 mm (about 10 times smaller than the initial sample thickness). All spectra were analyzed using the supplied OMNIC Spectra software. All measurements were done at room temperature (23±2°C).
### 2.3.2. Mass Density Measurements

For each catalyst content, three samples (approximate dimensions: 30 mm x 80 mm x 80 mm) were cut at room temperature in the centre of the foam bun (Foamat®) using a razor blade. A caliper was used to determine the real dimensions of each sample while scales (accuracy of 10⁻⁵ g) were used to measure its weight. The (apparent) density of each foam formulation was estimated through the average ratio of its weight and volume. The repeatability of the density measurements can be reasonably estimated to about ± 5%.

### 2.3.3. Open-cell Content

A gas pycnometer (Ultrapyc 1200E from Quantachrome Instruments) was used to determine the open-cell content of the various PIR foams in accordance with the method described in EN ISO4590:2016. Typically, three cubic samples (around 25 mm × 25 mm × 25 mm) were cut in the centre of the foam bun (Foamat®). The nitrogen gas pressure (P~50 kPa) was kept sufficiently low to avoid collapse of the cellular structure.

### 2.3.4. Morphology observation and image analysis

Foam samples fractured in liquid nitrogen were coated with gold and observed perpendicularly to the rise direction (z-axis) using a scanning electron microscope (SEM) (Hitachi, model S3500N) operated at a voltage of 10 kV. A semi-automatic method of image analysis (ImageJ software, U.S. National Institutes of Health) was used to quantify the cellular morphology of the various PIR foam samples. The average cell diameter (x-y plane) and cell height (z-axis) were given by the minor (d) and major axis (h) of the best fitting ellipse, respectively. The average shape ratio of the cells R (=h/d) was defined by major axis/minor axis ratio of the fitted ellipses. Since all cells were not sectioned at their widest point, many appeared smaller than they actually were, and the average diameter was therefore multiplied by a correction factor of x1.2739 (ASTM D 3576-98) in order to take into account this
statistical phenomenon. An average number of about 150 cells was used to evaluate cell morphology for each catalyst content.

The cell population density of a morphologically isotropic foam product, as defined by the number of cells per unit volume of the original bulk polymer, is usually evaluated by:

$$ \beta \approx \frac{6 \times 10^{+12} [(\rho_p / \rho_f) - 1]}{\pi d^3} \quad (1) $$

where $\beta$ is the cell population density (cell/cm³), $d$ the average diameter of the cells (µm), $\rho_p$ and $\rho_f$ the densities of the bulk and foamed polymer respectively. The density of the poly(urethane-isocyanurate) bulk material is taken from the literature: $\rho_p \sim 1200 \text{ kg/m}^3$ [35,36]. In order to take account of the cell elongation in the rise direction (R>1), the experimental foam density ($\rho_f$) was replaced by $\rho_f^*=\rho_f \times R$ where R (=h/d) is the average shape factor of the cells. This simple transformation permits to estimate $\beta$ for an equivalent foam characterized by a shape factor equal to unity (R=1).
## 3. Results and discussion

### 3.1. Influence of catalyst concentration on characteristic times, rise height and rise rate profiles

<figure><img src="image_4.png" /><figcaption>**Figure 2:** Evolution of characteristic times during foaming as a function of K-Oct content (pphp). The lines are only guides for the eyes.</figcaption></figure>

The evolution of characteristic times is reported in Figure 2 as a function of K-Oct content. Increasing the trimerization catalyst content from 0.5 to 6 pphp (an increase by a factor of 12) decreases the gel time from 260 s to about 40 s (Δt_gel~ -85%), but also reduces the cream time (a zoom view is reported in Figure S2) from 17 to 8.5 s (Δt_cream~ -50%). This supports the fact that the trimerization catalyst not only promotes the isocyanurate reaction but also the blowing (water/isocyanate) and/or urethane (polyol/isocyanate) reactions [37]. This is particularly important since the relative rates of isocyanurate and urethane formation will determine the chemical structure of the solid matrix and hence the physical properties of the final foam product. It is also apparent that the relationship between t_gel and catalyst content is not linear but shows an initially rapid decrease with increasing catalyst content, followed by a progressive levelling off beyond 3 pphp. The evolution of t_tack-free, characteristic of the
foam surface (top) is quite similar to the $t_{gel}=f(K-Oct)$ curve except that it is shifted to higher times by 50-80 s. Several authors assessed the kinetic rate or catalyst activity by comparing the inverse of the characteristic times [29,38]. Interestingly, plotting the evolution of $1/t_{gel}$ and $1/t_{tack-free}$ as a function of K-Oct content shows a linear relationship in both cases (r$^2$~0.98), as depicted in Figure 3.

<figure><img src="image_5.png" /><figcaption>Figure 3: Evolution of $1/t_{gel}$ (s$^{-1}$) and $1/t_{tack-free}$ (s$^{-1}$) as a function of K-Oct content (pphp). Each line corresponds to the best-fit line through all the data points with a linear law (r$^2$~0.98).</figcaption></figure>

Normalized rise profiles are usually compared by dividing the foam height obtained at instant t by the maximum height of each foam sample [39]. Generally speaking, the rise curve reflects the dynamics of blowing generation, which implies from Figure 4a that increasing the PIR catalyst content leads to faster bubble expansion, in accordance with the decrease in $t_{cream}$ highlighted in Figure S2. The corresponding rise rates (dH/dt) curves are reported in Figure 4b as a function of time and demonstrate that increasing the catalyst content from 0.5 to 6 pphp increased the maximum rise rate of the first
peak from about 1.5 to more than 7.1 mm/s, respectively (Figure S3). Then the slope of each
normalized height curve tends to decrease significantly and rises again beyond values ranging between
85 and 95%: the higher the catalyst content, the lower this percentage. This two-step profile is typical
of PIR foam formulations [18,32,37,40] and becomes more visible on the rise rate curves reported in
Figure 4b with the presence of two distinct peaks, thus suggesting that the two main reactions do not
occur simultaneously but rather sequentially. In the same way as the first peak, increasing the catalyst
content leads to an increase of the maximum rate of rise due to the additional heat brought by the
exothermic isocyanurate formation (maximum of the second peak) from about 0.1 to 3.1 mm/s (Figure
S3). In addition, the time to reach the second peak maximum, referred to as the isocyanurate peak or
the "trimer bump", is reported in Figure S4 as a function of the PIR catalyst content and fairly matches
the evolution of t<sub>gel</sub>, which tends to demonstrate that gelation is mainly attributed to the trimerization
reaction. For increasing catalyst concentrations, the position of the second peak is shifted to lower
times and its area seems to increase, which would suggest an increase in the final isocyanurate
content. It is also apparent from Figure 4b that increasing the catalyst content reduces the time
between the initial rise peak and the second peak (trimerization), but also increases the magnitude
difference between those two peaks. Eventually, it is interesting to note that increasing the
concentration of K-Oct increases the maximum foam height (H<sub>max</sub>) from 162 to 196 mm (Figure S5) and
therefore suggests that the overall density of the final foam product should decrease (see section 3.4).

The evolution of the time needed to reach Hmax of the foam bun as a function of catalyst content was
found to be relatively close to the tack-free time curve, as reported in Figure S4. It is also interesting
to note that the normalized height and rise rate curves (Figure 4) corresponding to 0.5 and 0.75 are
almost superimposed below 100 s, which may indicate that a kind of threshold must be reached to
increase the blowing and/or urethane reactions. One could have doubts about the accuracy of catalyst
content and/or homogenization of the liquid mixture at very low PIR catalyst content, but the shift in
the isocyanurate peak observed for longer times seems to prove the contrary (Figure S6).
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 4:** Evolution of (a) the normalized height ($h/h_{max}$ in percentage) and (b) the rise rate (mm/s) as a function of time and for various K-Oct contents (pphp).</figcaption></figure>
## 3.2. Influence of catalyst concentration on the temperature and temperature rate profiles

<figure><img src="image_8.png" /><figcaption>**Figure 5:** Evolution of foam temperature as a function of time and for various K-Oct content (pphp).</figcaption></figure>

The evolution of the foam temperature reported in Figure 5 as a function of time and for the different K-Oct concentrations may be separated into different phases:

(i) With the exception of the three lower catalyst concentrations (0.5, 0.75 and 1 pphp) which are overlapping for times below 160 s, the initial slope of the curves (dT/dt) becomes progressively greater as the catalyst content increases, which suggests that potassium ethyl hexanoate (the active ingredient in K-Oct) does not only impact the trimerization reaction but also the reactions between isocyanate groups and OH groups from water and polyol. However, the temperature increase tends to slow down beyond around 70°C with a kind of plateau for the lowest concentrations of K-Oct, while this effect is barely visible for the highest concentrations of PIR catalyst.

(ii) After this short break, the slope of the T=f(t) curve increases again according to the second step observed on the normalized height curves (Figure 4a). It is admitted that the kick-off temperature (as
defined by the onset temperature at which the heating rate increases again) is related to the start of the trimerization reaction of isocyanate groups that is highly exothermic [40,41]. The corresponding $dT/dt=f(t)$ curves are reported in Figure S7 in order to facilitate the characterization of the trimerization peak. The linear relationship between the time at the maximum values of $dT/dt$ of the trimerization peak and the time at the maximum value of $dH/dt$ (2nd peak) for the various catalyst concentrations unambiguously confirms the direct link between the expansion rate and the foam temperature (Figure S8). However, it can be noticed that the peak maximum of $dT/dt$ always occurs after the peak maximum of $dH/dt$. This mismatch is maximum at the lowest catalyst content with $\Delta t \approx 37$ s but decreases to about $\Delta t \approx 6$ s at the highest catalyst content. Even if foam expansion is mainly controlled by the internal temperature through the increase in gas pressure inside the cell, the amount of gas molecules ($CO_2$ and isopentane) present in the cells varies during foaming and has therefore to be taken into account to explain this discrepancy. The evolution of temperature rise rate ($dT/dt$) for the different contents of K-Oct is reported in Figure S9 not as a function of time but as a function of temperature. Increasing the catalyst concentration from 0.5 to 6 pphp tends to lower the temperatures corresponding to the kick-off and the maximum of the second peak (trimerization reaction) by about 17°C, as specifically shown in Figure S10. Sun et al. [41] compared the experimental adiabatic temperature rise of poly(urethane/isocyanurate) resins (bulk system) prepared at various levels of triethylenediamine catalyst ranging from 0.4 to 2 wt.% (with respect to polyol) and indicated that the trimerization reactions occurred at almost the same temperature (around 80°C). However, discrepancies between experimental and simulated $T=f(t)$ curves were observed at low catalyst concentration (typically, 0.4 wt.%) and explained by the change of the trimerization exotherm. These authors demonstrated using differential scanning calorimetry (DSC) curves that contrary to the expectations, the trimerization reaction exotherm was not constant; it was found to increase from 50 J/g to about 250 J/g as the catalyst concentration increased from $1.5 \times 10^{-4}$ g/ml to $1 \times 10^{-3}$ g/ml (with respect to the polyol content) and remained constant thereafter. They also demonstrated that the kick-off temperature of the trimerization reactions decreased significantly ($\Delta T \approx 32°C$) with the increase
of NCO/OH ratio from 2.4 to 7.5. Starting from the assumption that the formation of urethane preceded the formation of isocyanurate trimer, the authors explained that the latter was controlled by "the diffusion effect resulting from the urethane formation". The lower the NCO/OH ratio, the more the viscosity of the medium should increase because of formation of urethane links, thus limiting the diffusivity of NCO groups through the higher viscosity medium. The impact of higher viscosity had already been highlighted by Bernal et al. [42] who observed a decrease in isocyanate conversion rate with the increase in carbon nanotube content at the early stages, thus inducing a lower mobility of the molecules during foaming. Additional interesting data can be found in the work of Chiacchiarelli et al. [43] who studied the effect of curing temperature on the viscosity and conversion of poly(urethane-isocyanurate) thermosets based on MDI (f=2.1) and a polyether polyol (NCO/OH ratio greater than 1000) which were characterized by two glass transition temperatures and could thus be considered as heterogeneous. Polyaddition reactions between isocyanate and polyol were found to be favoured at low curing temperature (T<55°C) with respect to the isocyanate trimerization reaction. These authors claimed that the formation of the urethane network would create a premature increase in viscosity at a lower conversion than the theoretical gel point because of the vitrification effect. In addition to that, it is understandable that decreasing the NCO/OH ratio should also reduce the probability of contact between NCO groups. In our case, the NCO/OH ratio was fixed but the enhancement of urethane formation (see section 3.3) with the increase in K-Oct content may potentially increase the viscosity of the medium before the start of trimerization reactions; however, the lowering of the kick-off temperature with increasing catalyst content seems to indicate that this effect is of secondary importance.
<figure><img src="image_9.png" /><figcaption>**Figure 6:** Evolution of the maximum temperature reached during foaming as a function of the catalyst content. The dotted line is only a guide for the eyes.</figcaption></figure>

(iii) Each curve reported in Figure 5 is also characterized by a maximum temperature ($T_{max}$) which increases by about 35°C as the catalyst content increases from 0.5 to 3 pphp, as shown in Figure 6. However, this effect tends to level off beyond around 3-4 parts of K-Oct and $T_{max}$ remains almost constant thereafter, in accordance with the levelling of $t_{gel}$ beyond 3-4 parts of catalyst (Figure 2). This result may indicate that the proportion of isocyanurate formation (the main reaction that produces the heat) is tending to fade, either because all isocyanate groups available have reacted to produce isocyanurate and/or because of the restricted mobility of -NCO groups as the density of cross-linkages increases. This second explanation is preferred as unreacted isocyanate groups were found to be present even at the highest catalyst content (see section 3.4 for more details). This phenomenon could also explain the variation of the trimerization reaction exotherm reported by Sun et al. [41].
(iv) Eventually, it is interesting to note that the temperature reported in Figure 5 tends to decrease very slowly after reaching its maximum value, undoubtedly through the high insulation properties of the foam surrounding the temperature probe (adiabatic conditions should prevail).

### 3.3. Influence of catalyst concentration on the dielectric polarization

<figure><img src="image_10.png" /><figcaption>**Figure 7:** Evolution of dielectric polarization as a function of time (s) for the different K-Oct contents (pphp).</figcaption></figure>

Figure 7 shows the evolution of dielectric polarization measured by the FOAMAT apparatus as a function of reaction time and for the different proportions of K-Oct. After a sharp increase in dielectric polarization (DP) at low time of foaming, each polarization curve shows a drastic decrease until reaching an almost constant value (plateau) at longer times. On one side, the increase in dielectric polarization can be related to the decrease in foam density (during the rising phase), to the formation of the intermediates like urea (as a reminder, water is used as a co-blowing agent) and/or to the
increase in internal temperature which favors the molecular mobility. On the other hand, the decrease
in dielectric polarization is related to the reduced mobility of polymer chains and to the formation of
an ever more rigid network as crosslinking progresses. Increasing the K-Oct content was found not only
to shift the drop of DP to shorter times, but also to increase the slope of the curve, which may imply
that crosslinking occurs more quickly. The time needed to reach the maximum value of dielectric
polarization appears to decrease almost linearly with the K-Oct content (Figure S11). At the end of
experimental measurements (t~900 s), all dielectric polarization curves converge to very low values
(DP<100), demonstrating that the molecular mobility became very small in the final PIR networks, even
at the lowest catalyst content. Small differences in the dielectric polarization measured at t~900 s may
be related to kinetics differences and/or to the effect of difference in pressure exerted by the rising
foam on the surface of the CMD. Unlike in the present case, it was reported for tannin-based foams
(Condensation reaction between flavonoid-type phenols and formaldehyde, optionally with furfuryl
alcohol) that dielectric polarization was maximum when the temperature reached its highest value
[44]. The authors explained this similarity by the increase in molecular motion with the temperature
for a system in which polymerization had not started yet. In our case, despite large discrepancies for
K-Oct contents lower than 1.5 pphp, the time at the maximum of DP was found to be close to the gel
time curve (Figure S11) and is thus far below the time at the maximum temperature (Figure 2). In any
case, the interpretation of dielectric polarization curves must be performed carefully because the
sensor sensitivity is limited to the extreme surface (~0.1 mm) of the foam bun (bottom face), which
means that the thermal history of this thin layer could differ significantly from the evolution of
temperature measured in the core of the foam and displayed in Figure 5. Santiago-Calvo et al. [45]
used infrared expandometry to follow the expansion kinetics and surface temperature evolution of
PUR foam (isocyanate index=110) blown with water and reported an average maximum temperature
of the lateral surface of about 65°C for the system containing 2 ppw of blowing catalyst (N,N,N',N'',N''-pentamethyldiethylenetriamine or PMDTA) and 5ppw of H₂O. According to Raimbault et al. [34] who
developed an analytical model of the foaming process in the FOAMAT geometry, the temperature of
foam is lower in the vicinity of the vertical wall of the cardboard, but this finding could be extrapolated
to the bottom of the foam bun where the dielectric polarization measurement system is located.

3.4. ATR-FTIR spectroscopy analysis of the PIR foams

<figure><img src="image_11.png" /></figure>

**Figure 8:** ATR-FTIR spectra of PIR foam samples (taken from the core of Foamat buns) between 600 and 4000 cm⁻¹ measured after an aging period of about 3 weeks at room temperature. The PIR catalyst content (K-Oct) increases from the bottom curve to the top curve. Only part of the whole dataset is represented so as not to overload the graphic.

The complete ATR-FTIR spectra depicted in Figure 8 at selected catalyst contents confirms the
presence of chemical groups characteristic for rigid PIR foams [46-49]. The first point is the increase in
the intensity of the isocyanurate peak (C-N stretching band in the 1410 cm⁻¹ region) as the catalyst
concentration increases (from bottom to top). It is worth mentioning that those differences in trimer
content apply to samples taken in the center of the foam bun, but this is not necessarily the case at the surface of the foam [50] as a result of significant heat loss, leading to an under-cured system. To take the analysis one step further, the C=C stretching (phenyl) peak at 1595 cm⁻¹ was used as the reference peak [51,52] because phenyl groups were not found in the FTIR spectra of K-Oct (Figure S12) and as a result, phenyl concentration should not depend on the proportion of catalyst content (as a reminder, the polyol/isocyanate ratio was kept constant). The height of isocyanurate and phenyl peaks were estimated with respect to a baseline connecting the lower points on either side of the peaks (anchor points at 1350 cm⁻¹ and 1470 cm⁻¹ for the C-N stretching of isocyanurate, and at 1565 cm⁻¹ and 1630 cm⁻¹ for the C=C stretching vibration of the aromatic ring, respectively). The evolution of isocyanurate/phenyl peak height ratios (h<sub>1410</sub>/h<sub>1595</sub>) reported in Figure 9a as a function of catalyst content confirms this tendency, but it can also be seen that this ratio tends to level off beyond a catalyst concentration of about 5 parts. This result is also supported by the fact that T<sub>max</sub> was found to level off (Figure 6) beyond 3 parts of K-Oct and by the relationship between the isocyanurate content and T<sub>max</sub> highlighted in Figure 9b. Despite the large data spreading, the isocyanurate/phenyl peak height ratio definitely increases with T<sub>max</sub>. We recently studied the effect of mold temperature (T<sub>mold</sub>) on the structural units of PIR foams and found that the isocyanurate/phenyl ratio (measured near the surface in contact with the mold) increased from 1.2 to about 3.7 as T<sub>mold</sub> was increased from 30°C to 180°C [53]. In the same vein, Lenz et al. [31] studied the influence of potassium acetate (KAc) catalyst (dissolved in diethylene glycol) on the chemical structure of PIR foams with an index of 320. They reported a significant increase in the proportion of isocyanurate groups with the increase in the concentration of KAc, but it was also demonstrated that the isocyanurate content tended to level off above about 0.16 wt.% catalyst. Semsarzadeh et al. [54] demonstrated for dense polyisocyanurate polymers (NCO/OH=2) based on toluene diisocyanate (TDI) and poly(propylene glycol) that increasing the concentration of dibutyltin dilaurate (DBTDL) from 1 to 3 wt.% increased the isocyanurate content. This result was confirmed by the decrease in the swelling ratio (obtained in toluene at room temperature) and average molar mass between crosslinks (M<sub>c</sub>) with the increase in catalyst content.
The findings of Xu et al. [30] on PIR foams (isocyanate index=350) were somewhat different as they demonstrated from FTIR analysis that the isocyanurate content of PIR foams first increased from 3 to 5 parts of PU-1792 (a trimerization catalyst based on 25% potassium acetate dissolved with 75% diethylene glycol) and then decreased from 5 to 15 parts of trimerization catalyst. The presence of this maximum at 5 parts of trimerization catalyst does not seem to be in doubt because they clearly demonstrated from thermogravimetric analysis (TGA) and cone calorimeter that the thermal stability and fire performance of the PIR foam samples were maximum at the same catalyst content. Even if, in theory, gelation should not modify the kinetics, these authors explained the decrease in isocyanurate content observed at high catalyst concentration by the premature formation of a too highly crosslinked structure, thus hampering the trimerization reactions. However, it is difficult to say whether this could happen in all cases if enough catalyst is added; but one should be aware that PIR foams made with too much trimerization catalyst sometimes tend to be non-homogeneous [31]; this could be another explanation for the unusual result obtained by Xu et al. [30]. Apart from that, it is questionable whether the maximum (plateau value in our case) reported in Figure 9a corresponds to an isocyanurate yield (i.e. the proportion of isocyanate groups that actually produce isocyanurate with respect to the theoretical one) of 100%. This is apparently never the case because of the ever more limited mobility of -NCO groups as the cross-linking density increases [55], not to mention that in the particular case of MDI, the NCOs are attached to the phenyl groups which must also be moved. For instance, Brandl et al. [39] reported maximum PIR conversion varying between 72 and 76% without water (for catalysts mixtures based on potassium ethyl hexanoate, potassium acetate or quaternary ammonium carboxylate combined with a tertiary amine co-catalyst), but which were found to be even lower in presence of water in the PIR formulation. Another proof is given by the presence on all spectra reported in Figure 8 of a band at 2280 cm⁻¹ corresponding to the asymmetric stretching vibration of unreacted isocyanate (-N=C=O function), even after about 3 weeks of aging at room temperature. This isocyanate peak height seems to decrease as the PIR catalyst content increases which tendency is confirmed in Figure S13 where the isocyanate/phenyl ratio (h₂₂₈₀/h₁₅₉₅) is plotted as a function of PIR
catalyst content. Bechara [37] studied the effect of DABCO TMR catalyst (specific tertiary amine) on PIR foams (index 400) and demonstrated that the conversion of NCO groups increased from 80 to about 94% as the catalyst concentration increased from 1.31 to 2 pphp, respectively. Our results suggest that the final isocyanurate content increases with the catalyst content, but it is not the only NCO-consuming species that sees its proportion increase with the increase in catalyst concentration.

In our case, the proportion of urethane was estimated through the intensity of the peak at 1220 cm⁻¹ (C-O bond stretching) with anchor points between 1160 cm⁻¹ and 1345 cm⁻¹ [47]. Figure S14 shows that the final $h_{1220}/h_{1595}$ (urethane/phenyl) peak height ratio also increases with the increase in K-Oct concentration. This tendency seems less pronounced in the study of Lenz et al. [31], to the point where the authors say that “the content of urethane groups was hardly influenced” by the potassium acetate catalyst concentration. Beyond the consumption of isocyanate functional groups with hydroxyls (polyol and/or H₂O and/or glycols used as solvents), part of the isocyanate functions could also be consumed for the formation of carbodiimide functional groups (R-N=C=N-R'), as schematically reported in Figure 1. Tiny peaks between 2100 and 2150 cm⁻¹ (stretching vibration of carbodiimide) emerging at high catalyst content in the spectra reported in Figure 8 seem to confirm that hypothesis.

But it is also worth noting that carbodiimide could also be produced during the thermal degradation of the uretoneimine structure (often present in commercial pMDI). This phenomenon was found to occur above a minimum temperature of 40°C and its intensity was found to increase with processing temperature [48,56,57], which is also compatible with our data where it emerges for formulations made with high catalyst content and therefore associated with high temperature ($T_{max}$).
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 9:** Evolution of the isocyanurate/phenyl ratio (as probed by the $h_{1410}/h_{1595}$ peak height ratio) in the center of the foam bun as a function of (a) the catalyst content and (b) the maximum temperature ($T_{max}$). The number in parentheses associated with each data point corresponds to the catalyst content (pphp). The solid lines are only a guide for the eyes.</figcaption></figure>
The authors [57] recently studied the evolution of isocyanurate content as a function of depth in a sample group of PIR foam insulation panels taken from the European market. They reported the downwards frequency shift of the C-N stretching vibration (overall range of $v_{max}$ ~1412-1406 cm⁻¹ by compiling data from all panels) of the isocyanurate ring with the increase in isocyanurate content (from the surface to the core of each panel) and explained this phenomenon by the reduction of the hydrogen bonding between the N-H group of the urethane and the C=O within the isocyanurate ring.

This frequency shift of the isocyanurate peak as a function of isocyanurate content was also confirmed in our latest work [53] where PIR foams simulating real panels were prepared at different mold temperatures ($T_{mold}$). Increasing $T_{mold}$ was found to not only increase the isocyanurate content in the surface vicinity, but also to decrease the peak position from about 1413 cm⁻¹ to about 1407 cm⁻¹ as the surface temperature increased from 25 to 180°C. In the present study, the decrease in isocyanurate peak position ($v_{max}$) reported in Figure 10 in the core of the foam bun (close to the measure of $T_{max}$) as a function of $h_{1410}/h_{1595}$ peak height ratio seems to confirm this trend, despite somewhat scattered data: the higher the catalyst content, the higher the isocyanurate content and the lower $v_{max}$. More precisely, its position progressively decreases from about 1410 cm⁻¹ to about 1407 cm⁻¹ as the catalyst content increases from 0.5 to 5 pphp. However, it is worth noting that the range of $v_{max}$ is limited to $\Delta v_{max} \sim 3$ cm⁻¹ with respect to our previous study on the effect of $T_{mold}$ ($\Delta v_{max} \sim 6$ cm⁻¹). This may be explained by the rather narrow temperature amplitude ($\Delta T_{max} \sim 40°C$) occurring in the core of the foam bun by varying the catalyst content, while the variation of surface temperature ($\Delta T_{mold} \sim 155°C$) was much higher in our previous study. Even though the increase in the proportion of isocyanurate remains limited in the present work, the increase in catalyst content should be accompanied by an increase in fire resistance at the core of the foam bun [31,50,57].
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<figure><img src="image_14.png" /><figcaption>**Figure 10:** Evolution of the isocyanurate peak maximum ($v_{max}$) as a function of the isocyanurate content, as probed by isocyanurate/phenyl peak height ratio. For each data point, the number in parentheses corresponds to the PIR catalyst content (pphp). In a general way, the catalyst content of each data point increases from the top-left corner to the bottom-right corner of the graphic. The solid line corresponds to the best-fit line through all the data points with a linear equation.</figcaption></figure>
### 3.5. Effect of Catalyst Content on the Cellular Structure of PIR foams

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

**Figure 11:** Evolution of the foam density ($ρ_f$) as a function of (a) catalyst content and (b) the maximum temperature ($T_{max}$) measured during foaming. For each data point, the number in parentheses corresponds to the PIR catalyst content (pphp). The dashed line is only a guide for the eyes while the solid line corresponds to the best-fit line through all the data points with a linear equation ($r^2 \sim 0.92$).
As expected from the increase in maximum foam height reported in Figure S5, increasing the concentration of K-Oct in the PIR formulation leads to a decrease in foam density, as shown in Figure 11a. More precisely, ρ<sub>f</sub> decreases from 34.2 kg/m<sup>3</sup> at the lowest PIR catalyst content (0.5pph K-Oct) to about 28.0 kg/m<sup>3</sup> (average value for [K-Oct] ≥ 2.5 pphp) which represents a decrease of about 18.1%. Similarly, Xu et al. [30] demonstrated for PIR foams (isocyanate index=350) that the foam density decreased from 48.8 to 43.7 kg/m<sup>3</sup> as the trimerization catalyst content increased from 3 to 15 pphp. In the same vein, it was shown in a recent study [31] on PIR foams (isocyanate index=320) that increasing potassium acetate PIR catalyst from 0.08 to 0.23 wt.% slightly decreased the foam density from 40 to 38 kg/m<sup>3</sup>. At first sight, these results may appear counterintuitive because the main goal of the PIR catalyst is to facilitate the trimerization of isocyanate with the formation of a 3D chemical structure as shown by the decrease in the tack-free time with the increase in catalyst content reported in Figure 2. One could therefore expect the cellular morphology to be frozen more quickly, limiting the foam expansion. However, it must not be forgotten that increasing the catalyst content drastically increases the maximum temperature reached during foaming (T<sub>max</sub>) (Figure 6), which will generate more pressure (because of the ideal gas law: PV=nRT) in the cells and therefore a greater expansion of the foam. In addition, a lower loss of blowing agents (diffusion in the atmosphere) can be expected because the whole expansion phase takes place in a shorter time, both factors acting in the same direction. Arguments based on the increase of CO<sub>2</sub> content due to the presence of water molecules in the PIR catalyst are not enough to explain density variations since the maximum amount of CO<sub>2</sub> molecules generated by water molecules contained in the catalyst should be around 2.4% with respect to the total number of blowing agent molecules (1 pphp H<sub>2</sub>O + 25.4 pphp isopentane). It is 7.3 times lower than the magnitude of density variation and falls with the uncertainty of density measurements. In addition, this factor could not explain the presence of a plateau beyond a catalyst concentration of 2.5 pphp (Figure 11a) while the amount of catalyst and so the water is increasing. It should also be stressed that a small quantity of CO<sub>2</sub> molecules may be generated by the condensation of isocyanates with themselves (leading to carbodiimide functional groups) but it is the authors belief that this
secondary reaction should not significantly impact the foam density with respect to the total number of blowing agent molecules and the effect of $T_{max}$. To illustrate the dependence of the foam density on $T_{max}$, Figure 11b shows the almost linear decrease in foam density with the increase in $T_{max}$. In a general way, the PIR catalyst content increases from top-left to bottom-right despite a few discrepancies at low catalyst contents.

Variations in the density of free rise foams are often accompanied by changes in the cellular morphology (cell size and/or shape factor). SEM images of the cellular morphology (taken perpendicular to the rise direction) are shown in Figure S15 for each catalyst content while the distributions of cell size and cell height are reported in Figure S16. Both the arithmetic average cell diameter (perpendicular to the rise direction) and cell height (parallel to the rise direction) were found to decrease with the increase in catalyst content, as reported in Figure 12a. It could be expected that the lower density results from the increase in cell size but it is clearly not the case and it will be further demonstrated that this is made possible by the change of the cell population density. The results were rather variable in the literature: Xu et al. [30] compared the morphology of PIR foams prepared with 3 to 15 parts of trimerization catalyst and found that the PIR foam made with an intermediate catalyst concentration of 5 parts possessed the smallest cell size. Lenz et al. [31] demonstrated for PIR foams (NCO/OH ratio=320) that increasing potassium acetate content from 0.08 to 0.23 wt.% increased the cell size from 140 to 270 µm. In the authors' view, this increase in cell size was in accordance with the decrease in the foam density from 40 to 38 kg/m³ and was caused not only by the increase in temperature (higher reaction rate) but also by a lower number of open cells (higher blowing agent retention), both resulting in higher gas pressure and thus higher expansion volume.
<figure><img src="image_17.png" /><figcaption>**Figure 12:** Evolution of (a) the average cell size (height and diameter) and (b) the cell shape ratio ($R=h/d$) as a function of catalyst content. For each catalyst content, the error bars correspond to the standard deviation across the entire population of cells. The solid and dashed lines are only guides for the eyes.</figcaption></figure>
Eventually, it is interesting to note that the two curves reported in Figure 12a seem to remain roughly parallel over the whole range of catalyst content. To get more information about the relationship between cell size (d) and cell height (h), the cell shape aspect ratio (as defined by R=h/d) is reported as a function of PIR catalyst content in Figure 12b. It is well known that the cells of PUR/PIR foams prepared in open mold (where “free” rise conditions should prevail) tend to be elongated in the direction of foaming (R>1), as referred to the foam rise direction [58]. This was verified even for the slowest system in our study with R~1.5 for 0.5 pphp K-Oct. In addition, R was found to reach a maximum value of almost 2 for a catalyst content of about 4 pphp (ΔR~+35 %). However, it does not seem to increase further for higher catalyst concentrations, presumably because the maximum temperature reached during foaming remains relatively stable for PIR catalyst contents above 3-4 pphp. The monotonic increasing relationship between R and Tmax is reported in Figure 13a: The higher the Tmax, the higher the cell shape factor (R). Even if those results cannot be directly compared with cell aspect ratios taken from PIR foams made in different mold shapes, several interesting research findings were identified in the literature. Hejna et al. [19] prepared PIR foams (isocyanate index=200) at partial substitution (0-70%) of petrochemical polyol (trifunctional polyether based on glycerol) with a synthetized bio-based polyol (made from crude glycerol and castor oil) while keeping the same foam density (by adjusting the physical blowing agent content, a liquid hydrofluorocarbon blend). They observed an increase in cell aspect ratio from 1.72 to 2.19 as the proportion of bio-based polyol increased from 0 to 70wt%. According to the authors, this phenomenon should be related to the higher amount of heat generated during foaming and the faster evaporation of the (physical) blowing agent, but kinetics and maximum temperature were not disclosed. Lenz et al. [31] did not measure the cell aspect ratio (R) of their PIR foams (NCO/OH=3.2 with 38 ≤ ρf ≤ 40 kg/m³) but compared their compression strength (Fmax) estimated in the rise direction. Clearly, Fmax was found to increase with the increase in catalyst content, which could potentially be explained by the increase in cell aspect ratio [59]. Surprisingly, the authors did not retain this explanation and rather based their argument on the decrease in the matrix plasticization (lower pentane solubility) as the crosslink density of the PIR matrix
increased, which does not exclude the other. Similar conclusions were found in the case of PUR foams ($\rho_f$~104 kg/m$^3$) [60].

<figure><img src="image_18.png" /><figcaption>**Figure 13:** Evolution of shape ratio ($R=h/d$) as a function of (a) the maximum temperature and (b) the foam density ($\rho_f$). For each data point, the number in parentheses corresponds to the PIR catalyst content (pphp). The dashed and solid lines correspond to the best-fit line through all the data points with a second-order polynomial equation.</figcaption></figure>
In parallel to these works based on the variation of catalyst content, several authors [61-63] reported the decrease in geometrical anisotropy of cells of PUR foams (less elongated in the rise direction) with increasing density. In our case, the decrease of R with the increase of ρf reported in Figure 13b seems to ascertain this trend.
### 3.6. Effect of catalyst content on nucleation and cell population density

<figure><img src="image_19.png" /><figcaption>**Figure 14:** Evolution of the cell population density ($\beta$) of the PIR foam as a function of (a) the catalyst content and (b) $\Delta t=t_{gel}-t_{cream}$. For each data point, the number in parentheses corresponds to the PIR catalyst content (pphp). The dashed line is only a guide for the eyes while the solid line corresponds to the best-fit line through all the data points with a power equation ($r^2=0.97$).</figcaption></figure>
The data of foam density and cell size reported in Figures 11 and 12 allow to determine the evolution of cell population density (β) as a function of catalyst content. This parameter is often used to compare the “nucleation” efficiency of different samples because it takes into account the difference in foam density of the final product. This parameter plays a key role in the case of insulation foams, as increasing β (cell size reduction) generally leads to a reduction in thermal conductivity [6,14,64,65].

Figure 14a indicates that β increases by more than a factor x15 with the increase of catalyst content from 0.5 to 6 pphp, but does this result mean that nucleation was really enhanced? We recently used a cryo-SEM to study the morphology of an isopentane-blown polyurethane foam matrix as a function of foaming time and concluded that isopentane liquid droplets (undissolved part of the blowing agent) did not vaporize to create their own bubbles but dissolved into the continuous matrix with time and diffused into pre-existing air bubbles [5]. And contrarily to the expectation, bubble nucleation (CO₂) formed by the reaction between H₂O and pMDI was not found to occur at the interface between polyol and pMDI. These observations were confirmed by showing that the cell population density (~10⁶ cell/cm³) of the final foam was of the same order of magnitude than the number of air bubbles trapped into the liquid during mixing (~10⁶ bubble/cm³). Following this study, Brondi et al. [26] studied the effect of air bubbles inclusion on the foaming of water-pentane blown PIR foams (isocyanate index 200) using a dedicated optical device and concluded that the introduction during fast mixing (1000 RPM for 8 s) of a large number of air bubbles (Nmax>10⁶ bubble/cm³) prevented the formation of new CO₂ (water/isocyanate reaction) and/or pentane bubbles. By contrast, it is only when the mixing stage was slow (50 RPM for 20 s) that new bubbles were found to appear (Nmax~10⁴ bubbles/cm³).

These results were recently confirmed by Hamann et al. [27] with the use of an innovative double-syringe mixing device for the preparation of PUR foams to control the air bubble density in the liquid reactive mixture. They clearly demonstrated the correlation between the air bubble density in the reacting mixture and the final pore radius of the foam for air bubble density higher than 200-300 bubbles/cm³. In the same vein, Merillas et al. [28] demonstrated that the addition of nanoclays had no effect on the cell density of a PU foam when the mixing phase was conducted under vacuum (no air
can be trapped) while mixing under atmospheric pressure was found to promote cell nucleation
through the incorporation of a higher number of air bubbles entrapped within the reactive mixing
because of the increase in the viscosity caused by the presence of fillers. In our case, intensive mixing
conditions are used and it can be considered that the number of air bubbles is high enough, in such a
way that blowing agent molecules (isopentane and CO₂) should simply diffuse into the existing air
bubbles rather than nucleate their own bubbles. However, it is questionable whether the addition of
varying parts of K-Oct could affect the initial distribution of air bubbles entrapped during the mixing
stage. Apart from the mixing conditions (type of propeller, rotating speed, mixing time, air pressure
above the liquid mixture, etc.) which are kept constant in our case, the size and number of air bubbles
entrapped during mixing should mainly depend on the surface energy and the viscosity of the liquid
mixture. Making the hypothesis that the variation of K-Oct content (from 0.5 to 6 parts) is too small to
significantly affect the viscosity of the unreacted mixture (according to the suppliers, the viscosity of
K-Oct and PS-2412 are close to each other: η<sub>K-ZERO 3000</sub>~3000 mPa.s vs η<sub>PS-2412</sub>=2000-4500 mPa.s), and
that the surface tension of the liquid mixture is already minimized by the silicone-type surfactant, it
can be fairly postulated that the number of air bubbles initially entrapped in the reaction mixture
during mixing should not significantly vary within the range of PIR catalyst content investigated in our
study. In the case of PUR foams prepared with polyether polyols, pMDI and water as chemical blowing
agent, similar results were obtained by Choe et al. [38] who demonstrated that increasing the gelling
catalyst content (triethylene diamine dissolved in dipropylene glycol) from 0.6 to 1.8 pphp reduced the
cell size from 307 to 132 µm while keeping almost the same density (ρ<sub>f</sub>~80 kg/m³). Even if the authors
did not estimate the cell population density (according to eq.1, β∞1/d³), this cell size reduction should
lead to an increase in β by a factor of about x12. At this point, it is essential to mention that solid foams
such as PUR/PIR foams result from low viscosity precursors (without being as low as that of water). As
such, the final morphology of the solid foam (cell size, cell wall thickness, strut volume fraction) is
dictated (in addition to the expansion) by all the aging processes (such as coalescence, Oswald ripening
and cell wall drainage) that modify and shape the cellular morphology of the liquid foam during its
solidification process [66]. Coalescence between two adjacent bubbles results from cell wall rupture because of cell wall drainage and/or foam expansion, while Ostwald ripening (the latter is also called coarsening, inter-bubble gas diffusion or disproportionation) is related to the pressure difference between cells of different size leading to inter-bubble gas diffusion. Unlike liquid foams which are inherently unstable, the progressive increase in viscosity of the PUR/PIR foam matrix occurring during polymerization should slow down and eventually stop the aging process, leading to the final morphology of the foam product. Recalling that $t_{gel}$ was also found to correspond to the occurrence of the trimerization reaction, it can be postulated in the case of PIR foams that $t_{gel}$ indicates the end of the morphological aging process, which means that beyond this characteristic time, the cellular morphology is not expected to change significantly. In this context, $\beta$ is plotted in Figure 14b as a function of $\Delta t=t_{gel}-t_{cream}$, a rough estimate of the amount of time during which the cell morphology can evolve, including foam expansion time (the evolution of $\Delta t=t_{gel}-t_{cream}$ is plotted in Figure S17 as a function of K-Oct content). The cell population density ($\beta$) of the final foam product drops abruptly from about $14 \times 10^6$ cell/cm$^3$ ($\Delta t \sim 31$ s) to about $2 \times 10^6$ cell/cm$^3$ ($\Delta t \sim 100$ s) and remains almost constant thereafter. As $t_{cream}$ is relatively small with respect to $t_{gel}$ (Figure 2), it implies that the faster the structure freezes (smaller value of $t_{gel}$), the less time the cell structure has to evolve (in the sense of an increase in the average cell size) and the higher the value of $\beta$. In other words, gelation seems to not only determine the maximum height and the apparent density of our free-rise foam, but primarily the cell population density and hence the cell size of the final foam product.

In order to try to obtain more information about the influence of the catalyst content on the aging processes, Weibull distribution curves are fitted on the experimental values of cell size distribution (Figure S16) as suggested in other works on PUR foams [9,67]. As there is no physical reason that the starting point of the cell size is zero, the probability density function of the three-parameter Weibull distribution is used in our case
$$f(t, \alpha, \beta, \eta) = \frac{\beta}{\eta} \left(\frac{t-\alpha}{\eta}\right)^{\beta-1} e^{-\left[\frac{(t-\alpha)}{\eta}\right]^\beta} \quad \text{for } t>\alpha$$

$$f(t, \alpha, \beta, \eta) = 0 \quad \text{for } t \le \alpha \quad (2)$$

where α, β, η are the location, the shape and the scale parameters, respectively (α, β, η≥0) [68]. While the Weibull distribution is typically used in survival analysis (probability of a component failure over time), Schümann et al. [67] explained that it can also be applied in the case of foams if the merging of two pores resulting in one larger pore is considered as a generating event. In addition, Yang et al. [68] underlined that three-parameters Weibull distribution is very flexible (in particular by varying the shape parameter) and thus can be applied to a wide range of experimental data. For the sake of clarity, only the Weibull distribution curves are compared in Figure 15 for the different catalyst content. Starting from the fastest system (6 pphp K-Oct) which should offer the less time (Δt=t_gel-t_cream~31s) for cell wall drainage, cell coalescence and Ostwald ripening, decreasing the catalyst content shifts the cell size distribution towards higher cell sizes in accordance with the evolution of arithmetic average cell size reported in Figure 12a. Note that the peak maximum of each Weibull distribution curve is always higher than the corresponding average cell size and this effect is enhanced for the cell height with respect to the cell diameter (Figure S18). Unfortunately, it is difficult to determine whether one of the aging processes predominates over the other, namely coalescence or Ostwald ripening since they both lead to an increase in cell size. In specific cases coalescence can be countered, as observed by Pardo-Alonso et al. [13] in a PU-nanoclay foamed system (ρ_f~52 kg/m³) using dedicated high-resolution microfocus X-ray radioscopy. They demonstrated that coalescence only occurred for the neat PU system (without nanoclay) with a slight decrease in the cell density (N_v) from 3x10⁵ cell/cm³ (t~50 s) to about 1.8x10⁵ cell/cm³ (t~450 s). According to certain authors [69] working on liquid foams, the presence of very large bubbles would be directly linked to the coalescence phenomenon, but their absence does not seem to guarantee that coalescence did not occur when the whole distribution curve
was shifted to higher values. In our case, both foam expansion and cell wall drainage lead to film thinning and potentially to coalescence of two adjacent cells. Hopefully, specific silicon-based surfactants are used to limit this phenomenon but without direct visualization using specific equipment, coalescence cannot be completely excluded. By contrast, Bisperink et al. [69] explained in the case of beer (liquid) foam made by CO₂ or N₂ that Ostwald ripening did practically not take place within 2.5 minutes time in the case of N₂ because of the low solubility of nitrogen in beer. In that case, only coalescence could explain the increase in bubble size while both mechanisms (coalescence and Ostwald ripening) took place for the carbon dioxide beer foam. The increase in the number of small cells could also be a sign of the presence of the Ostwald ripening mechanism [69]. In our case, isopentane is relatively soluble in the PU liquid matrix [5] which implies that isopentane should diffuse through the polymerizing liquid matrix to equilibrate gas pressure between cells of different sizes. Therefore, Ostwald ripening should necessarily occur. Things can even be more complex since both coalescence and Ostwald ripening can interact with each other. For instance, Kostoglou et al. [70] demonstrated for liquid foams that small bubbles reducing their size by Ostwald ripening can coalesce before they disappear due to ripening.
<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 15:** Evolution of probability density function of the three-parameters Weibull distributions fitted to experimental (a) cell height and (b) cell diameter as a function of catalyst content.</figcaption></figure>
Further information could potentially be provided by following the evolution of the cell size polydispersity factor, as defined by

$$ \varepsilon = \frac{FWHM}{h_{peak}} \qquad (3) $$

where FWHM represents the full width at half maximum and h<sub>peak</sub> the height at the peak of the distribution, as a function of catalyst content (Figure S19). Despite higher ε values obtained for the cell height (ε<sub>average</sub>=1.007±0.064) with respect to those obtained for the cell diameter (ε<sub>average</sub>=0.875±0.042), they both seem relatively independent of the catalyst concentration within the experimental error. All the above results may suggest that the increase of catalyst content does not appear to drastically change the aging processes (coalescence vs Ostwald ripening) excluding the decrease in aging time.

Eventually, it is worth noting that the open-cell content of the various foam samples remained below 4% despite the significant variation in the amount of trimerization catalyst (Figure S20). This is quite remarkable since an increase in the open-cell rate was not to be ruled out for the lowest and highest concentrations of K-Oct. In the former case, the time (Δt=t<sub>gel</sub>-t<sub>cream</sub>) allowed for the liquid foam to evolve before trimerization (~t<sub>gel</sub>) was maximum and the increase of wall drainage may potentially have promoted cell wall rupture. In the latter case, the increase in kinetics should lead to a maximum elevation of pressure inside the cells (due to the temperature rise), which could also facilitate cell wall rupture. Please note that the main characteristics of the PIR foams prepared at the different K-Oct contents are summarized in Table S1.
4. Concluding remarks

A series of PIR foams were prepared with different contents of PIR catalyst (K-Oct) in order to investigate the effect of reaction kinetics on the base material chemistry and the cellular morphology of the foams. Obviously, it was found that increasing the amount of catalyst from 0.5 to 6 pphp led to faster foam reactions with a reduction of gel time from 260 to about 40 s (Δt_gel~ -85%), while the cream time was also decreased from 17 to 8.5 s (Δt_cream~ -50%). From a chemical point of view, this acceleration of chemical reactions resulted in the marked increase in isocyanurate content (by a factor more than x2) which was attributed to the increase in the maximum temperature reached during foaming (ΔT_max~40°C). Increasing the amount of trimerization catalyst was also found to significantly change the cellular morphology of the PIR foam with a decrease in the foam density from 34 to 27 kg/m³ (Δρ_f~21%), a decrease in the average cell size (in the rise direction) from 532 to 279 µm (Δh~47%) and an increase in cell aspect ratio from 1.46 to 1.96 (ΔR~34%). Accordingly, the cell population density (β) was found to increase by a factor of about x15 with the increase in PIR catalyst content; this was attributed to the reduction of t_gel, giving less time to the cell structure for evolving (mainly by a cell size increase) by coalescence and Ostwald ripening. These results suggest essential guidelines that could enable mastering the foam morphology and the resulting mechanical and thermal properties. The impact of curing kinetics on the thermal conductivity of the above PIR foams will be addressed in another paper.

5. Supporting information

**Figure S1** Evolution of height (H), temperature (T), pressure (P) and dielectric polarization (D) as a function of time for the various catalyst concentrations (K-Oct).

**Figure S2** Evolution of cream time ($t_{cream}$) during foaming as a function of K-Oct content (pphp). The line is only a guide for the eyes.
**Figure S3** Evolution of the maximum rise rate (dH/dt) assimilated to the maximum of the first and second peaks as a function of K-Oct content (pphp).

**Figure S4** Evolution of characteristic times during foaming as a function of K-Oct content (pphp).

**Figure S5** Evolution of the maximum height (mm) as a function of K-Oct content (pphp).

**Figure S6** Evolution of the rise rate (mm/s) as a function of time and for K-Oct content of 0.5, 0.75 and 1 pphp.

**Figure S7** Evolution of the temperature rise rate (dT/dt) as a function of time and for the various contents of K-Oct (pphp).

**Figure S8** Evolution of the time at the maximum values of dT/dt of the trimerization peak as a function of the time at the maximum value of dh/dt (2nd peak).

**Figure S9** Evolution of foam temperature rise rate for the second peak (isocyanurate) as a function of temperature for the different K-Oct content (pphp).

**Figure S10** Effect of catalyst concentration on the temperature corresponding to the kick-off and maximum of the second peak of dT/dt (assimilated to isocyanurate formation), respectively.

**Figure S11** Evolution of the time needed to reach the maximum value of dielectric polarization (t@DPmax) and the gel time (tgel) as a function of K-Oct content (pphp).

**Figure S12** FTIR spectra of K-Oct showing the absence of phenyl groups in the PIR catalyst.

**Figure S13** Evolution of the isocyanate/phenyl ratio (as probed by the h<sub>2280</sub>/h<sub>1595</sub> peak height ratio) as a function of the K-Oct content (after about 3 weeks of aging at room temperature).
**Figure S14** Evolution of the urethane/phenyl ratio (as probed by the $h_{1220}/h_{1595}$ peak height ratio) as a function of the K-Oct content (a) and $T_{max}$ (b).

**Figure S15** SEM images of the cellular structure, taken perpendicular to the rise direction, for the various catalyst concentrations (K-Oct).

**Figure S16** Effect of K-Oct content on the cell height (Major axis) and cell diameter (minor axis) distributions of PIR foams.

**Figure S17** Evolution of $\Delta t=t_{gel}-t_{cream}$ as a function of the K-Oct content.

**Figure S18** Relation between the peak maximum of each Weibull distribution curve and the average cell size for the various K-Oct contents.

**Figure S19** Evolution of pore size polydispersity factor ($\epsilon$) obtained from the Weibull distributions reported in Figure 15 as a function of catalyst content.

**Figure S20** Evolution of the open-cell content (%) as a function of (a) the K-Oct content and (b) cell height.

**Table S1** Main characteristics of the PIR foams prepared at the different K-Oct contents

## 6. Acknowledgements

The authors are grateful to Vincent Barraud and Alexandre Fougeron (R&D SOPREMA, Saint-Julien-du-Sault) for fruitful discussions. The authors also wish to thank Isabelle Dhenin (R&D technician SOPREMA) for sharing her outstanding experience of PIR foaming and for providing the open-cell content measurements of our foam samples. This project was made possible with the financial support of SOPREMA.
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