Determination of the Crosslinking Density of a Silicone Elastomer

Laboratory Experiment Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

pubs.acs.org/jchemeduc

Determination of the Crosslinking Density of a Silicone Elastomer Julie Schweitzer,†,‡ Souhila Merad,†,‡ Gautier Schrodj,†,‡ Florence Bally-Le Gall,†,‡ and Laurent Vonna*,†,‡ †

Institut de Science des Matériaux de Mulhouse (IS2M) CNRS−UMR 7361, Université de Haute Alsace, 15 rue Jean Starcky BP2488, 68057 Mulhouse, France ‡ Université de Strasbourg, 67081 Strasbourg, France

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S Supporting Information *

ABSTRACT: A laboratory experiment for the determination of the crosslinking density of silicone elastomers is described on the basis of swelling experiments and mechanical tests. In the experiment, the macroscopic swelling and mechanical behaviors of the elastomers were discussed as a function of the cross-linking density, which can be easily controlled by varying the base-to-curing-agent ratio during elastomer synthesis. The crosslinking density and the average molecular weight between cross-links were calculated from the swelling degree at equilibrium through the Flory− Rehner theory and from a simple mechanical model. The results have shown a good convergence of the average molecular weight between crosslinks calculated from the two methods, respectively. On a more general note, the suggested experiments and the associated results offered numerous opportunities for discussions on macromolecular architectures, interactions between polymers and solvents, and mechanical properties of elastomeric materials. KEYWORDS: Upper-Division Undergraduate, Laboratory instruction, Hands-On Learning/Manipulatives, Polymer Chemistry, Physical Chemistry, Materials Science, Polymerization, Solid State Chemistry

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scientific works.6,19−26 Its synthesis simply consists of the mixture of a liquid base and a liquid curing agent, followed by a subsequent cross-linking step in an oven. Different crosslinking densities can thus be achieved by varying the base-tocuring-agent ratio for a given time and curing temperature. Last but not least, cross-linked Sylgard 184 is extremely easy to handle and its properties are well-defined. In this experiment, the cross-linking density is obtained independently from swelling and elongation experiments. Whereas swelling experiments were performed in a conventional manner by measuring the mass increase of a sample as a function of time, the mechanical properties (i.e., the strain− stress curves) were obtained using a smartphone to measure elongation of the sample. Indeed, conventional mechanical tests actually require specific setups that are rarely available for students and thus needed to be simplified for this laboratory experiment. In addition, such experimental approaches based on the use of smartphones were shown to appeal to students, hence recent proposals for several laboratory experiments based on this approach.27−35 The elongation can, however, also simply be estimated using a ruler. For three years, we have successfully conducted this laboratory experiment with undergraduate students in their

INTRODUCTION Silicone elastomers are cross-linked polymers with unique mechanical and chemical properties. They have been used for many years in a wide range of commercial and industrial applications1 and are still the subject of intense research for the development of innovative advanced materials such as microfluidic chips or microelectromechanical systems.2−10 These materials are of particular interest because their anticipated high deformability can be easily fine-tuned by varying the cross-linking density (degree of cross-linking). This parameter is of fundamental importance and often needs to be quantified for material development and the quality control of manufactured products. From an academic perspective, it is related to the molecular weight between two cross-links, which facilitates the representation of the cross-linked macromolecular architecture of elastomeric materials for students. The cross-linking density of elastomers can be determined using various characterization techniques but the most common methods are swelling experiments, mechanical tests, and NMR spectroscopy.11−18 The aim of this laboratory experiment is to quantify the cross-linking density of a silicone elastomer on the basis of swelling experiments and mechanical tests that can be easily performed in a chemistry lab. The silicone elastomer considered in this study is a commercial poly(dimethylsiloxane), namely, Sylgard 184 (Dow Corning, Midland, MI), which is widely used as a model silicone elastomer in fundamental studies as well as in educational © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: February 13, 2019 Revised: May 3, 2019

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DOI: 10.1021/acs.jchemed.8b00911 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

Figure 1. (A) Bone-shaped-cutting-tool shape (4 mm width, 75 mm length). (B) Photograph of the experimental setup for the mechanical tests.

third year as part of a chemistry course on polymer science. In the classroom, the macroscopic behavior of the elastomer observed during the laboratory experiment can be discussed in terms of its cross-linking density or the related molecular weight between two cross-links in order to correlate the properties of the material with its macromolecular structure. Furthermore, determination of cross-linking density from swelling experiments paved the way for discussions on the interaction between a solvent and a polymer, including the Hildebrand solubility parameter and the Flory−Huggins parameter.

app for measuring distances on photographs after proper calibration (ImageMeter by Dirk Farin, for example36). The swelling experiments and the tensile tests run over a 4 h experimental session. A second session (of at least 2 h) is dedicated to the measurement of the elastomer mass in the swollen state at equilibrium (after at least 24 h in the solvent) and to the discussion of the average molecular weight between cross-links obtained from the swelling experiments and the tensile tests. However, the samples need to be prepared 24 h before this experiment. Indeed, the Sylgard 184 elastomers made with different base-to-curing-agent ratios should be prepared at least 1 day before the experiments because they have to be cured in an oven overnight.6,37 Although a large range of base-to-curing-agent ratios between 10/2 and 10/0.4 might be considered, we recommend five of these that led to distinct swelling and mechanical behaviors: 10/1, 10/0.8, 10/ 0.6, 10/0.5, and 10/0.4. An Excel file provides Supporting Information in the form of tabulated parameter values and calculations to facilitate determination of the cross-linking density and average molecular weight between cross-links from both the swelling measurements and mechanical tests.

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EXPERIMENT A full description of the experimental procedure is given in the Supporting Information, including the synthesis of the silicone elastomer. The swelling experiments and the mechanical tests were each performed on samples with the same dimensions (same width, height, and thickness). Indeed, the swelling degree, which is based on diffusion, may depend on the geometry of the sample, whereas determination of the elastic modulus requires knowledge of the cross-section area of the sample. Ideally, a bone-shaped cutting tool designed for standard mechanical tests should be used (Figure 1A). Because of the transparency of Sylgard 184, the gravimetric approach was preferred over the volumetric one to determine the swelling degree of the elastomer. The gravimetric approach is indeed simple and low-cost, but accurate measurements might be more difficult to obtain because of the evaporation of the solvent during the weighing step. As discussed below, the swelling degree of the elastomer in the different solvents was measured during the laboratory experiment in order to demonstrate immediately the impact of the base-to-curingagent ratio or polymer−solvent affinity on the swelling process. The calculation of the cross-linking density requires, however, a measurement of the sample mass at least 24 h after swelling in the solvent (at swelling equilibrium). The mechanical tests were elongation tests performed at constant load on samples of known geometry. Increasing loads were attached to the bottom of the sample, which was suspended in front of graph paper as a distance marker (Figure 1B). The elongation was measured between two marks drawn on the sample for the different weights by using a smartphone

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HAZARDS Throughout the laboratory experiment, including elastomer preparation, students should wear a laboratory coat, gloves, and safety glasses. The swelling experiments should be performed under a fume hood. The swollen samples have to be handled with tweezers and weighted on a scale placed under a fume hood. All solvents and solids should be disposed of using appropriate containers for subsequent waste treatment. Cyclohexane is highly flammable (liquid and vapor); it can causes skin irritation, drowsiness, or dizziness and may be fatal if swallowed and allowed to enter airways; it is very toxic to aquatic life with long-lasting effects. Ethyl acetate is also highly flammable (liquid and vapor), can cause serious eye irritation, may be harmful if inhaled, and may cause drowsiness or dizziness. Because of their low surface tension, silicone oils can disperse extremely easily, leading to pollution of the lab. During the preparation step of the elastomer, we recommend cleaning up all spills immediately with a solvent and placing waste in a suitably labeled container for waste disposal. Major spills may present a slip hazard! In this case, spills should be B




Figure 2. (A) Sylgard 184 swelling degree in cyclohexane for three different base-to-curing-agent ratios: 10/1 (circles), 10/0.6 (squares), and 10/ 0.4 (triangles). (B) Sylgard 184 swelling degree for two base-to-curing-agent ratios, 10/1 (circles) and 10/0.4 (triangles), in cyclohexane and ethyl acetate (white and gray, respectively).

curing-agent ratios. Indeed, only a few hours are needed to highlight the influence of the cross-linking density on the swelling of the elastomer, as shown in Figure 2A. At this point, the students have easily noticed that, as expected, the swelling degree is higher for lower cross-linking densities (i.e., higher base-to-curing-agent ratios). In addition, each pair of students plotted SD versus time for their own elastomers with different base-to-curing-agent ratios in cyclohexane and ethyl acetate. Figure 2B shows the variation of SD with time for two different base-to-curing-agent ratios in cyclohexane and ethyl acetate obtained by a pair of students. It clearly appears that for a given base-to-curing-agent ratio, swelling is more important in cyclohexane, which has more affinity with Sylgard 184, compared with in ethyl acetate, which displays lower affinity with Sylgard 184.38 This result, which could easily be obtained by the students, led to in-depth discussion about polymer−solvent interactions.19,39 The curves in these figures are quite distinct, but samples with the same geometry have to be considered in order to obtain such a result. These findings also show that the swelling of elastomers with low curing-agent contents is quite slow compared with that at 10/1 for example, for which equilibrium is reached after 3 to 4 h. This demonstrates that the mass of the swollen sample needs to be measured after at least 1 day (24 h) of immersion in the solvent, to ensure that the system has reached its state of equilibrium.

contained with sand, earth, or vermiculite. Then, the solid residue should be collected and sealed in labeled drums for disposal. Finally, the area should be washed carefully with appropriate solvents.

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RESULTS AND DISCUSSION This laboratory experiment was run in groups of two students, each group carrying out the experiments for one or two baseto-curing-agent ratios. The elastomers were prepared by the students 1 day before the experiment but can also be prepared only by the instructor. The swelling experiments and the tensile tests were carried out simultaneously over a 4 h session. The results were then collected for comparison and further discussion during a supplementary 2 to 4 h session that included the measurement of the mass of the sample in the swollen state at equilibrium (after at least 24 h of immersion in the solvent). The following results were obtained by five pairs of students who carried out the experiments in 2017. Swelling Experiments

The swelling of Sylgard 184 elastomers was carried out by each pair of students in cyclohexane and ethyl acetate, with their own base-to-curing-agent ratios chosen at the beginning of the experiment. Figure 2A shows the swelling degree, SD, obtained by students who had considered Sylgard 184 with three different base-to-curing-agent ratios in cyclohexane. The experimental datum required to determine the cross-linking density is indeed the swelling degree, SD, expressed as the increase in elastomer volume in relation to its initial volume (before swelling experiments): SD =

Tensile Tests

The elongation experiments were performed at a constant load using increasing loads attached to the elastomer sample. Figure 3 shows the stress-versus-strain curves built by the students with cured Sylgard 184 of different base-to-curing-agent ratios. The stress, σ (in MPa), was calculated from

m0 /ρe + (m − m0)/ρs m0 /ρe

(1)

where m0 and m refer to the masses of the unswollen and swollen elastomer (in g), respectively, and ρe and ρs refer to the densities of the elastomer and the solvent (in g cm−3), respectively. Although the determination of the cross-linking density requires the swelling degree of the elastomer after 24 h of immersion in the solvent (according to the normalized test ASTM D2765-95), the variation of SD with time was plotted during the experiment on a single graph for different base-to-

σ=

mL g s

(2)

where mL is the weight of the load (in kg), g is the gravitational constant, and s is the area of the cross-section of the sample (in m2). The strain ε (dimensionless) in this figure was expressed according to C




where ρe refers to the density of the elastomer (in g cm−3). It can be noticed that the value of Mc was often easier for students to work out than the cross-linking density. The swelling of the elastomer is driven by the affinity between the elastomer and the solvent. This affinity can be expressed using the solubility parameter or the Hildebrand solubility parameter, δ (in cal1/2 cm−3/2). It is assumed that solvents with δ similar to that of the polymer will swell the cross-linked polymer effectively. From a thermodynamic point of view, the swelling is associated with (i) the heat of mixing of solvent and polymer (related to their affinity), (ii) the increase in the entropy caused by the mixing of solvent and polymer, and (iii) the decrease in entropy caused by the stretching (i.e., organization) of the elastomer chains. The balance of the corresponding forces at the equilibrium swelling state is expressed through the Flory−Rehner equation, according to the theory of the same name. In this equation, Mc is related to the swelling degree, SD (eq 1), which is expressed as ϕ = 1/SD (ϕ thus being the volume fraction of elastomer in the equilibrium swollen state):14,40 Figure 3. Stress-versus-strain curves obtained for Sylgard 184 with different base-to-curing-agent ratios: 10/1 (open squares), 10/0.8 (open circles), 10/0.6 (gray triangles), 10/0.5 (gray squares), and 10/ 0.4 (gray circles).

ε=

L − L0 L0

Mc = −

)

ln(1 − ϕ) + ϕ + χϕ2

(5) −1

where Vs is the molar volume of the solvent (in cm mol ), f is the functionality of the cross-link (f = 4 in our case), and χ is the Flory−Huggins polymer−solvent-interaction parameter (dimensionless). Moreover, the pioneering work of Ellis and Welding14,43,44 has demonstrated that the nonswelling of the silica fillers contained in the elastomer formulation has to be taken into account when results of swelling experiments are exploited. The volume fraction of elastomer in the equilibrium swollen state, ϕ, is thus more exactly defined as

(3)

ϕ=

(m0 − m0fsilica )/ρe (m0 − m0fsilica )/ρe + (m − m0)/ρs

(6)

where fsilica is the weight fraction of silica fillers in the Sylgard 184. Although Sylgard 184 datasheets indicate a weight fraction of silica fillers ranging from 30 to 60%, TGA analyses performed in our lab gave a more precise value of around 53%. In eq 6, the mass of the sample in the swollen state, m, has to be measured after at least 24 h in the solvent. This measurement was done by the students at the beginning of this second session. Here, the use of Flory−Rehner theory based on the expression of the mixing and elastic components of elastomer free energy in the swollen state provides an interesting opportunity for theoretical developments in the classroom. From the mechanical tests, the average molecular weight between cross-links, Mc, (in g mol−1) was calculated by the students using40 Mc =

Calculation of the Crosslinking Density

In a second session of this laboratory experiment, the results of the swelling experiments and mechanical tests were gathered to determine and discuss the average molecular weight between cross-links, Mc (in g mol−1), which is directly related to the cross-linking density, ν (in mol cm−3), which is defined by

3ρe RT E

(7)

where E is the elastic modulus as previously described (in MPa), R is the gas constant, and T is the temperature (with RT = 2436 J mol−1 at 20 °C). All calculations and parameters considered in this laboratory experiment are presented in the form of an Excel file (Supporting Information), which can be provided to the students. Other potentially less harmful solvents could be considered, but we suggest using those most compatible with

ρe Mc

2ϕ f

3

where L is the length of the sample (distance between the two marks), and L0 is the initial length of the sample. In what follows, one assumes that the sample width is constant, especially at low strains, so that only the extension in length is considered. The stretching behavior of the elastomers is expected to be nonlinear and can be modeled using the neoHookean, Mooney−Rivlin, or Ogden model.40−42 As already discussed in the literature for the case of Sylgard 184,42 this behavior was clearly observed with the 10/1 and 10/0.8 baseto-curing-agent ratios, for which a nonlinear increase of the stress is observed when the strain is increased (Figure 3). For the 10/0.4, 10/0.5, and 10/0.6 base-to-curing-agent ratios (Figure 3), a more linear behavior pattern was observed up to a relatively high strain (close to 100% strain). But, the most important point easily noticed by the students was the increase of the stress with increasing cross-linking density for a given strain. In other words, the deformability of the elastomer decreases as the cross-linking density increases. In order to calculate the cross-linking density from these mechanical experiments, the value of the elastic modulus, E, also named Young’s modulus, of the elastomer is required. Thus, students have determined from these stress-versus-strain curves the elastic modulus, E, corresponding to the slope of the curve in the linear domain (i.e., at low strain, 0 ≤ ε ≤ 0.5 range).

ν=

(

ρe Vs ϕ1/3 −

(4) D




Figure 4. (A) Average molecular weight between cross-links, Mc, determined from the mechanical tests (white bars) and the swelling experiments in cyclohexane (gray bars) and ethyl acetate (black bars). (B) Elastic modulus, E, obtained from the mechanical tests (white bars) and from the Mc calculated from the swelling in cyclohexane (gray bars) and in ethyl acetate (black bars).

the elastomer. We recommend the work of Lee et al.,38 in which the authors considered the compatibilities of different solvents with Sylgard 184. This work allows the Flory− Huggins polymer−solvent-interaction parameter, χ, to be evaluated following the relation given in eq 8 (also in the supplementary Excel file in the Supporting Information): χ=

Vm(δe − δs)2 RT

widely used approach in rubber science to determine Mc, the Flory−Rehner model is still under debate in the literature. One important point for discussion is, for example, the exact value of the Flory−Huggins polymer−solvent-interaction parameter, χ, or even the model chosen to describe the swollen elastomer.14,40,45−48 Moreover, the presence of silica fillers in the elastomer formulation disturbs the swelling of the elastomer despite the attempt to consider the weight fraction of fillers to correct the measured value of the swelling degree. Additionally, the mechanical tests performed here clearly did not reach the requirements of normalized tests performed on a calibrated dynamometer. However, the swelling experiments and the elongation tests described in this laboratory experiment constitute an initially satisfying approach for determining the cross-linking densities of elastomers and trigger fundamental theoretical discussions about polymer science and the properties of elastomers.20,49−55

(8)

where Vm is the molar volume of the elastomer (in cm3 mol−1); δe and δs are the Hildebrand solubility parameters (in cal1/2 cm−3/2) of the elastomer and solvent, respectively; R is the gas constant; and T is the temperature (with RT = 580 cal mol−1 at 20 °C). Finally, the students calculated the average molecular weight between cross-links, Mc, from the swelling experiment using the mass of the elastomer in the swollen state at equilibrium (eq 5) for the two solvents and from the mechanical tests using the elastic modulus, E (eq 7). The average molecular weights between cross-links, Mc, determined in this way are given in Figure 4A. As expected, Mc increases when the curing-agent content is decreased. The average molecular weight between cross-links determined from the swelling experiments performed in cyclohexane and ethyl acetate are quite similar. Higher values of Mc are, however, obtained from the mechanical tests, especially in cases with lower curing-agent contents, even if they remain in the same order of magnitude as those obtained from the swelling experiments. The students also calculated the elastic modulus from the swelling data in order to compare it with the one obtained in the mechanical tests (Figure 4B). A similar discrepancy is, of course, observed between the results obtained with the two methods. Different explanations may be proposed for the discrepancy observed between the average molecular weights between cross-links, Mc, obtained from the swelling experiments and the mechanical tests. First, the deformation of the elastomer resulting from the elongation under load (uniaxial) and swelling (tridimensional) lead to different loads of the polymer chains between cross-links and, finally, to different Mc. Moreover, although the swelling experiment is the most

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CONCLUSION This laboratory experiment has provided students an opportunity to explore and discuss the macromolecular architecture of elastomers on the basis of two different macroscopic tests. It is an experiment that can be applied to any kind of elastomer. The calculations of the average molecular weight between cross-links from the swelling experiments and the tensile tests gave a clear idea of the concept of cross-linking density, which governs the properties of this material that is encountered in everyday life. Additionally, the explanations of the lecturer can be provided at different comprehension levels, from the most simple, describing the elastomer as a polymer network, to the most challenging, being the demonstration of eqs 5 and 7. This experiment based on the use of a smartphone is fully collaborative because elastomers with five different crosslinking degrees of distinct swelling and mechanical behaviors can be easily prepared with Sylgard 184, with each student or group of students being in charge of one or two cross-linking densities. We have observed that this approach finally made this laboratory experiment appealing for the students. E



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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b00911. Note for instructor (PDF, DOCX) Information for students (PDF, DOCX) Parameters and calculations performed from experimental data (XLSX)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Florence Bally-Le Gall: 0000-0003-4140-053X Laurent Vonna: 0000-0003-1764-1691 Notes

The authors declare no competing financial interest.

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