In practice, polymers are subjected to swelling agents, such as biomaterials, contact lenses, automotive gaskets, and materials used in extracting organic contaminants from water. However, our current understanding of the physical properties of polymer/diluent systems is far from complete. Traditionally, equilibrium swelling is used to extract the average molecular weight between crosslinks using the Flory-Rehner theory.1 However, there are some drawbacks with this method. In addition to the fact that it gives only a mean value for the molecular weight between crosslinks, some of the underlying assumptions for the theory are questionable.2–8 Recently, another method called thermoporosimetry has been developed by some researchers to deduce the size and size distribution of nanoscale heterogeneities in polymer networks by using melting (or freezing) point depression of the solvents.9–15 In this method, the Gibbs-Thomson (GT) equation16 is used in conjunction with the Flory-Huggins (FH) model17, 18 to obtain the size and size distribution of solvent crystals, which are comparable with the nanoscale mesh size and distribution in polymer networks. Nevertheless, previous results on the melting (or freezing) behavior of swelling agents confined in polymer networks are complicated and contradictory, and the mechanisms of melting (or freezing) point depression are not well understood.
A prerequisite for combining the GT equation16 and the FH model17, 18 is that the FH model can predict the melting point depression of the organic solvent in the polymer solution, but this was found to be not true by Qin and McKenna.10 Furthermore, as pointed out by Jackson and McKenna,19 the FH model, which predicts the melting point depression according to the decrease of the chemical potential of the solvent molecules in polymer solution, is only applicable to the equilibrium melting behavior, because of the supercooling effect during cooling run. However, much of the works focuses on the freezing point depression.9, 20–22 Kuhn et al.9 were the first to observe the freezing point depression (ΔTf) and found that ΔTf is underestimated by the FH model. They attributed the excess ΔTf to the confinement effect exerted by the network mesh which reduced the crystal sizes of the solvent. The work of Kuhn et al. lead to several subsequent studies.19–22 Honiball et al.20 suggested that it was the difficulty in nucleation of the solvent which lead to the excess ΔTf. Using X-ray measurements to study the crystal size of benzene, Boonstra et al.21 concluded that there was no significant difference of crystal size in uncrosslinked and crosslinked rubbers. This work, however, was found to be inconclusive by Jackson and McKenna.19
Although most of the previous work focused on melting or freezing temperatures, the heat of fusion (ΔHm) of the solvent confined in polymer networks has been less discussed. One underlying assumption for the application of the FH model and the GT equation is that ΔHm of the solvent in the polymer solution is the same as that in bulk. However, Qin and McKenna10 found that the change of ΔHm depends on the solvent type in polyisoprene; ΔHm of benzene deceases with increasing polymer fraction, but ΔHm of hexadecane remains constant. They found that the glass transition temperature (Tg) of polyisoprene in the benzene/polyisoprene system follows the prediction of the Fox equation when the polymer volume fraction is higher than 53%, but it jumps to a value that is very close to the bulk Tg of polyisoprene below 53%, suggesting complete phase separation takes place. It was concluded that plasticization effects account for only part of the observed decrease of ΔHm of the benzene.23 Honiball et al.20 also found that the enthalpy change on freezing for cyclohexane in crosslinked and uncrosslinked natural rubber is reduced with increasing polymer fraction, and they attributed part of the reduction to polymer–solvent interactions. Such a phenomenon can also be observed in water/polymer membrane systems.24, 25 In addition to the plasticization and potential polymer–solvent interaction effects, more complications can arise because small size has been observed to decrease the heat of fusion of organic liquids confined in nanopores.23
As a continuation to previous work from Texas Tech,10 the present work further explores the validity of the FH model prediction and the method of thermoporosimetry. Differential scanning calorimetry (DSC) is used to characterize the melting behavior of cyclohexane and cyclooctane in poly(dimethyl siloxane) (PDMS) precursors and model networks.
Cyclohexane (99.9%, Fisher Scientific) and cyclooctane (99+ %, Aldrich) were used directly without further treatment and are denoted as C6 and C8, respectively. Four vinyl-terminated bifunctional poly(dimethyl siloxane) (PDMS) precursors with different viscosities were supplied by Gelest and are denoted as V5, V25, V33, and V42. The viscosities and approximate weight average molecular weights (Mw) for these precursors are provided by the manufacturer and listed in Table 1.
Table 1. Viscosities and Manufacturer Supplied Weight Average Molecular Weights for PDMS Precursors
PDMS model networks, denoted as CV5, CV25, CV33, and CV42, were prepared by end-linking the four different precursors with tetrakis(dimethylsiloxy)silane (Aldrich) and cis-dichlorobis(diethyl sulfide)platinum (II) (Aldrich), which were used as crosslinker and catalyst, respectively. The molar ratio of silane hydrogen in the crosslinker to vinyl group in the precursor was 1.5. Cis-dichlorobis(diethyl sulfide)platinum (II) was dissolved in toluene to obtain a solution concentration of 0.0023 g/1.0 mL solvent. Five grams of PDMS precursor was added into a beaker and mixed with appropriate amount of crosslinker and 60 μL catalyst solution by rigorous stirring for 10 min. The mixture was then poured into a Teflon mold. The mold was put in a vacuum oven at 75 °C for at least 24 h to ensure complete reaction. The sol of the resulting vulcanizate was extracted by cyclohexane to determine the sol fraction (ws). Thereafter, equilibrium swelling which is characterized by the polymer volume fraction (v) at room temperature in cyclohexane and cyclooctane was measured by the standard gravimetric method. In this method, the preweighed dry rubber is swollen to equilibrium and weighed after wiping the excess solvent on the surface with a tissue, and v is calculated assuming the volume additivity of the polymer and the solvent. As supplied by the manufacturer, the density of V5 is 0.93 g/mL, whereas it is 0.97 g/mL for the other three precursors at room temperature. The latter value was also taken as the density of the PDMS networks. The densities of cyclohexane and cyclooctane are 0.774 g/mL and 0.834 g/mL, respectively, provided by the manufacturer at room temperature. The values of ws and v are listed in Table 2.
Table 2. Network Characteristics of PDMS Model Networks
Sol Fraction (%)
v (%) in Cyclohexane
v (%) in Cyclooctane
The melting behavior of cyclohexane and cyclooctane in PDMS precursors and model networks was determined by DSC (Perkin–Elmer Pyris1). Polymer and solvent were weighed separately into a preweighed hermetic pan, which was then sealed and kept at room temperature for at least 24 h. Before testing, the pan was reweighed to ensure no solvent leakage. The sample pans were cooled from 20 to −65 °C at a cooling rate of 5 °C/min and stabilized at −65 °C for 10 min then heated at the same rate to 20 °C. The heat flow of the sample pans was recorded for both the cooling scan and the heating scan. Because of the inevitable supercooling effect during the freezing process, we discuss, primarily, the melting behavior of the solvents. However, the freezing data are used in the case of the PDMS networks as these provide further insight into the melting behavior of the solvents. Onset melting temperature (Tonset), peak melting temperature (Tpeak), and heat of fusion (ΔHm) were determined from the melting region of the thermogram. Melting point depression was calculated in terms of onset melting temperature and peak melting temperature: ; , where and are the bulk onset melting temperature and peak melting temperature of the solvent, respectively.
RESULTS AND DISCUSSION
Melting Behavior of Cyclohexane in PDMS Precursors
The typical heat flow curves of the heating scan for PDMS precursor/cyclohexane systems are displayed in Figure 1, which shows the V5/cyclohexane system as an example. It is obvious that the volume fraction of polymer (v2) has a significant effect on the melting behavior of cyclohexane. As v2 increases, the melting peak of cyclohexane shifts to lower temperature and becomes broader and smaller, finally no melting peak can be detected when v2 >65% (this limit is slightly higher for the other three PDMS precursors). The resulting ΔTonset and ΔTpeak of cylcohexane in different PDMS precursors are shown in Figure 2 as well as the FH predictions for melting point depression.17
Tm,1 and are the melting temperatures in the solution and in the bulk of the solvent, respectively. refers to the heat of fusion in the bulk state of the solvent. v2 is volume fraction of the polymer, x is the degree of polymerization of the polymer. χ is the polymer–diluent interaction parameter. x is approximately taken as 11, 236, 574, and 980 for V5, V25, V33, and V42, respectively. χ = 0.435 – 0.014v2 for PDMS and cyclohexane was taken from the work of Brotzman and Eichinger.26
As can be seen in Figure 2, cyclohexane exhibits the greatest melting point depression in the V5, whereas it has nearly the same melting point depression in the other three precursors. The melting point depression of solvents on addition of solutes is a colligative property.27, 28 The magnitude of the melting point depression is proportional to the solute concentration which is expressed as molality, that is, in moles of solute per kilogram of solvent. Therefore, at the same volume fraction, the solute having the lower molecular weight exhibits the greater melting point depression of the solvent. This colligative property is also used to determine the molecular weight of the solute.29 However, when the molecular weight of the solute exceeds a few thousand, the difference in molecular weight has very small effect on the melting point depression of the solvent.30 Our observation is consistent with this expectation.
Similarly, the FH model predicts this trend. The FH predictions for x = 236, 574, and 980 are much the same as that of x = ∞, whereas it is higher for x = 11. Therefore, we use x = ∞ to calculate the FH prediction for the three high molecular weight PDMS precursors in our subsequent discussion. However, ΔTonset is significantly underestimated by the FH model, especially for cyclohexane in V5. In the case of the peak melting point depression, the FH prediction is close to the experimental data for cyclohexane in the three high molecular weight PDMS precursors, but a large deviation still exists in the V5. The magnitude of the melting point depression for cyclohexane in the PDMS precursors varies from 0 to 70 °C, which is much larger than what is observed for many other systems, such as benzene and hexadecane in polyisoprene or natural rubber.9, 10, 20, 19 In these systems, the melting point depression of the solvents generally does not exceed 40 °C. Honiball et al.20 also examined a number of solvents and found that cyclohexane exhibits large melting point depressions in natural rubber.
The heat of fusion decreases almost linearly with the increase of polymer content, as indicated in Figure 3. After the volume fraction of polymer reaches a certain value, cyclohexane shows no melting peak, thus zero heat of fusion. This linear relationship was also observed for cyclohexane in crosslinked and uncrosslinked natural rubber.20
Melting Behavior of Cyclohexane in Model Networks
The heat flow curves of the heating scan for PDMS model network/cyclohexane systems are quite different from those of PDMS precursor/cyclohexane systems, as shown in Figure 4(a), which depicts the CV5/cyclohexane system as an example. Unlike some other systems in which the solvent displays two independent melting peaks (corresponding to the melting of bulk solvent on the surface of the gel and confined solvent inside the gel),13, 20, 31 cyclohexane just has one melting peak when v2 < v. As the polymer volume fraction increases from 0 to 14%, the shape and position of the melting peak of the cyclohexane remains unchanged, but the area becomes smaller as discussed subsequently. Thereafter, the position of the melting peak slightly shifts to lower temperature and then stays at the same temperature until v2 > v. At the same time, a low-temperature tail appears and increases with the increase of the polymer concentration. Therefore, the melting peak is composed of the low-temperature tail and the high-temperature sharp peak. After v2 ≥ 47%, the high-temperature sharp peak disappears and the low-temperature tail dominates the melting peak, which shifts toward lower temperature with the increase of polymer concentration. We remark here that the determination of heat of fusion and onset melting temperature may be subject to relatively large errors (possibly as large as 5 °C for the onset melting temperature and 1 J/g for the heat of fusion), because of baseline curvature combined with the breadth of the transition.
In Figure 5, ΔTonset and ΔTpeak are plotted against v2 for PDMS model network/cyclohexane systems. As we only obtain the peak melting temperature and onset melting temperature of the single sharp peak when the v2 < v, ΔTonset and ΔTpeak do not change up to v2 = 39% for the CV5/C6 system. Above this volume fraction, there is an abrupt change of ΔTonset and ΔTpeak, as these values of ΔTonset and ΔTpeak now represent the low-temperature tail. Although v for CV25/C6, CV33/C6, and CV42/C6 are 23%, 19%, and 17%, the v2 value where the abrupt change of ΔTonset and ΔTpeak takes place is much higher than the v for the three systems and close to that observed in the CV5. The FH model even overestimates ΔTpeak in this case, whereas ΔTonset follows linear relationships with v2 both above and below the point of abrupt change.
Surprisingly, molecular weight between crosslinkages (i.e., molecular weight of the PDMS precursor) of the model networks has little effect on the melting behavior of cyclohexane. This is contrary to the widely observed phenomenon that higher crosslinking density results in greater melting point depression. As first suggested by Kuhn et al.9 the mesh of polymer network is very much like a pore of porous materials and, consequently, it exerts a confinement effect on the growth of the solvent crystals. Hence, the smaller the mesh, the smaller the solvent crystal. In our case, the molecular weights of the PDMS precursors vary from 700 to 80,000 g/mol, but this large range seems to not affect the melting behavior of the cyclohexane. Because the molecular weights of the PDMS precursors in this study are below or not extremely far above the critical molecular weight for entanglements of PDMS, which is approximately 2.8 × 104 g/mol,32 we do not expect trapped entanglements to have a significant effect on the network structure of the PDMS model networks.
Furthermore, it should be noted from comparing Figure 5 and Figure 2 that the melting point depression of the cyclohexane in the PDMS precursors is much higher than that in the PDMS model networks, especially for the lowest molecular weight PDMS precursor. This is unexpected, because it is generally considered that it is the lowering of solvent chemical potential that contributes to the melting point depression in polymer solution systems, whereas for swollen crosslinked polymers, the additional confinement effect should lead to a further melting point depression of the solvent due to finite crystal size effects.
As shown in Figure 6, the heat of fusion for the four systems is almost the same and decreases linearly with increasing polymer volume fraction.
Freezing Behavior of Cyclohexane in Model Networks
To further explore the problem, we examined the heat flow curves from the cooling scans. These are shown in Figure 4(b). The cooling thermograms for cyclohexane in CV5 are like reciprocal heating curves. Another interesting phenomenon is that there seems to be no bulk crystallization of cyclohexane in CV5 when v2 ≥ 39% even though bulk melting was still observed up to v2 ≤ 47%, which is slightly higher than the equilibrium swelling value. A possible reason for this may be that a small amount of solvent on the surface of the gel can be easily supercooled to have the same freezing point as that of the gel solvent.
As shown in Figure 4(a), when the polymer volume fraction is lower than a certain value, we can divide the whole melting peak into two parts with one being the sharp peak and another being the tail. A and B represent the areas of the sharp peak and the tail, respectively. It is clear that as the polymer concentration goes up, A is depressed gradually whereas B increases. When the solvent is in excess (i.e., the solvent volume fraction is higher than that at equilibrium swelling), the polymer is in the equilibrium swollen state, the solvent concentration confined in the gel remains constant with further increase of solvent. As a result, two kinds of crystal exist in the system: bulk state crystal on the surface of the gel which increases as the solvent concentration increases, and confined crystal particles in the gel which remain unchanged. Therefore, if A and B are assigned to melting of the bulk state crystal on the surface of the gel and crystal particles inside the gel, respectively, the area of B should remain unchanged. Evidently, our result is contrary to this expectation.
As shown in Figure 4(b), the crystallization peak can also be divided into A and B when the polymer volume fraction is low. Honiball et al.20 proposed that if the bulk state solvent crystal exists on the surface of the gel, it can play a role as nucleation sites for the solvent in the gel. Because of the melting point depression of the solvent in the gel, after the formation of the bulk crystal on the surface (represented by A), the solvent molecules in the gel still retain their mobility and then diffuse out of the gel and add to the bulk state crystal, which results in a tail to the crystallization peak of the bulk solvent (represented by B). They also found that when the solvent is in excess, just 20% solvent in the gel diffuses to the surface independent of concentration, whereas the other part still crystallizes in the gel. In our case, if we attribute B to the crystallization of gel solvent which diffuses to the surface, there should be just bulk crystal melting when the sample is heated. This does not seem to be the case here, because the sharp peak and the tail are both observed on heating, as can be seen in Figure 4(a).
Jackson and McKenna33 found that when there is enough excess solvent that wets the outside surface of the controlled pore glass grains, nuclei readily form on the outside surface or interstitial spaces of the controlled pore glass powder during the cooling cycle and the crystallization propagates to the interior of the pores. But the existence of such a phenomenon also depends on the properties of the solvent, such as hydrogen bonding, molecular size, and asymmetry. For example, a network is formed between molecules by hydrogen-bonding for benzyl alcohol, which helps the exterior nuclei to propagate into the pores; however, o-terphenyl does not have such a network and is a slow crystallizer, so the propagation of the crystallization from the outside is not observed. In the present case, although cyclohexane has small molecular size and symmetric structure, the intermolecular interactions are very weak.
On examining the heating thermograms of the cyclohexane in CV5, it is clear that the position of the melting peak of the cyclohexane in the gel when v2 = 47% corresponds to the position of the tail when v2 = 39%, indicating the tail should originate from the melting of the solvent in the gel. Further decrease of polymer volume fraction results in suppression of B whereas A increases in area. When v2 < 14%, there is no longer a part B. This is strange and may suggest that phase separation takes place when the polymer volume fraction is below a certain value. When a nucleus is formed, the solvent molecules around it will diffuse and add to the nucleus, after the crystal reaches the mesh size, it still keeps growing and exerts a tension force on the mesh, which finally results in the rupture of the mesh due to the fragility of PDMS networks. As a result, the network confinement effect becomes negligible and phase separation takes place. Moreover, higher solvent content means larger crystals and phase separation, resulting in the melting point of the crystal in the gel approaching that of the bulk state. Finally, it is difficult to discriminate the mechanisms from each other. This may account for the fact that there is just one sharp peak when the polymer volume fraction is lower than 20%. Therefore, both bulk crystal and big crystal particles in the gel contribute to peak A, whereas the peak B originates from the small confined crystal particles.
The mechanisms leading to the reduction of heat of fusion may be a plasticization effect and polymer–solvent interaction effect. Qin and McKenna10 studied the plasticization effect of benzene in polyisoprene by measuring the Tg of the polymer, and the result demonstrated that plasticization accounts for only part of the reduction in the heat of fusion. Honiball et al.20 attributed the excess part of the decrease to polymer–solvent interactions. Based on the results of proton nuclear magnetic resonance, it was suggested that a certain amount of the solvent remains in the solvated state with the polymer chains after the formation of solvent crystals.34 Klein and Guenet35 proposed that the crystal cohesive energy of cyclohexane is weaker than some other solvents, and as a result, solvation tends to take place between cyclohexane molecules and polymer molecules. This leads to a large reduction of the heat of fusion. It is also proposed that when the polymer volume fraction is higher than a certain value, there are no longer crystallizable “free” solvent molecules; rather, polymer molecules interact with solvent molecules, which prevents the formation of solvent crystals.35, 36 The concentration (polymer weight faction, C0) at which such a phenomenon takes place is that where ΔHm = 0. A parameter a, which means the average number of solvent molecules that are bonded to a polymer monomer unit, can be used to characterize the degree of solvation. For amorphous polymer solution,
where Ms and Mp are the molecular weight of the solvent and the monomer unit, respectively.35, 36
From Figure 3 and Figure 6, C0 can be determined for PDMS precursors and model networks by extrapolating the linear fitting lines to ΔHm = 0. These values are listed in Table 3 as well as the calculated a values. Surprisingly, a for cyclohexane in PDMS is close to the values for benzene and trans-decalin observed by Klein and Guenet.35 This is contrary to their expectation that cylcohexane would have a much higher value of a. The reason for this discrepancy is unknown. Furthermore, a has the highest value in the lowest molecular weight PDMS precursor, whereas it is independent of the crosslinking density of the PDMS model networks, suggesting that solvation tends to occur more readily in the low molecular weight PDMS precursor.
Table 3. Values of C0 and a for Cyclohexane and Cyclooctane in PDMS Precursors and Networks
C0 (wt %)
Melting Behavior of Cyclooctane in PDMS Precursors
As shown in Figures 7 and 8, cyclooctane shows similar melting behavior to that of the cyclohexane in the PDMS precursors. The FH predictions are also given in Figure 7, in which χ was taken as 0.66 for cyclooctane and PDMS.37 The magnitude of the melting point depression increases with decreasing solvent fraction. Both ΔTonset and ΔTpeak are underestimated by the FH model. Cyclooctane in V5 exhibits the largest melting point depression, whereas similar melting behaviors in the other three PDMS precursors are observed. The deviation of ΔTonset and ΔTpeak from the FH model is also greatest for the V5/cyclooctane system. It is clear in Figure 8 that the heat of fusion of cyclooctane decreases linearly with polymer volume fraction in all the PDMS precursors. Cyclooctane in V5 has the lowest heat of fusion, whereas in the other three PDMS precursors the heat of fusion is almost the same.
Melting Behavior of Cyclooctane in PDMS Model Networks
Cyclooctane also has similar melting behavior to that of the cyclohexane in the CV5 model network. However, in the other three model networks, the melting behavior of cyclooctane is quite different from that of cyclohexane, as indicated in Figure 9. In the CV25 model network, cyclooctane does not show two melting peaks until the polymer volume fraction reaches 21%. In the CV33 and the CV42 model networks, cyclooctane has two melting peaks in all samples. If we designate the melting peak of the cyclooctane at higher temperatures as Peak 1 and that at lower temperatures as Peak 2, we find that, as the polymer volume fraction increases, the position of Peak 2 changes smoothly toward lower temperatures. However, the v2 dependence of Peak 1 is similar to what was observed for the cylcohexane in the PDMS model networks. The position of Peak 1 is nearly the same as the bulk state crystal and remains constant until a certain v2 value, which is about 43%, and then moves to lower temperature. The v2 dependence of Tonset and Tpeak was displayed in Figure 10 for PDMS model network/cyclooctane systems. Tonset and Tpeak of cyclooctane in V5-C8 remain nearly constant until v2 = 52% and then show abrupt change. Below this concentration Tonset and Tpeak reflect the melting of the bulk state crystal on the surface of the gel and big crystal particles in the gel. Subsequently, bulk state crystals disappear, Tonset and Tpeak reflect the melting of the crystal confined in the gel, so they shift to lower temperature due to the melting point depression. Tonset above this concentration can be predicted by the FH model, whereas Tpeak is overestimated. As shown in Figure 7(b–d), the melting behavior of Peak 1 is nearly the same as that of the single peak of cyclohexane in model networks. Both Tonset,1 and Tpeak,1 exhibit an abrupt change around 43% for all three systems, whereas Tonset,2 and Tpeak,2 are depressed gradually with increasing polymer fraction. It is also worth noting that on the high polymer fraction side, Tonset,1 and Tpeak,1 go down faster than Tonset,2 and Tpeak,2, consequently the two peaks merge together if their heat of fusion has not drop to zero. For example, when the polymer fraction is as high as 68% in the CV33/cyclooctane system, Peak 1 and Peak 2 merge together, as shown in Figure 9(b).
The heat of fusion behavior for the PDMS model network/cyclooctane systems is shown in Figure 11. ΔHm of the CV5-C8 nearly follows a linear relationship with v2. As there are two peaks in the other three systems, we use ΔHm,1 and ΔHm,2 to represent the heat of fusion of Peak 1, Peak 2, and ΔHm is denoted as the total heat of fusion of cyclooctane. In the case of the CV25-C8 system, linear relationships between ΔHm,1, ΔHm,2, ΔHm, and v2 can be observed, whereas for the CV33-C8 and V42-C8 systems, there are no such linear relationships. From Figure 11, ΔHm,1 appears to tend toward zero above a certain polymer fraction, but ΔHm,2 seems to change slowly or not at all. However, no melting signal was measurable above a polymer fraction of 75%. Therefore, both ΔHm,1 and ΔHm,2 are zero after this concentration.
It should be noted that only the CV42 model network shows the melting peak of PDMS crystals. However, such a peak was not observed in any of the other systems investigated here, suggesting the crystallization process of PDMS is completely suppressed or shifted to lower temperatures beyond our testing range by the presence of the cyclohexane or the cyclooctane. As the polymer volume fraction increases, the peak becomes stronger. Although the melting temperature for the PDMS crystal in the CV42-C8 system is lower than that of the pure CV42, it is independent of v2 in the presence of the cyclooctane. This is contrary to the FH model, which also predicts a continuous melting point depression for polymer crystals in the presence of a solvent17
where and are the melting temperatures of the polymer in solution and in the bulk, respectively. and Vu refer to the heat of fusion and volume per mole repeat unit, respectively. v1 is volume fraction of the solvent.
As discussed previously, here we can also divide Peak 1 into two parts: A and B. A reflects the melting of the bulk crystal on the surface of the gel and large crystal particles in the gel, whereas B represents the melting of small crystals confined in the gel. At low polymer volume fraction, the A component dominates Peak 1, but the area of A decreases with v2 until it disappears, and then B dominates Peak 1 and shifts gradually to lower temperature. Therefore, there are two states of cyclooctane in the three PDMS model networks: one is represented by Peak 2 and the other by B in Peak 1. Actually, such a double-melting-peak structure of confined solvent has also been observed in some other systems. Jackson and McKenna23 found that n-decane displayed a bimodal pore melting in 85 Å glass pores. They suggested that the two-peak structure may be due to a confinement effect in the glass pores which leads to polymorph crystals of the solvent. This speculation needs verification by X-ray diffraction. The work of Higuchi and Iijima38 indicated that water had two melting peaks when it was mixed with NaCl or urea, and they argued that such a phenomenon was due to phase separation, which leads to the coexistence of dense solution and dilute solution.
C0 values of cyclooctane in PDMS precursors and CV5 and CV25 are tabulated in Table 3. Because ΔHm of cyclooctane does not follow a linear relationship with v2 in CV33 and CV42, C0 values cannot be obtained from extrapolation. a values calculated by eq 2 are also listed in Table 3. The highest a value is observed in the lowest molecular weight polymer and crosslinking density has little effect on it. Compared with cyclohexane, cyclooctane has lower a values. Guenet36 proposed that the solvation takes place through the notion of cavities that form in association with the side groups of the polymer chain in which solvent molecules are “trapped” and interact with polymer molecules. If this process does happen, it would be anticipated that solvent molecules with smaller volume have higher a value, vice versa. Cyclooctane molecules are larger than the cyclohexane, consistent with the lower a value.
The basic hypothesis underlying the method of thermoporosimetry is that the melting point depression of small molecule solvents in polymer solutions can be quantitatively described by the FH model combined with a confinement effect exerted by network meshes that leads to a finite size induced melting point depression of solvents in crosslinked polymers consistent with the GT equation. However, this method is not applicable to the current systems. First of all, except the case of ΔTpeak of cylohexane in the three high molecular weight PDMS systems, systematic deviation between the FH predictions and ΔTonset (or ΔTpeak) of cyclohexane and cyclooctane is observed, especially in the lowest molecular weight PDMS. Furthermore, cylcohexane in PDMS model networks has a weaker melting point depression than that in the PDMS precursors due to phase separation, and cyclooctane even shows two melting peaks in the PDMS model networks. Finally, a prerequisite for the application of both the FH model and the GT equation is that the heat of fusion of the solvent in the polymer solution is the same as that in bulk. This requirement is not satisfied because in all these systems the heats of fusion of the solvents decrease with increasing polymer volume fraction.
Summary and Conclusions
The melting behavior of cyclohexane and cyclooctane in PDMS precursors and model networks has been studied. It was found that in addition to the breakdown of the FH predictions for solvents in the PDMS precursors, cyclohexane exhibits a weaker melting point depression in PDMS model networks than in the precursors. The cyclooctane also shows two melting peaks. The heats of fusion of the solvents decrease with increasing polymer volume fraction. Based on these observations, the method of thermoporosimetry is not applicable in the current systems. The reasons that lead to the anomalous melting behavior of cyclohexane and cyclooctane in PDMS precursors and model networks need further exploration by other techniques such as small angle X-ray scattering.
The authors are thankful to the National Science Foundation under grant number DMR-0307084 and to the Paul Whitfield Horn Professorship at Texas Tech University for partial support of this project. One of the authors (JRW) also thanks the China Scholarship Council for awarding him the financial support to visit TTU. We also thank S. L. Simon for making the thermal analysis equipment available for our use.