Effect of a Porous Medium on the Phase Transitions and Mobility of Cyclohexane Molecules B. I. Gizatullin and G. G. Pimenov Kazan State University, ul. Kremlevskaya 18, Kazan, 420008 Tatarstan, Russia Received May 21, 2008
Abstract—The effect of a porous medium on the phase transitions and molecular mobility of cyclohexane at a liquid content corresponding to a monolayer is studied by pulsed NMR. The times of longitudinal T1 and transverse T2 magnetic relaxation of protons of cyclohexane introduced into granulated porous glasses of the Vycor type with average pore diameters of 4, 11, and 32 nm are measured in the temperature range of 128–293 K. In spite of a relatively low liquid content, two phase transitions are observed for all porous glass samples at temperatures lower than those inherent in pure cyclohexane. At low temperatures, nonfreezing cyclohexane volumes with characteristic times of T2 ~ 100–200 µs and relative populations of 5–10% remain preserved due to the presence of a small number of micropores commensurable with molecular sizes. The appearance of an additional component with T2 ~ 200 µs upon temperature elevation to 148 K attests to thawing out of some cyclohexane volumes, which begins long before the crystal–plastic crystal phase transition. The nonexponential character of the transverse magnetization decay of cyclohexane above the temperature of the plastic crystal– liquid phase transition in the porous glass with a pore diameter of 4 nm suggests the existence of barriers for rapid molecular exchange. The obtained experimental results are indicative of the cluster mechanism of cyclohexane adsorption in the studied porous glasses. DOI: 10.1134/S1061933X09030041
INTRODUCTION The effect of the surface of porous materials on the molecular mobility of liquids and gases is considered in many works reviewed in . Geometrical confinements and the nature of surfaces significantly affect the phase equilibrium and molecular mobility of adsorbed substances. In many works dealing with porous materials, such as zeolites, porous glasses, and Aerosils, the properties of adsorbed substances are studied at a completely filled pore space. In this work, attention is focused on the fraction of an adsorbed matter that is affected by a porous material surface to the highest extent. The effect of the surface on the properties of adsorbed substances can be followed upon the filling of a pore space at the level of one adsorption monolayer. Many problems may arise when studying porous glasses with the aforementioned degrees of pore space filling. For example, glasses are polar materials, which can affect the distribution of liquid molecules over their surface and the formation of polar adsorption sites. The presence of polar adsorption sites (paramagnetic centers, metal ions, or hydroxyl groups) on the surface can prevent from the uniform distribution of nonpolar cyclohexane molecules over the surface. This, in turn, gives rise to the formation of aggregates (clusters) of molecules. In this work, cyclohexane was used as an adsorbate. Cyclohexane has a suitable (high) melting temperature and is characterized by two phase transitions, namely, a
monoclinic crystal–plastic crystal with a cubic lattice (C–PC) transition and PC melting occurring at 186.1 and 279.8 K , respectively. EXPERIMENTAL Granulated porous glasses of the Vycor brand with channels 4, 11, and 32 nm in diameter were used as adsorbents. The basic characteristics of the examined porous glasses are listed in the table. Before sample preparation, the porous glasses were treated as follows. Initially, they were washed with concentrated hydrochloric acid for 24 h to remove ferroand paramagnetic impurities from the surface. Then, the glasses were washed with distilled water to remove residual hydrochloric acid, while controlling the acidity using a litmus indicator. The specific magnetic susceptibility was measured by the Gouy method  before and after washing with acid. Before washing, the magnetic susceptibility was positive (paramagnetic impurities, metal particles). After washing, it became negative and almost the same for all glasses (see table). A test tube with an inner diameter of 8 mm was filled with a porous glass to a height of 12 mm. Immediately prior to the addition of cyclohexane, the porous glass was calcined at 520 K for 3 h to remove adsorbed moisture. Cyclohexane (reagent grade) was added in the amount needed to fill one monolayer. When calculating the concentration corresponding to a monolayer ωm, the surface area occupied by one cyclohexane molecule was
EFFECT OF A POROUS MEDIUM ON THE PHASE TRANSITIONS
Characteristics of Vycor porous glasses: channel diameter d, granule size D, pore specific surface area SP, pore specific volume inside granules VP, specific magnetic susceptibility χsp, porosity Φ, calculated cyclohexane concentration ωm necessary for filling of porous glasses on the level of one monolayer d, nm
32 11 4
100–200 <50 100–300
138 254 200
VP × 103, m3/kg χsp × 109, m3/kg 1.1 0.7 0.2
taken equal to 0.35 nm2. After cyclohexane was added, the tube was sealed and the sample was allowed to stand at room temperature for 2 h to reach the thermodynamic equilibrium. The measurements were performed in the course of heating beginning from 128 K. The samples were cooled by liquid nitrogen vapor. The temperature was measured with an accuracy of 0.1 K. The relaxation times were measured on an NMR relaxometer operating at a proton resonance frequency of ν = 19.08 MHz. Transverse relaxation times í2 were measured by the Karr–Purcell–Meyboom–Gill (KPMG) method and, at low temperatures, they were found by analyzing the free induction decay (FID). Longitudinal relaxation times í1 were mainly measured by the null method using the 180°–t–90° pulse sequence. RESULTS AND DISCUSSION Transverse Magnetic Relaxation of Cyclohexane in Porous Glasses Figure 1 shows the temperature dependences of transverse magnetic relaxation times for cyclohexane introduced into porous glasses with pores (a) 4, (b) 11, and (c) 32 nm in diameter. For subsequent correlation of the components of the transverse magnetization decay, í2 times were numerically estimated. The í2 time of the crystalline phase below the C–PC transition temperature (Fig. 1, curve 6), was assessed using the following formula : 2
T 2 = 2/M2,
where å2 is the second moment of cyclohexane molecules in a crystal, which is equal to 1.93 × 1010 rad/s2 . The í2 time of crystalline cyclohexane, as calculated by Eq. (1), proved to be 10 µs. For all samples in the range of 128–148 K, FID of cyclohexane consists of two components characterized by different í2 times. The component with shorter time í2c = 10–14 µs was assigned to cyclohexane molecules that had formed a crystal lattice. The component with time í2b = 100 µs and population pb = 0.05–0.12 is probably related to few cyclohexane molecules filling micropores, i.e., pores with sizes comparable with the molecule diameter. In these micropores, the rotational and translational molecular mobility is sterically hindered, thus the COLLOID JOURNAL
–0.354 –0.391 –0.342
ωm, wt %
40 34 18
5.2 9.2 7.4
transverse relaxation time of this component remains rather low. Upon sample heating within a range of 145–150 K (below the C–PC transition temperature), an additional third component appears in FID with í2a = 200 µs. The í2a time and the relative fraction pa of this component increase with temperature (Figs. 1 and 2). The existence of this component indicates that a fraction of cyclohexane molecules forms imperfect crystallites, in which the mobility manifests itself earlier compared to more perfect and large crystallites . This is confirmed by a gradual decrease in the fraction of molecules pc characterized by the í2c time with temperature elevation (Fig. 2). In the region of the C–PC phase transition (Fig. 1, curve 6), the crystalline component with í2c time increases stepwise from 20 to 50 µs. At the same time, the FID shape changes like that for pure cyclohexane in the region of the C–PC phase transition, with the beats characteristic of ordered spin systems being observed. Figure 3 shows FIDs for pure cyclohexane at two temperatures, i.e., before and after the C–PC phase transition. In this region, í2 time of pure cyclohexane stepwise increases from 15 to 40 µs, the shape of FID changes, and pronounced beats arise in the range of PC phase. In our opinion, such changes observed for adsorbed cyclohexane in all porous glasses suggest that, upon cooling, the liquid forms clusters in which cyclohexane further crystallizes, rather than distributes uniformly over the solid surface. At the uniform distribution of cyclohexane, crystal nuclei cannot be formed with sizes that exceed the critical one, at least in the direction perpendicular to the solid surface; hence, the C–PC and PC–liquid (L) phase transitions cannot be observed. Beginning with 193 K, for all samples, the decay of the long-time FID component with time í2a depends on the nonuniformity of the magnetic field of the magnet; therefore, it was analyzed by the KPMG method. As a first approximation, the decay of this transverse magnetization component was described by the sum of two exponents with T ''2a = 1 ms and T '2a = 10 ms (at 193 K, see Fig. 1). The deviation from the exponential character can be indicative of the structural nonuniformity of the amorphous phase of cyclohexane in this temperature range. The melting of the plastic crystalline phase (Fig. 1) characterized by í2c ~ 50–80 µs is accompanied by an abrupt increase in T ''2a and T '2a , once this
GIZATULLIN, PIMENOV T2, ms 1000
1 2 3 4 5
100 10 1 0.1 0.01 (b)
0.01 (c) 1000
8 1000/T, K–1
Fig. 1. Temperature dependences of transverse relaxation times of cyclohexane in Vycor porous glasses with pore diameters of (a) 4, (b) 11, and (c) 32 nm after the expansion of transverse magnetization decay measured by the method of KPMG: ((1) (T '2a and (2) T ''2a ) and FID ((3) í2a, (4) í2b, and (5) í2c). Vertical lines correspond to the temperatures of phase transitions (6) C–PC and (7) PC–L for pure cyclohexane . COLLOID JOURNAL
EFFECT OF A POROUS MEDIUM ON THE PHASE TRANSITIONS p 1.0
0.8 10 1 2 3
150 t, µs
7 8 –1 1000/T, K
Fig. 2. Temperature dependences of relative populations of components (1) pa, (2) pb, and (3) pc, as determined from FID expansion for cyclohexane occurring in porous glass with a pore diameter of 11 nm. Vertical lines indicate the temperatures of phase transitions (4) C–PC and (5) PC–L for pure cyclohexane .
transition is completed, the cyclohexane transverse magnetization decay in porous glasses with pores 11 and 32 nm in diameter becomes exponential. At the same time, for porous glass with a pore diameter of 4 nm, the nonexponential character of the transverse magnetization decay remains preserved, even at room temperature, i.e., in the liquid-state range of cyclohexane. The latter fact testifies that, in this porous glass, the complete (rapid) exchange of molecules between the states with different relaxation times í2 does not occur by some reasons. The translational displacement of cyclohexane molecules over the longest time T2 = 200 ms may be estimated from the self-diffusion coefficient at room temperature D = 1.1 × 10–9 m2/s . This estimate gives the displacement value on the order of 20 µm that far exceeds the pore sizes. We assume that, in the above porous glass (with a pore diameter of 4 nm), barriers (hindrances) arise in necks or narrow regions, and polar adsorption sites present on their surface create additional energy barriers for translational motion of nonpolar molecules along these pore channels.
Fig. 3. Free induction decay of pure cyclohexane at (1) 198 and (2) 183 K.
nents with close í1 times. However, due to the low content of protons in the sample (low signal-to-noise ratio), the resolution into the components is not quite correct. Therefore, in this temperature range, í1 values were, to save time, also measured by the null method, which gives somewhat overestimated (by 5–10%) í1 times, as compared with the average values determined from the initial slopes of longitudinal magnetization decays; however, the measurements of the latter take a good deal of time. In the temperature dependences of the average í1 time, the most pronounced is the C–PC phase transiT1, ms 1000
1 2 3 100
Longitudinal Magnetic Relaxation Figure 4 shows the temperature dependences of the average time of longitudinal relaxationí1 measured by the null method for cyclohexane in porous glasses. In the temperature range of 233–293 K, the longitudinal magnetization decay is of exponential character. At low temperatures of 128–233 K, the longitudinal magnetization decay is not only exponential but, as a first approximation, it can be described by three compoCOLLOID JOURNAL
7 8 1000/T, K–1
Fig. 4. Temperature dependences of the average longitudinal relaxation time í1 for cyclohexane in porous glasses with pore diameters of (1) 4, (2) 11, and (3) 32 nm. Vertical lines indicate temperatures of phase transitions (4) C–PC and (5) PC–L for pure cyclohexane .
∆T, K 50
40 30 20 10 0
0.3 1/d, nm–1
Fig. 5. Temperature shifts of cyclohexane phase transitions (1) C–PC and (2) PC–L vs. the inverse pore diameter in porous glasses at monolayer filling; the straight line corresponds to calculation by formula (2) at K = 182 K nm for PC–L phase transition.
tion, at which í1 increases stepwise by a factor of three, from 50 to 150 ms (for porous glasses with pore diameters of 4 and 11 nm) (Fig. 4). It is known that, upon the C–PC transition, the monoclinic lattice of cyclohexane crystals is changed for a cubic one, and cyclohexane molecules acquire the rotational mobility . The absence of abrupt changes in í1 time upon the PC–L transition suggests that, in this range, the rotational mobilities of cyclohexane molecules occurring in a plastic crystal and in the liquid state are equal, with their translational mobilities being different . The point is that the molecular rotation makes a predominant contribution to the rate of spin-lattice relaxation compared to the translational motion of multispin molecules. As a result of the isotropic rotation of cyclohexane molecules, the intramolecular interaction is fully averaged and the intermolecular dipole–dipole interaction is also averaged to a significant extent , while only an insignificant residual fraction of the total second moment is averaged as a result of the translational molecular motion. In the previous study of the same porous glasses, but with pores completely filled with hexane , the longitudinal relaxation rate 1/í1 was found to almost linearly depend on inverse pore diameter 1/d in a range of 11– 80 nm. In this work, this correlation is not observed due to the fact that, upon pore filling at the monolayer level, the surface effects, which result in the formation of liquid clusters, whose sizes may not coincide with the pore sizes, play a key role.
Temperatures of Phase Transitions of Cyclohexane in Porous Glasses Figure 5 demonstrates the temperature shifts ∆í of the phase transitions of cyclohexane occurring in porous glasses, as depending on the inverse pore diameter. The temperatures of the phase transitions of cyclohexane in porous glasses were determined from the temperature dependences of relaxation times. The temperature of the C–PC phase transition corresponded to a stepwise change in í2c time (Fig. 1) and an analogous change in the average í1 time (Fig. 4). The temperature of the PC–L phase transition was found from the temperature of disappearance of the component characterized by the í2c time (Fig. 1). The straight line refers to the ∆í–1/d dependence calculated by the Gibbs–Thomson formula ∆í = K/d, (2) where ä = 182 K nm is a constant, which was taken for cyclohexane from  and d is the pore diameter. In some studies of analogous systems performed by the cryoporosimetry method at the complete pore filling , linear ∆í–1/d dependences were observed. We did not found a similar dependence, although some nonlinear correlation between ∆í and 1/d was observed (Fig. 5). This may indicate that the transverse pore size affects the sizes of the largest liquid clusters and, hence, the sizes of crystallites. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 07-03-01004-a. REFERENCES 1. Christenson, H.K., J. Phys: Condens. Matter, 2001, vol. 13, p. 95. 2. Aksnes, D.W., Forland, K., and Kimtys, L., J. Mol. Struct., 2004, vol. 708, p. 23. 3. Selwood, P.W., Magnetochemistry, New York: Wiley, 1956. 4. Abragam, A., The Principles of Nuclear Magnetism, Oxford: Clarendon, 1961. 5. Andrew, E.R. and Eades, R.G., Proc. R. Soc. London, A, 1953, vol. 216, p. 398. 6. Ubbelohde, A.R., Melting and Crystal Structure, Oxford: Wiley, 1965. 7. Dmitrieva, L.V. and Moskalev, V.V., Fiz. Tverd. Tela (Leningrad), 1963, vol. 5, p. 2230. 8. Sitnitsky, A.E., Pimenov, G.G., and Anisimov, A.V., J. Magn. Reson., 2005, vol. 172, p. 48. 9. Strange, J.H. and Webber, J.B.W., Meas. Sci. Technol., 1997, vol. 8, p. 555. 10. Vargas-Florencia, D., Petrov, O.V., and Furo, I., J. Colloid Interface Sci., 2007, vol. 305, p. 280.