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The melting line for ethylene on graphite
L172
Surface Science North-Holland
SURFACE
SCIENCE
THE MELTING J.Z. LARESE
LETTERS
LINE FOR ETHYLENE
ON GRAPHITE
*
** and R.J. ROLLEFSON
Physics Department,
Wesleyan University,
Received
1982; accepted
6 October
127 (1983) L172-L178 Publishing Company
Middletown,
for publication
Connecticut 06457, USA
24 January
1983
Using the minimum in the nuclear magnetic spin-lattice relaxation time versus temperature as an indicator of melting we have mapped out the solid-fluid phase boundary for ethylene adsorbed on graphite. At low coverages the ethylene forms a self-bound monolayer solid with a melting temperature of about 68 K. The molecules in the solid retain orientational mobility down to 55 K, the lowest temperatures explored.
The study of phase diagrams for adsorbed monolayer films has attracted considerable attention over the past decade [ 11. For smooth, uniform substrates and weakly bound adsorbates the surface does little more than confine the adsorbed species to two dimensions, and the properties of the phase diagram are largely determined by the adsorbate-adsorbate interactions. Thus these sytems offer the possibility of experimentally approximating two-dimensional matter. A variety of experimental probes have been used to study adsorbed monolayers, including adsorption isotherms, specific heats, LEED, and X-ray and neutron scattering. In cases where the adsorbate is an organic molecule, nuclear magnetic resonance of the molecular protons offers another attractive probe. The NMR relaxation times are particularly sensitive to the mobility of the system [2]. If the correlation time - or mean time between jumps - for some aspect of the motion is decreasing, it effects both the spin-lattice relaxation time, T,, and the spin-spin relaxation time, T2. For long correlation times, TV, the spin-lattice relaxation is slow. As the correlation time shortens, the relaxation becomes more rapid, passing through a minimum when +,T~ = 1, where w0 is the Larmor frequency. At shorter correlation times the spin-lattice relaxation again becomes slow. On the other hand for long correlation times * Supported in part by a grant from Research Corporation. ** Present address: Physics Department, Pennsylvania State University, sylvania 16802, USA.
0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
University
Park,
Penn-
J. 2. Larese, R.J. Rollefson/ Melting line for ethyleneon graphite
Ll73
the spin-spin relaxation is rapid and independent of r,, being given approxiwhere M, is the second moment [3]. As 7c becomes mately by (M2)-“2, shorter than this “rigid lattice” value, T, begins to lengthen due to motional averaging of the local field variations. Thus a phase transition which involves an increase in mobility will be signaled by a minimum in T, and an increase in T2. Within a given phase the degree of molecular motion can be determined, at least qualitatively, by the value of T,. Extensive molecular motion results in a long T, while rigidly oriented molecules give a very short T2. In principle, more quantitative information can be extracted from NMR data, but it becomes increasingly model-dependent. For the present we will confine ourselves to more qualitative conclusions, which are largely model-independent and are often of considerable interest. For example; when a molecular solid forms an important question is: To what extent do the molecules in the solid retain rotational mobility? In some bulk solids rotational and translational mobility are both lost when the solid forms, while in others the molecules continue to have rotational freedom to considerably lower temperatures [4]. The value of T2 gives a direct measure of the rate of reorientation. This sensitivity to molecular rotation within a solid makes NMR a valuable probe for molecular systems. We have initiated a study using nuclear magnetic relaxation of molecular monolayers adsorbed on a Grafoil substrate. The Grafoil provides a widely studied surface of known uniformity with a fairly high specific area. We report here on the melting transition for an ethylene adsorbate. Ethylene (C,H,) has a simple, rigid structure with no internal rotation, and the four hydrogen atoms give sufficient signal for NMR measurements at all temperatures of interest without excessive signal averaging. By measuring the spin-lattice relaxation time as a function of temperature for a closely spaced mesh of coverages, we have carefully traced out the melting line for this system. At low coverages we find evidence for a self-bound monolayer solid phase with a melting temperature of about 68 K. The molecules in the solid are found to retain orientational mobility at least down to a temperature of 55 K, the lowest temperature of this study. The Grafoil substrate material was prepared by baking in vacuum at 1000°C for 12 h. It was then sealed in a Macor sample cell with 12.7 pm Teflon sheets for electrical insulation between the pieces of Grafoil (see inset, fig. 1). The cell was oriented so that the Grafoil sheets were parallel to the magnetic field. The grafoil surface area was calibrated by measuring the deregistry feature [5] on a nitrogen isotherm (fig. 1). This made it possible to determine precisely the amount of gas needed to form a registered 6 x fi monolayer (density 0.0636 molecule/A2): in the present case 1.18 X 10” molecules. To take advantage of the precision of this method of surface calibration for comparison of results from different laboratories, we specify unit coverage for the ethylene
Ll74
J. 2. Lorese, R.J. Rollefson / Melting line for ethylene on graphite
3.6 I
I
3.41 0.0
2.0
4.0
Pressure
6.0
8.0
10.0
(mm)
Fig. 1. Nitrogen isotherm on Grafoil, T= 77.4 K. The inset shows the construction of the Macor sample cell. The sheets of Grafoil are parallel with the cylinder axis and heat sunk by fine gold wires.
films as 0.0636 molecule/A2. To emphasize that we do not mean to imply that ethylene forms a registered monolayer, we will hereafter refer to this amount of gas as a nominal monolayer. In fact we found no evidence in our NMR measurements for registry. To assure sample purity, ‘the ethylene (Matheson CP grade) was distilled until the equilibrium vapor pressure at 77.4 K was less than 1 pm before it was admitted to the sample cell. The magnetic resonance measurements were made using a coherent pulsed spectrometer described previously [6]. Signal recovery was performed with a Tracer Northern digital signal analyzer. The data were taken at 24 MHz, with a typical 7r/2 pulse of 8 ~“s and a receiver deadtime following the pulse of about 40 ps. The spin-lattice relaxation time was measured with a n-r-n/2 sequence, while the spin-spin relaxation time was obtained from the free induction decay. Thermometry was provided by a Rosemount model 146 MA platinum thermometer. The data were taken as a function of temperature for coverage steps of about 0.05 nominal monolayer between x = 0.55 and x = 2.0. Temperatures ranged from 55 to 110 K. At all coverages examined T, was found to exhibit a distinct minimum. At coverages below 0.81 the minimum occurred at 68 K, independent of coverage, as shown for representative coverages in fig. 2a. For coverages between 0.81 and 1.3, the temperature of the minimum increased with increasing coverage (fig. 2b), while above x = 1.3 the temperature of the
J. 2. Larese, R.J. Rollefson / Melting line for ethylene on graphite .
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Fig: 1. (a) Spin-lattice relaxation time at low coverages. Curves are displaced vertically for clarity. From bottom to top x = 0.65, 0.72, and 0.81. (b) Spin-lattice’ relaxation time at higher coverages. From bottom to top x = 0.81, 0.90, and 1.00.
miaimum was again independent of coverage. The free induction decay time wad 60 ps, independent of density and temperature. Previous studies [7] have indicated that the Grafoil substrate produces local field variations which set an upfler limit on the free induction’decay. For an applied field of the magnitude used in these experiments 60 1~s is a typical value. Thus for the temperatures and coverages of the present study, the decay time of the free induction signal puts only a lower bound on the true value of the spin-spin relaxation time. However, as shown below, this limit is sufficient to distinguish between rotationally mobile and rotationally ordered molecules. tie interpret the minimum in the spin-lattice relaxation time to indicate the mellting of the ethylene film. This interpretation is in accord with preliminary neuitron scattering result? from Brookhaven [8]. Thus a plot of the temperature of tihe minimum as a function of coverage traces out ,the melting line on the ethylene phase diagram. This is shown in fig. 3. The vertical portion of the melking line for coverages less than 0.8 1 indicates that here the ethylene solid is selfibound, covering only a fraction of the surface. Increases in coverage resu1.t in an increase in the fraction of the graphite surface covered by this solid, with no changes in its properties. The sharp break in the phase diagram .at x = 0.81 martks the point at which the entire graphite surface is covered with a solid modolayer, thus determining the density of .this solid as 0.05 15 molecule/A’.
Ll76
J. 2. Larese, R.J. Rollefson / Melting line for ethylene on graphite
1.4.
1.2.
X
1.0.
0.8.
0.8'
0.4 1
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50
60
70
50
90
100
110
T(K) Fig. 3. Plot of the temperature of the minimum in the spin-lattice relaxation time as a function of coverage, interpreted as indicating the melting line of ethylene on Grafoil. The dashed line indicates the limits of temperature and coverage explored.
Given the density, with an assumption for the lattice structure we can determine the lattice constant. Since the molecules are rapidly reorienting it is reasonable to assume that they will appear roughly spherical. Under these circumstances a triangular array (the closest packing in two dimensions) would be expected to form, for which we calculate a nearest neighbor distance of 4.7 A. This is in excellent agreement with the neutron results in which two diffraction peaks were observed. These indexed as the 1,0 and 1,l peaks of a triangular solid with a lattice spacing of 4.8 A at 68 K [8]. A comment is in order regarding the nature of the melting transition and the precise shape of the T, minimum. For adsorbed monolayer films, both first order and continuous transitions have been reported in the literature (see, for example, ref. [9]). At a first order melting transition a discontinuous increase in the diffusion coefficient would be expected resulting in a discontinuity in the spin-lattice relaxation time. Such a discontinuous increase in T, is seen in bulk ethylene [lo]. In a continuous transition no such discontinuity would occur. The lack of a discontinuity in the present data might be interpreted as indicating that the melting transition in ethylene monolayers is continuous. However, another interpretation is possible. Due to slight inhomogeneities in the graphite substrate, the melting transition may take place at slightly different temperatures at different locations on the surface. Thus at a given
J. 2. Lurese, R.J. Rollefson / Melting line for ethylene on graphite
I_117
temperature in this range of melting temperatures the sample would consist of two! parts, one those regions in which melting has already occurred, the other those regions in which the film is still solid. The relaxation of the magnetization seen in the NMR would be a combination of two components with different relaxation times, a long one for the liquid and a short one for the solid. Just such behavior was in fact seen in the present measurements. At temperatures below the T, minimum where the entire sample is solid the relaxation of the magnetization was purely exponential. On the high temperature side of the minimum, however, the relaxation was non-exponential, indicating that here there is not a single relaxation time. The data shown in fig. 2a Cere obtained from the initial slope of the decay of the magnetization and thus change continuously from the short value to the long value as the fraction of the film having the long relaxation time (the fluid) increases. By graphically subtracting the long relaxation time component of the magnetization from the total on a semi-logarithmic plot of magnetization versus pulse spacing, we obtained a semi-quantitative separation of the short and long time components and determined both relaxation times. They were found to be roughly constant in the region of melting with a long relaxation time on the order of one second and a short relaxation time of about 150 ms, although signal-to-noise limitations made this determination rather uncertain. Thus our data seem more consistent with first order melting broadened by substrate inhomogeneities. As noted above, we find that even in the solid the ethylene molecules undergo rapid reorientation. This conclusion is based on the fact that T, is at leasit 60 ps at all temperatures explored. For an ethylene molecule rigidly fixed in a lattice, a second moment calculation predicts a decay time of just 12 ps from intramolecular interactions alone. Intermolecular interactions would reduce this further; in orientationally ordered bulk solid ethylene a decay time of less1than 10 ps is observed [lo]. Rotation about any one of the symmetry axes of the molecule will not provide enough local field averaging to give a 60 ps T, [ 111. Thus some more complex reorientational motion must be taking place. For coverages between 0.8 1 and about 1.3 the melting temperature increases smoothly with increasing coverage. On the basis of the present measurements alone we cannot say precisely what is taking place in this region. The long free induction decay indicates that there, as at lower coverages, the molecules retain orientational mobility in the solid phase. It seems highly unlikely that the ethylene film remains in a single layer at coverages as high as x = 1.3, especially in view of the rapid reorientation. On the other hand we can rule out the’ formation of bulk monoclinic ethylene solid since at these temperatures and pressures this solid is orientationally ordered [lo]. All we can say is that some type of orientationally-disordered solid phase seems to occur. Further neutron scattering experiments are planned which may shed light on this situation. For coverages above 1.3 monolayer the temperature of the T, minimum
Ll7X
J. 2. Lmese, R.J. Rollefson / Meliing line for ethylene on graphite
again becomes coverage independent. However, there is a significant difference between this region and the region below 0.81 monolayer. In the low coverage region, and indeed at all coverages up to x = 1.3, the total nuclear magnetization as measured by the amplitude of the free induction signal increased proportionally with the coverage. For coverages above x = 1.3 no change in the size of the free induction signal was observed, nor were there any changes in the observed spin-lattice behavior. It appears that the film consists of two parts, one of which is unaffected by subsequent additions to the system. Furthermore the molecules added beyond x = 1.3 are not seen in the free induction signal. This could happen if the contribution to the magnetization of these additional molecules decayed so rapidly that it was lost in the dead time of the receiver. For coverages x Q 2.0, where only 0.7 nominal monolayer contributes to the rapidly decaying signal, the magnetization decays to a peint where it is immeasurable by the time the receiver recovers. Therefore we made a sample with x = 10.0, so that there would be a sufficiently large contribuCon from this rapidly decaying magnetization to still be observable after the receiver dead time. The expected signal was observed, with a decay time of approximately 10 ps. Using this component of the FID we measured the spin-lattice relaxation time as a function of temperature. It reproduced the known bulk (monoclinic) solid relaxation behavior exactly [ 10). Since the molecules in the bulk solid at these temperatures and pressures are riddly oriented, a rapid free induction decay is to be expected. Thus we speculate that molecules added beyond x = 1.3 form bulk ethylene crystallites (perhaps nucleated at the edges of the graphite flakes) leaving the initial part of the film - amounting to 1.3 nominal monolayers - undisturbed. It is known from adsorption isotherm studies [12] that the number of uniform ethylene monolayers on graphite is limited at low temperatures. Further neutron scattering studies should prove illuminating on this point. It is a pleasure to acknowledge many Passe11 during the course of this work.
fruitful
conversations
with Dr. L.
References [I) SK. Sinha, Ed., Ordering in Two Dimensions
(North-Holland, New York, 1980). [2] A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, London, 1961). [3] J.H. Van Vleck, Phys. Rev. 74 (1948) 1168. (41 J. Timmermans, J. Phys. Chem. Solids 18 (1961) 1. [S] D.M. Butler, G.B. Huff, R.W. Toth and G.A. Stewart, Phys. Rev. Letters 35 (1975) 1718. [6] R. Buzerak and R.J. Rollefson, J. Low Temp. Phys. 38 (1980) 105. [7] D.C. Hickernell, D.L. Husa, J.G. Daunt and J.E. Piott, J. Low Temp. Phys. 15 (1974) 29. [S] L. Passell, private communication. [9] P.A. Heiney, R.J. Birgeneau, G.S. Brown, P.M. Horn, D.E. Moncton and P.W. Stephens, Phys. Rev. Letters 48 (1982) 104. [IO] N.J. Trappeniers and F.A.S. Ligthart, Chem. Phys. Letters 19 (1973) 465. [I I] H.S. Gutowsky and G.E. Pake, J. Chem. Phys. 18 (1950) 162. [12] J. Menancourt, A. Thorny and X. Duval, J. Physique 38 (1977) C4-195.
Surface Science North-Holland
SURFACE
SCIENCE
THE MELTING J.Z. LARESE
LETTERS
LINE FOR ETHYLENE
ON GRAPHITE
*
** and R.J. ROLLEFSON
Physics Department,
Wesleyan University,
Received
1982; accepted
6 October
127 (1983) L172-L178 Publishing Company
Middletown,
for publication
Connecticut 06457, USA
24 January
1983
Using the minimum in the nuclear magnetic spin-lattice relaxation time versus temperature as an indicator of melting we have mapped out the solid-fluid phase boundary for ethylene adsorbed on graphite. At low coverages the ethylene forms a self-bound monolayer solid with a melting temperature of about 68 K. The molecules in the solid retain orientational mobility down to 55 K, the lowest temperatures explored.
The study of phase diagrams for adsorbed monolayer films has attracted considerable attention over the past decade [ 11. For smooth, uniform substrates and weakly bound adsorbates the surface does little more than confine the adsorbed species to two dimensions, and the properties of the phase diagram are largely determined by the adsorbate-adsorbate interactions. Thus these sytems offer the possibility of experimentally approximating two-dimensional matter. A variety of experimental probes have been used to study adsorbed monolayers, including adsorption isotherms, specific heats, LEED, and X-ray and neutron scattering. In cases where the adsorbate is an organic molecule, nuclear magnetic resonance of the molecular protons offers another attractive probe. The NMR relaxation times are particularly sensitive to the mobility of the system [2]. If the correlation time - or mean time between jumps - for some aspect of the motion is decreasing, it effects both the spin-lattice relaxation time, T,, and the spin-spin relaxation time, T2. For long correlation times, TV, the spin-lattice relaxation is slow. As the correlation time shortens, the relaxation becomes more rapid, passing through a minimum when +,T~ = 1, where w0 is the Larmor frequency. At shorter correlation times the spin-lattice relaxation again becomes slow. On the other hand for long correlation times * Supported in part by a grant from Research Corporation. ** Present address: Physics Department, Pennsylvania State University, sylvania 16802, USA.
0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
University
Park,
Penn-
J. 2. Larese, R.J. Rollefson/ Melting line for ethyleneon graphite
Ll73
the spin-spin relaxation is rapid and independent of r,, being given approxiwhere M, is the second moment [3]. As 7c becomes mately by (M2)-“2, shorter than this “rigid lattice” value, T, begins to lengthen due to motional averaging of the local field variations. Thus a phase transition which involves an increase in mobility will be signaled by a minimum in T, and an increase in T2. Within a given phase the degree of molecular motion can be determined, at least qualitatively, by the value of T,. Extensive molecular motion results in a long T, while rigidly oriented molecules give a very short T2. In principle, more quantitative information can be extracted from NMR data, but it becomes increasingly model-dependent. For the present we will confine ourselves to more qualitative conclusions, which are largely model-independent and are often of considerable interest. For example; when a molecular solid forms an important question is: To what extent do the molecules in the solid retain rotational mobility? In some bulk solids rotational and translational mobility are both lost when the solid forms, while in others the molecules continue to have rotational freedom to considerably lower temperatures [4]. The value of T2 gives a direct measure of the rate of reorientation. This sensitivity to molecular rotation within a solid makes NMR a valuable probe for molecular systems. We have initiated a study using nuclear magnetic relaxation of molecular monolayers adsorbed on a Grafoil substrate. The Grafoil provides a widely studied surface of known uniformity with a fairly high specific area. We report here on the melting transition for an ethylene adsorbate. Ethylene (C,H,) has a simple, rigid structure with no internal rotation, and the four hydrogen atoms give sufficient signal for NMR measurements at all temperatures of interest without excessive signal averaging. By measuring the spin-lattice relaxation time as a function of temperature for a closely spaced mesh of coverages, we have carefully traced out the melting line for this system. At low coverages we find evidence for a self-bound monolayer solid phase with a melting temperature of about 68 K. The molecules in the solid are found to retain orientational mobility at least down to a temperature of 55 K, the lowest temperature of this study. The Grafoil substrate material was prepared by baking in vacuum at 1000°C for 12 h. It was then sealed in a Macor sample cell with 12.7 pm Teflon sheets for electrical insulation between the pieces of Grafoil (see inset, fig. 1). The cell was oriented so that the Grafoil sheets were parallel to the magnetic field. The grafoil surface area was calibrated by measuring the deregistry feature [5] on a nitrogen isotherm (fig. 1). This made it possible to determine precisely the amount of gas needed to form a registered 6 x fi monolayer (density 0.0636 molecule/A2): in the present case 1.18 X 10” molecules. To take advantage of the precision of this method of surface calibration for comparison of results from different laboratories, we specify unit coverage for the ethylene
Ll74
J. 2. Lorese, R.J. Rollefson / Melting line for ethylene on graphite
3.6 I
I
3.41 0.0
2.0
4.0
Pressure
6.0
8.0
10.0
(mm)
Fig. 1. Nitrogen isotherm on Grafoil, T= 77.4 K. The inset shows the construction of the Macor sample cell. The sheets of Grafoil are parallel with the cylinder axis and heat sunk by fine gold wires.
films as 0.0636 molecule/A2. To emphasize that we do not mean to imply that ethylene forms a registered monolayer, we will hereafter refer to this amount of gas as a nominal monolayer. In fact we found no evidence in our NMR measurements for registry. To assure sample purity, ‘the ethylene (Matheson CP grade) was distilled until the equilibrium vapor pressure at 77.4 K was less than 1 pm before it was admitted to the sample cell. The magnetic resonance measurements were made using a coherent pulsed spectrometer described previously [6]. Signal recovery was performed with a Tracer Northern digital signal analyzer. The data were taken at 24 MHz, with a typical 7r/2 pulse of 8 ~“s and a receiver deadtime following the pulse of about 40 ps. The spin-lattice relaxation time was measured with a n-r-n/2 sequence, while the spin-spin relaxation time was obtained from the free induction decay. Thermometry was provided by a Rosemount model 146 MA platinum thermometer. The data were taken as a function of temperature for coverage steps of about 0.05 nominal monolayer between x = 0.55 and x = 2.0. Temperatures ranged from 55 to 110 K. At all coverages examined T, was found to exhibit a distinct minimum. At coverages below 0.81 the minimum occurred at 68 K, independent of coverage, as shown for representative coverages in fig. 2a. For coverages between 0.81 and 1.3, the temperature of the minimum increased with increasing coverage (fig. 2b), while above x = 1.3 the temperature of the
J. 2. Larese, R.J. Rollefson / Melting line for ethylene on graphite .
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. 70
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, 100
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Fig: 1. (a) Spin-lattice relaxation time at low coverages. Curves are displaced vertically for clarity. From bottom to top x = 0.65, 0.72, and 0.81. (b) Spin-lattice’ relaxation time at higher coverages. From bottom to top x = 0.81, 0.90, and 1.00.
miaimum was again independent of coverage. The free induction decay time wad 60 ps, independent of density and temperature. Previous studies [7] have indicated that the Grafoil substrate produces local field variations which set an upfler limit on the free induction’decay. For an applied field of the magnitude used in these experiments 60 1~s is a typical value. Thus for the temperatures and coverages of the present study, the decay time of the free induction signal puts only a lower bound on the true value of the spin-spin relaxation time. However, as shown below, this limit is sufficient to distinguish between rotationally mobile and rotationally ordered molecules. tie interpret the minimum in the spin-lattice relaxation time to indicate the mellting of the ethylene film. This interpretation is in accord with preliminary neuitron scattering result? from Brookhaven [8]. Thus a plot of the temperature of tihe minimum as a function of coverage traces out ,the melting line on the ethylene phase diagram. This is shown in fig. 3. The vertical portion of the melking line for coverages less than 0.8 1 indicates that here the ethylene solid is selfibound, covering only a fraction of the surface. Increases in coverage resu1.t in an increase in the fraction of the graphite surface covered by this solid, with no changes in its properties. The sharp break in the phase diagram .at x = 0.81 martks the point at which the entire graphite surface is covered with a solid modolayer, thus determining the density of .this solid as 0.05 15 molecule/A’.
Ll76
J. 2. Larese, R.J. Rollefson / Melting line for ethylene on graphite
1.4.
1.2.
X
1.0.
0.8.
0.8'
0.4 1
I
50
60
70
50
90
100
110
T(K) Fig. 3. Plot of the temperature of the minimum in the spin-lattice relaxation time as a function of coverage, interpreted as indicating the melting line of ethylene on Grafoil. The dashed line indicates the limits of temperature and coverage explored.
Given the density, with an assumption for the lattice structure we can determine the lattice constant. Since the molecules are rapidly reorienting it is reasonable to assume that they will appear roughly spherical. Under these circumstances a triangular array (the closest packing in two dimensions) would be expected to form, for which we calculate a nearest neighbor distance of 4.7 A. This is in excellent agreement with the neutron results in which two diffraction peaks were observed. These indexed as the 1,0 and 1,l peaks of a triangular solid with a lattice spacing of 4.8 A at 68 K [8]. A comment is in order regarding the nature of the melting transition and the precise shape of the T, minimum. For adsorbed monolayer films, both first order and continuous transitions have been reported in the literature (see, for example, ref. [9]). At a first order melting transition a discontinuous increase in the diffusion coefficient would be expected resulting in a discontinuity in the spin-lattice relaxation time. Such a discontinuous increase in T, is seen in bulk ethylene [lo]. In a continuous transition no such discontinuity would occur. The lack of a discontinuity in the present data might be interpreted as indicating that the melting transition in ethylene monolayers is continuous. However, another interpretation is possible. Due to slight inhomogeneities in the graphite substrate, the melting transition may take place at slightly different temperatures at different locations on the surface. Thus at a given
J. 2. Lurese, R.J. Rollefson / Melting line for ethylene on graphite
I_117
temperature in this range of melting temperatures the sample would consist of two! parts, one those regions in which melting has already occurred, the other those regions in which the film is still solid. The relaxation of the magnetization seen in the NMR would be a combination of two components with different relaxation times, a long one for the liquid and a short one for the solid. Just such behavior was in fact seen in the present measurements. At temperatures below the T, minimum where the entire sample is solid the relaxation of the magnetization was purely exponential. On the high temperature side of the minimum, however, the relaxation was non-exponential, indicating that here there is not a single relaxation time. The data shown in fig. 2a Cere obtained from the initial slope of the decay of the magnetization and thus change continuously from the short value to the long value as the fraction of the film having the long relaxation time (the fluid) increases. By graphically subtracting the long relaxation time component of the magnetization from the total on a semi-logarithmic plot of magnetization versus pulse spacing, we obtained a semi-quantitative separation of the short and long time components and determined both relaxation times. They were found to be roughly constant in the region of melting with a long relaxation time on the order of one second and a short relaxation time of about 150 ms, although signal-to-noise limitations made this determination rather uncertain. Thus our data seem more consistent with first order melting broadened by substrate inhomogeneities. As noted above, we find that even in the solid the ethylene molecules undergo rapid reorientation. This conclusion is based on the fact that T, is at leasit 60 ps at all temperatures explored. For an ethylene molecule rigidly fixed in a lattice, a second moment calculation predicts a decay time of just 12 ps from intramolecular interactions alone. Intermolecular interactions would reduce this further; in orientationally ordered bulk solid ethylene a decay time of less1than 10 ps is observed [lo]. Rotation about any one of the symmetry axes of the molecule will not provide enough local field averaging to give a 60 ps T, [ 111. Thus some more complex reorientational motion must be taking place. For coverages between 0.8 1 and about 1.3 the melting temperature increases smoothly with increasing coverage. On the basis of the present measurements alone we cannot say precisely what is taking place in this region. The long free induction decay indicates that there, as at lower coverages, the molecules retain orientational mobility in the solid phase. It seems highly unlikely that the ethylene film remains in a single layer at coverages as high as x = 1.3, especially in view of the rapid reorientation. On the other hand we can rule out the’ formation of bulk monoclinic ethylene solid since at these temperatures and pressures this solid is orientationally ordered [lo]. All we can say is that some type of orientationally-disordered solid phase seems to occur. Further neutron scattering experiments are planned which may shed light on this situation. For coverages above 1.3 monolayer the temperature of the T, minimum
Ll7X
J. 2. Lmese, R.J. Rollefson / Meliing line for ethylene on graphite
again becomes coverage independent. However, there is a significant difference between this region and the region below 0.81 monolayer. In the low coverage region, and indeed at all coverages up to x = 1.3, the total nuclear magnetization as measured by the amplitude of the free induction signal increased proportionally with the coverage. For coverages above x = 1.3 no change in the size of the free induction signal was observed, nor were there any changes in the observed spin-lattice behavior. It appears that the film consists of two parts, one of which is unaffected by subsequent additions to the system. Furthermore the molecules added beyond x = 1.3 are not seen in the free induction signal. This could happen if the contribution to the magnetization of these additional molecules decayed so rapidly that it was lost in the dead time of the receiver. For coverages x Q 2.0, where only 0.7 nominal monolayer contributes to the rapidly decaying signal, the magnetization decays to a peint where it is immeasurable by the time the receiver recovers. Therefore we made a sample with x = 10.0, so that there would be a sufficiently large contribuCon from this rapidly decaying magnetization to still be observable after the receiver dead time. The expected signal was observed, with a decay time of approximately 10 ps. Using this component of the FID we measured the spin-lattice relaxation time as a function of temperature. It reproduced the known bulk (monoclinic) solid relaxation behavior exactly [ 10). Since the molecules in the bulk solid at these temperatures and pressures are riddly oriented, a rapid free induction decay is to be expected. Thus we speculate that molecules added beyond x = 1.3 form bulk ethylene crystallites (perhaps nucleated at the edges of the graphite flakes) leaving the initial part of the film - amounting to 1.3 nominal monolayers - undisturbed. It is known from adsorption isotherm studies [12] that the number of uniform ethylene monolayers on graphite is limited at low temperatures. Further neutron scattering studies should prove illuminating on this point. It is a pleasure to acknowledge many Passe11 during the course of this work.
fruitful
conversations
with Dr. L.
References [I) SK. Sinha, Ed., Ordering in Two Dimensions
(North-Holland, New York, 1980). [2] A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, London, 1961). [3] J.H. Van Vleck, Phys. Rev. 74 (1948) 1168. (41 J. Timmermans, J. Phys. Chem. Solids 18 (1961) 1. [S] D.M. Butler, G.B. Huff, R.W. Toth and G.A. Stewart, Phys. Rev. Letters 35 (1975) 1718. [6] R. Buzerak and R.J. Rollefson, J. Low Temp. Phys. 38 (1980) 105. [7] D.C. Hickernell, D.L. Husa, J.G. Daunt and J.E. Piott, J. Low Temp. Phys. 15 (1974) 29. [S] L. Passell, private communication. [9] P.A. Heiney, R.J. Birgeneau, G.S. Brown, P.M. Horn, D.E. Moncton and P.W. Stephens, Phys. Rev. Letters 48 (1982) 104. [IO] N.J. Trappeniers and F.A.S. Ligthart, Chem. Phys. Letters 19 (1973) 465. [I I] H.S. Gutowsky and G.E. Pake, J. Chem. Phys. 18 (1950) 162. [12] J. Menancourt, A. Thorny and X. Duval, J. Physique 38 (1977) C4-195.