X-ray Techniques for Probing Self-Assembled … · X-ray Techniques for Probing Self-Assembled Monolayer Structures ... Yous avons étudié la possibilité d'utiliser les rayons X

X-ray Techniques for Probing Self-Assembled Monolayer Structures

Mat t hew A. Bort hwick

Department of Physics YcGill University

Mont réal. Québec. Canada May. 1997

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Contents Abstract

Résumé v

Acknowledgernents vi

1 Introduction 1

2 Metal Alkylphosphonate Salts: Powder Diffraction . . . . . . . . . . . . . . . . . . . 2.1 Background and Perspective

. . . . . . . . . . . . . . . . . . . . . '3.1.1 KnownStructure . . . . . . . . . . . . . . . . . . 2.1.3 Potential Applications

2 Applications of Powder Diffraction . . . . . . . . . . . . . . . 2.2. 1 Review of Powder Diffraction . . . . . . . . . . . . . . 2.2.2 Variable Temperature. Low Resolution . . . . . . . . . 2 . 3 Room Temperat ure . High Resolut ion . . . . . . . . . .

2.3 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 The Powder Diffractorneter

. . . . . . . . . 2.3.2 Variable Temperature . Low Resolution . . . . . . . . . . 2.3.3 Room Temperat ure . High Resolut ion

. . . . . . . . . . . . . 2.3.4 Comparison Between The Two 2.4 Resuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . 2.4 1 Phase Transit ions 2.4.2 Interlayer Spacing as a Function of Temperature . . . . 2.4.3 Unit Ce11 Dimensions and Space Group at Room Tern-

perature . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Chain Orientation and In-Plane Structure at Room Tem-

. . . . . . . . . . . . . . . . . . . . . . . . . . perature 2. 5 Ideas for Future Studies . . . . . . . . . . . . . . . . . . . . .

Alkanethiolate-Capped Gold Nanoclusters: Small-Angle Scat- tering 38 3.1 Background and Perspective . . . . . . . . . . . . . . . . . . . 38

. . . . . . . . . . . . . 3.1.1 Description of Known St mcture 38 . . . . . . . . . . . . . . . . . . 3.1.2 Potentid Applications 39

3.2 Applications of Small- Angle Scattering . . . . . . . . . . . . . 40 3.3 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . -11

3.3.1 Transmission Geomet ry . . . . . . . . . . . . . . . . . 42 . . . . . . . . . . . 3.3.2 Minirnizing Background Scat tering 43

3.3.3 Resolution-Limiting Factors . . . . . . . . . . . . . . . u 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.4.1 Nanocluster Size . . . . . . . . . . . . . . . . . . . . . 46

3.1.2 Intercluster Spacing . . . . . . . . . . . . . . . . . . . . 50 3.1.3 Nanocluster Shape and Size Distribution . . . . . . . . 60

3.5 Ideas for Future Studies . . . . . . . . . . . . . . . . . . . . . 60

4 Conclusion 61

References 63

C C .

111

Abstract

We investigated the leasibility of using X-rays to study self-assembled monolayers on inorganic surfaces. Variabletemperature X-ray powder diffraction measurements of metal alkylphosp honate salts measured the contract ion and expansion of planar inorganic layers as the material passed through a series of phase transitions when heated and cooled. Small-angle .Y-ray scat tering measurements of aikanethiolate-capped gold nanoclusters allowed the determination of the average nanocluster size and the average distance between nanoclusters. These techniques have been demonst rated to contri bute usefiil information which. wben cornbined with results from other probes. lead to a detailed mode1 of the materials' structures and properties.

Résumé

Yous avons étudié la possibilité d'utiliser les rayons X pour examiner des mono- couches auto-assemblées sur des surfaces inorganiques. Les mesures de diffraction rayon X à température variable de poudres de sels métalliques de phosphonates d'alkyle montrent la contraction et I'expansion des couches planaires inorganiques au fur et à mesure que le matériau chauffé et refroidi subit une série de transit ions de phase. Les mesures de diffusion rayon '< a petits angles de grappes nanométriques d'atomes d'or recouvertes de thiolates d'alkyle ont permis de déterminer la taille moyenne des grappes et la distance moyenne entre les grappes. Ces techniques ont démontré qu'elles peuvent. lorsque com- binées à d'autres méthodes. conduire à t'élaboration d'un modèle détaillé des structures et propriétés du matériau étudié.

Acknowledgement s

1 must fint and foremost extend my gratitude to Prof. Mark Sutton for suggesting this project and keeping an eye on me as it proceeded. As a result of his guidance 1 not only learned a great deal about .Y-ray experimentation. but also developed the skills and desire to continue on in this intriguing field. Prof. Linda Reven. Prof. Bruce Lennox. Wei Cao. and ..\ntonella Badia provided samples. I am indebted to them for this and for their accessibility and patience in explaining these materiais to this non-chemist. 1 thank Rahma Tabti for her help wit h translation. This research was assisted in many intangible and non- quantifiable ways by discussions wit h Randa A bdouche. Michel Beauchamp. Eric Dufresne. Brett Ellman. Peter Grütter. Philip LeBlanc. Dok Won Lee. Christian Lupien. Mark Roseman. Tarek Saab. Sajan Saini. Rahma Tabti. Gianni Taraschi. Johan van Lierop. and Philippe Westreich; some discussions were direct ly relevant to t his work and some not - s e relevant. but al1 were useful and appreciated. 1 thank Prof. Sutton for his financial support. Dr. Ken Finkelstein For taking a chance and introducing me to this field. and Arlene Borthwick. Bill Borthwick. and Jane Borthwick for their consistent support and interest. Finally. 1 thank Lisa McGiIl for giving me a reason to finish.

1 Introduction

Self-assembled monolayers (SAMs) hold the potential for designing materials on a molecular level and fabricating those materials in bulk quantities. The characterist ics of SAMs and the surfaces on which they form are controllable, well-behaved, and can be selected from a wide range of possibilities [l, 31. The intricacy of such systems is rather limited at present, though it is growing. The first SAMs were fomed on Bat Au(1ll) surfaces [3]. There is an ongoing trend toward producing more complicated geometries with more diverse com- positions. but most systems are still studied for their mode1 properties rather t han t heir immediate applications to ot her problems 121. - .

.A great deal of work is currently being done to characterize the structure of SAM materials and understand the connections between the structure and t hese materials' macroscopic propert ies [ -2 ,5 ,6] . '< rays are a probe well-sui ted

to answering many structural characterization questions. so we assessed the usefulness of .Y-ray techniques in obtaining information about several SAM materials of recent interest. We perf'ormed variable-tem perat ure X-ray diffraction studies of several metal alkylphosphonate salts. specifically the following five materials (abbreviations used hereafter are listed in the rightmost column):

Na2H,03P(CH2)11CH3 4H20, (YaPCi2) ?Ja2Hn03P(CH2)i;CH3 - lHzO. ('iaPCls) N'a2Hn03P(CH2)2rCH3 = 1H20, (YaPCZ2) Mg03P(CH2)I;CH3 H20 (;C1gPCI8)

and Zn03P(CH2)7CH3. (ZnPCs)

We also performed small-angle S-ray scat tering st udies of alkanet hiolate-capped gold nanoclusters. specificdly:

CH3(CH2)ïS - AU (C& - AU) and CH3(CH&+3 - Au. (CIBS - AU)

While we did work to extract some first-pass structural information about these materials. our primary objective was to examine the strengths and weak- nesses of the techniques we chose for probing t hese materials. and to determine what would be necessary for frequent investigations of a wide variety of SAM materials in the future.

Metai-Oxide Layer

1 (CH 4, Chain

Figure 1: Schematic diagram of the metal alkylphosphooate sait st ructttre

Figure 2: Schematic diagram of an all-tram alkyl chain wit h seven CH? uni t s

2 Metal Alkylphosphonate Salts: Powder Diffrac- t ion

2.1 Background and Perspective 2.1.1 Known Structure

The metal alkylphosphonate salts have a lamellar, or layered. structure [7. Y]. which is depicted in Figure 1, and is similar to the structure of many other materials such as phenylphosphonate salts and perovskites [9, 10, 11. 12, 131. The structure consists of planar metal-oxide layers with alkyl chains at tached on both sides. For some metals, such as Mg and Na, water is aiso present in the metal-oxide layen. For other metals, such as Zn, it is not (4. The exact arrangements of atoms in the layers is a matter of some debate (14, 81, so we attempted to determine it in the materials we studied.

The chains, shown in Figure 2, consist of a series of CH2 units which are teiminated on one end by P and on the other by CH3. The chain is attached to

the inorganic layer when the P bonds to three O atoms in the layer. These O atoms are also bound to a metal atom so there is at most one chain attached per metal atom in the Iayer. Only the P atoms bond to the planes, so the chains extend off the planes. The chains do not bond to each other. This means that once the inorganic layer surface is Yilled up" with chains. no more chains at tach themselves to eit her the inorganic layers or the ot her chains. Thus. the chains assemble into monolayers on each face of the inorganic layers.

In fact. the chains may not necessarily reside in the perpendicular orientation shown in Figure 1. or in the all- trans (fully extended) conformat ion shown in Figitrr 2 [7. 8. 10. 121. While they do not bond to each other. the rhains do interact via electrostatic and van der Waals forces. These chain-chain interactions determine the chain configuration. which can depend on the chain length ( L e . number of CH2 units), the type of metal. and the temperature. Since the chain behavior is crucial to the material's properties. ive studied the effects of al1 three of the above factors.

2.1.2 Potential Applications

The most immediate use of metal alkylphosphoaate salts is as solid-state phase-change materials (see (41 and references therein). They couid serve as a nonhazardous. odor-free alternat ive to existing heat storage materials. Wi t h enough understanding of t heir structure and behavior. a heat storage system could be tailored to have a specific transition temperature and latent heat by choosing a metal akylphosphonate salt with the appropriate metal and chain lengt h.

Another potential use for these materials is as shape-selective sorbents and catalysts (see [7] and references therein). By replacing the CH3 functional group on the ends of the chains with another molecule. one could effectiveiy create a *molecular sieve,' to which only certain types of molecules would adsorb. Controlling the orientation and motion of the chains is of paramount importance to successfully using metal alkylphosphonate salts this way.

2.2 Applications of Powder Diffraction 2.2.1 Review of Powder Diffraction

In powder diffraction, a monochromatic X-ray beam strikes a sarnple corn- posed of many randomly-oriented crystallites [15]. The intensity of b r a y s emerging fiom the sample is measured as a function of angle. 20, away from the incident beam direction. If the sample's structure is periodic on a length

scale, d, then an intense diffracted beam will be seen at an angle.

where n is an integer 2 1 and X is the wavelength of the incident .Y-ray beam. Powder diffraction requires rneasurements in only one dimension rather than two as would be necessary for a single crystal sample. However. no direct ional information about the periodicity is available in a powder diffraction pattern. Even though powder diffraction by itself cannot be used to completely determine the structure of a sample, it is a simple technique which can reveal a great deal about that structure.

2.2.2 Variable Temperature, Low Resolution

Phase Tkansitions Phase transitions in a material are often accompanied by significant structural changes. In order to see these changes in metal alkylphosphonate salts. we performed a number of powder diffraction measurements while holding our samples at various temperatures. As a sample is heated. it naturally expands. so one expects to see the diffraction peaks move gradually to lower angles. Aside from this effect. if there is a distinct M e r - ence in the diffraction patterns just above and below a phase transition, then a significant structural change takes place during that transition. Generally speaking, a shift in a peak's angle indicates a change in the material's unit cell size. h change in the intensity of the peak indicates a reorganization of the atoms within the unit cell. If a peak becomes broader. the order in the material has decreased,

We selected the ternperatures at which to measure the powder diffraction pattern by looking at Differential Scanning Calorirnetery (DSC) results [1] such as those in Figure 3 . Each peak corresponds to a phase transition in the sample. There are three peaks. two small and one large. in each curve of the NaPCts thennogram. but only one in the ZnPCs thennogram. The transition temperatures of the samples we studied. as deterrnined from the DSC thermograms. are Iisted in Table 1. These served as a guide to the temperatures which might give interesting changes in the diffraction patterns.

Interlayer Spacing In the met al alkylphosphonate salts. the hydrocarbon chains, being made up of relatively Light elements, do not scatter X rays very strongly. The inorganic layers, containhg heavier metal, oxygen, and phosphorous atoms, scat ter far more st rongly. Therefore, any Kray diffraction pattern gives us primarily information about the planes. It is possible, though, to infer sorne of the chain behavior by watching the layers. More importruitly, we can use the results of other studies wbich are sensitive to the chains and see the effects which the chah behavior has on the inorganic Layen.

Temperature ( C )

Figure 3: Differential Scanning Calorimetry thermograms for NaPC 18 ( top Iwo curves) and ZnPCe (bottom two cu.mes). In each thennogram. the upper curve corresponds to heating and the bottom to cooling. Reproduced from [4].

Transition Ten .perature ( O C ) 1 I heat ing - 1 1st 1 main 3rd

Table 1 : Phase transit ion temperat ures of some met al alkylphosp honate salts as determined by DSC. Values taken from [1. 161

One technique which is sensitive to the chains is Nuclear Magnetic Res- onance ( M I R ) . Variabletemperature NMR studies of our samples [4] have shown that the chains are in an dl-trans conformation at room temperature. lipon heating to the point of the first phase transition. the chains begin to rotate while they remain fully extended. .At the main phase transition. the chains melt . developing many gauche defects. When cooled. the chains return to a mostlytrans conformation. but not one which is identical to their original state. We can see what effects. if any. this chain behavior has on the overall structure of these materials by comparing the interlayer spacing before and after t hese transitions.

The regular interlayer spacing is a periodicity in the y-direction. as shown in Figure 1. and as such gives rise to a set of diffraction peaks with (OkO) Miller indices [15]. Monitoring the position. intensity. and width of these (OkO) peaks as a function of ternperature reveals information about how the interlayer spacing is affected by any phase transitions which the sample undergoes.

Chain Orientation and In-Plane Structure .A large set of (Ok0) peaks can reveal structural information which the individual peaks alone cannot. Their intensities relative to one anot her depend on the electron densit y dist ri- bution inside the unit cell. We can therefore use the relative pe* intensities to find out how thick the inorganic layen are. or how close to the neighboring layers the chains extend. This is especially useful for finding out whether or not the choins attached to neighboring layers are interdigitated. In an interdigitated configuration, the c h a h on one layer extend between those on the neighboring layer (see Figure 17). The interdigitation or lack thereof has significant repercussions on the behavior of the material when using different functional groups in place of the CHs. Such determinations cannot be made using techniques such as NMR; so far this aspect of the chain configurations has only been inferred from measurements of the interlayer distance as a

function of chain length [8]. Our technique of looking at the diffraction peak intensities provides an independent means of confirming such results.

If a set of peaks which are not of the (OkO) family are present in the diffraction pattern, then the in-plme structure of the layen can be probed as well. The t- and r-locations of the metal? oxygen, and phosphorous atoms in the unit ceil will similarly affect these non-(0k0) peaks' intensity pattern just as the structure in the y-direction affects that of the (Ok0). This allows for com- puisons between the intensity patterns for the proposed intra-layer structure in the literature [8] and the actual measured intensity pattern.

2.2.3 R o o m Temperature, High Resolution

Unit Ce11 Dimensions '4s can be seen in Figure 1. the unit ce11 size in the y-direction. b. is much larger than a and c. the sizes in the x- and :-directions. respectively. Consequently. the angular separation of the (0k0) peaks will be far smaller than the separation of other peaks. As a result. many of the non-(0k0) peaks may be -hiddenV beneath the more comrnon (OkO) peaks. If enough non-(0k0) peaks can be found. their Miller indices could be determined. With that information. calculations of a and c are simple and can be used as a straightforward check of the structures of the inorganic layers proposed in the literature [8. 141.

Space Group Cao et al. [Il determined the structure of a manganese phenylphosphonate salt by single-crystd .Y-ray diffraction. and found it to be orthorhombic- more specifically in the space group. Pmn&. They then concluded. through powder X-ray diffraction studies. that the metal aikylphosphonate salts are also consistent with that space group. In order to test those findings wi th our samples. we looked for two possible signs of inconsistency. First. if certain Torbidden" peaks (such as (100) or (202)) appear, then our samples are not in pm112~ because the symrnetry of the atoms in a Pmn& structure cause the intensity of those peaks to drop to zero. Second. if we detect double-peaks. for instance if the (130) and (730) peaks are separately visible. then the unit ce11 is not art horhombic because not al1 of the unit ce11 angles are right angles.

2.3 Experimental Apparat us 2.3.1 The Powder Diffractorneter

The general Iayout of the powder diffractometer we used is shown in Figure 4. A measurement of the diffracted beam emerging from the sample's surface. as done here, is said to be done in the reflection geometry. Cu Ka radiation was produced by a Philips PW 2273/20 Cu X-ray tube which was powered by a Philips PW 1729 X-ray Generator. During normal operation, the power was

I X-Ray Tube

Monochromator, Analyzer Crystals

X-Ray Bearn Sample - Collimating Slits Detector

1 : -11 Flight Tube

Figure 4: Schematic diagram of the diffractometer used for powder diffraction measurements. viewed from above. Components are not drawn to scale.

set at 40 kV and 40 mA. A monochromator crystal set at the fi, bragg angle diffracted monochromat ic radiation toward the sample. The bearn passed through a hollow copper flight tube with Iiapton windows on both ends. The fiight tube was evacuated with a mechanical pump so as to reduce absorption by air in the fiight path.

Samples were placed on a Huber 5203 Goniometer Head which allowed translation of the sample in two directions and rotation of the sample about two axes, al1 in the plane of scattering. The Goniometer Head was seated on a Huber 421 Twc4ircle Goniometer which set the 0 and 20 angles. respect ive15 of the sample and detector. The goniometer was driven by two Superior Elec- tric Type M091-FD09 SynchronouslStepping Motors. Directly in front of the detector, an aaalyzer crystal set at the bragg angle for Cu K, functioned as a directional filter, selecting a narrow range of wavevectors and thereby en- hancing the angular resolution of the system. Both the monochromator and analyzer crystals were mounted on Huber 1000-series Goniometer Heads which dowed for optimization of their orientations. A Bicron Mode1 1XMP.040B-X Scintillator was used to detect the diffracted X-rays.

Three sets of Huber Tungsten Metd Slits were used to collimate the beam both horizontally and vertically. One set was placed between the source and the monochromator, and the other two sets were placed at either end of the

Bight tube. Pb slits (not shown in Figure 1) were positioned next to the monochrornator and analyzer crystals so as to prevent any X-rays from con- timing on through the system without first being diffracted by the crystals. Sample positioning and detector positioning and readouts were handled re- motely using the spec data acquisition package running under the Linux op- erating system on a computer containing an Intel 80456 rnicroprocessor.

The zero angle of the detector was found by positioning it in the Location of maximum beam intensity when no sample was present. Since this position was not always perfectly accurate. a constant offset was allowed in the data analysis to account for srnall misalignments. The sarnple \vas translated into the beam until it occluded half of the beam as seen by the detector. The O angle was rocked to a point where the intensity as seen by the detector was a maximum. making the sarnple surface paralle1 to the incident beam direction. This position was set to be the zero angle of the sample. For the sake of geometricd simplicity. 0 was kept at half of 26 t hrough al1 scans. though this condit ion is not strictly necessary when using powder samples [L 51.

2.3.2 Variable Temperature, Low Resolution

In the low-resolut ion configuration. pyrolyt ic graphite crystals were used as the monochromator and analyzer. While the analyzer crystal was Rat. the monochromator was bent so as to focus the .Y-ray beam on the sample and enhance the intensity of the beam. Graphite was chosen because of its relatively large (0.5' full-width at hdf-maximum) angular acceptance range. so as to maximize the flux.

The temperature of the sarnple was regulated by an oven in which it rvas mounted. The sarnple was held in position against a Union Carbide Boroelec- tric Heater. .4 voltage was applied across the heater to cause resistive heating. The heater sat against a copper base through which cold water Aowed to p r e vide cooling. A type I\: thermocouple stuck between the sample and the heater allowed for measurements of the temperat ure. This ent ire assembly was sealed inside a srna11 chamber attached to a mechanicd pump and evacuated for thermal isolation. .A beryllium window in the side of the chamber allowed S rays to enter and exit unirnpeded. and a plexiglass viewport on the top allowed direct visual inspection of the sample during heating. The base of the vacuum chamber was attached to the Goniometer head. and the entire assembly was rotated accordingly during scans. Diffraction patterns for the samples recorded in air and in vacuum at room temperature were identical. In practice it was found that upon heating, a s m d portion of the sample occasionally fell out of the sample holder and onto the base of the h a c e . This precipitated a minor drop in the overall diffraction intensity, but did not in any way affect

the widt hs or relative intensities of diffraction peaks which we were interested in measuring. In the future. the sarnple holder will be redesigned to prevent this from happening.

The t hermocouple was connected to an Omega CN76000 temperat ure controller, which displayed and adjusted the temperat ure. Adjustment s were accomplished via signals the temperature controller sent to a Kepco Bipolar Operational Amplifier which produced the voltage across the filament. Pie set a desired temperature on the controller and then allowed the system to equilibrate at that temperature before measuring any diffraction. Heating and cooling took place on the order of a few degrees Celcius per minute. Diffraction patterns were recorded every 10 to 30 O C in a range from room temperature to 200°C.

2.3.3 Room Temperature, High Resolution

For the most part. the high-resolution equipment was identical to the low- resolution, wi t h two major changes. First . Rat germanium ( LI 1 ) crystals were used as the monoctirornator and analyzer. Ge ( 11 1 ) has a much smaller angular acceptance range than graphite (0.006" full-width at half-maximum). and thus provides significantly enhanced angular resolving power. The system was able to clearly distinguish the K,, and Ka, components of the beam. even t hough the two differ in wavelength by less than 0.25% [13]. Second. the heater was not used in the high-resolution configuration. Instead. the sarnple was mounted on a simple stage which was attached to the Goniorneter Head. In principle. variable-temperature. high-resolution scans could be performed. but they would take substantially longer than the low-resolution scans. and it was not immediately evident that such high-resolution scans would reveal any informat ion not at tainable by the low-resolut ion met hod.

2.3.4 Cornparison Between The Two

Why do we choose the low-resolution mode for some measurements and the high-resolution mode for others? Because there is always a. tradeoff between resolving power and the signal-to-noise ratio. This is illustrated in Figure 5. A system with a narrow angular acceptance range can resolve finer angles, but will collect fewer photons than a system with a wide angular acceptance range. As a rough estimate of how our two modes compare, we can look at the width and height of the middle peak in Figure 5. In the high-resolution mode, the peak is far more accurately localized. The full width at half-maximum (FWHM) of the peak is 0.13*, as compared to a FWHM of 0.58' for the low-resolution mode. The high-resolution mode offers a factor of at least 4.5 improvement in angular resolution, and as such can distinguish closely-spaced diffraction peaks which axe smeared together in the low-resolution mode. It

1 o + ~ n O Q) CI1 \ VI g IO+' 1

2, -m

2 a2 z 10+O œ

5 10

28 (degrees)

Figure 5 : Cornparison of measurements of the same diffraction peak in the low- resolution mode ( upper curve ) and the high-resolution mode ( lower cume ).

can also make far more precise measurements of peak positions. which can lead to more precise latt ice constants.

The noise. however. is significantly less in the low-resolution mode. due to its higher signal. The error in counting measurernents of this sort is the square root of the total number of counts [15]. For the peak at 7.1' in Figure 5. the maximum count rate is 7700 counts per second (CPS) in the Low-resolution mode. cornpared to only 4Y2 CPS in the high-resolution mode. a factor of 1600 difference. The data in Figure 5 took 30 seconds per point to collect in the low-resolution mode. ln the regions between 3.0 and 3.5". between 7.0 and 7.5". and between 10.6 and 11." in the high-resolution data. the rate was 70 seconds per point. While far less noisy than the rest of the high-resolution data shown (taken at a rate of 20 seconds per point), the curve in these regions is still not as smooth as the low-resolution curve. Not only is the time per point higher in the high-resolution mode, a greater number of points must be rneasured. To detect these peaks at dl. we must scan in steps of at most - 0.05' in the high-resolution mode, but we could scan in - 0.3" steps in the Iow resolution mode and still see them clearly. The higher signal is usefd for detecting very dim diffraction peaks, makes it possible to accurately compare the relative intensites of different diffraction peaks, and minimizes scanning time.

(e) T = 22.0 O C , cooling 1000. - -

d

1 -

10 20 30 28 (degrees)

\ rn (c)T = 140 OC, heatiag -

d

Figure 6: Variabletemperat ure diffraction results for ?laPCZ2.

*rl

2 10.0- Q)

2.4 Results

, I 1 I I 1 I 1 I l I I 1 -

2.4.1 Phase Transitions

C, (d)T = 105 OC, cooling -

N a Samples Figure 6 shows the X-ray intensity as a function of diffraction angle for NaPC22 at five different temperatures. Qualitatively similar results were obtained for NaPCls and NaPC12. Initally at room temperature, in ( a ) , the diffraction pattern is a series of regularly-spaced peaks. These pealrs arise due to the periodicity of the inorganic layers. According to Table 1. upon heating, a phase transition occurs at - 100.5 O C . This transition causes only a minor change in the diffraction pattern, as seen in ( 6 ) . The peak positions move slightly, indicating a change in one or more of the lattice constants.

The main transition, which takes place at - 132.2 O C , causes a substantial change in the stmcture. The diffraction pattern in ( c ) is vastly different than that in (b). Almost d l of the regularly-spaced peaks have disappeared, re- placed by a very broad peak centered around 15.2" (1.34 kl). This implies that the sarnple is disordered in at least one dimension. forming an arnor- phous structure with an average "nearest neighbor" distance of 5 4.70 A. However, the first few layer peaks remain visible and are not noticably broad- ened. Therefore the layered structure persists on shorter length scales. Since the higher-angle peaks do not appear. the long-range ordering of the layers has

been disrupted. Diffraction patterns of this sort are consistent with a smectic liquid crystal structure. Ot her investigations. such as optical mirrosropy [4]. also suggest that our sarnples enter this type of phase. -4 third phase transition, which occurs around 151 O C on heating and around 130.9 O C on cooling according to Table 1. does not affect the diffraction pattern and thus does not substantially change the structure of the inorganic layers. .-\ diffraction pattern measured at 160 O C was identical to ( c ) and thus is not included in the figure.

When cooling to room temperature, the main transition at -- 123.0 O C does not return the sample to its original structure. This is evident in comparing the diffraction pattern in ( e ) with that in ( a ) . Instead. the pattern in ( e ) resembles that in (d), but has a geater nurnber of visible peaks at tow angles and also a sharpening of the amorphous peak. Both traits indicate that the sample "freezes" into a more ordered structure than the liquid-crystal phase. but never regains the sarne crystallinity it originally possessed.

These diffraction patterns can be understood by considering separately the behavior of the alkyl chains and that of the inorganic layers. The chains. which scatter weakly, rotate at the first phase transition and melt at the second (main) transition. The layers, which scatter strongly. are not significantly altered by the first transit ion: t herefore the diffraction pattern remains relatively unchanged. The generd organization into planar inorganic layers and chah monolayers persists at al1 temperatures examined. However. it appears that the layers' interna1 structure becomes disordered above the second transition temperature. Partial re-ordering of the layers' structure occurs on cooling. Perhaps by cooling slowly the layers' structure could be completely re-ordered, but since this did not happen at rates well below 10 "C/min, it seems unlikely.

Mg Sample At room temperature, the diffraction pattern of MgPCls is not as regular as that of the Na samples, but still shows the characteristic series of peaks denoting a layered structure. This can be seen in Figure i (a) . Unlike the Na samples, only the main phase transition was detected. The liquid- crystdine structure brought about by the main transition and the partial

20 (degrees)

Figure 7: Variabletemperature diffraction results for MgPC

28 (degrees)

Figure Y: Variable-temperature diffraction results for ZnPC8.

ordering upon cooling were similar to those in the Zia samples. as evidenced by Figures f ( b ) and ( c ) .

Zn Sarnple Figure 8 shows the X-ray intensity as a function of diffraction angle for ZnPCs at three different temperatures. While the room temperature diffraction pattern of the Zn sample. in (a) , closely resembles those of the Na and Mg samples. this material's higher-temperature properties are strikingly diferent. As with the M g sample, only one phase transition was seen. Surpris- ingly, above the transition temperature of - 160.2 OC. in (b), the diffraction pattern is almost identical to the pattern in (a). Some of the peaks have chânged positions, but none seem to have died away or become broader. It is not a liquid-crystal-like pattern. Even more surprising is that on cooling below the transition at .Y 152.1 O C , the diffraction returns to its original pattern. as seen in (c) .

The variable-temperature diffraction results tell us that the transition in ZnPCs is a reversible one; that is. the material returns to the same structure when heated and then cooled. The reversibility of the transition makes it a potentially reusable heat-storage material. However. the relatively low eni hdpy of the transit ion-23.2 J /g-makes it a poor candidate for common use [4]. Since the inorganic layers dominate the scattering, their structure is not significantly altered in the transition. This could be due to a number of possible factors:

a the Zn atoms bind more strongly to the lattice and keep the layers' interna1 structure stable

a the longer alkyl c h a h in the other sarnples influence the disordering of the inorganic layers

a the techniques used to prepare the samples differed in a way which affected the melt ing propert ies of the layers

.4 conclusive determination of which of these Factors. if any. affect the reversibility of the phase transition will require a more t horough st udy of each of t hem.

2.4.2 Interlayer Spacing as a Function of Temperature

Ai; dysis Techniques For a part icular interlayer spacing, b. the kt h di ffrac- tion peak will appear at an angle,

G'sing this relation. a simple cornputer program was written to calculate peak positions for a given spacing. The positions can then be compared wit h t hose in the measured diffraction pattern. An example of t his is shown in Figure 9. The value of b was varied until the Iines were separated by an amount equal to the peak separation. In ( a ) , the bvalue is slightly too large. which is evident at higher angles. The correct bvalue is achieved in (6). but the lines do not pass through the centers of the peaks. This is due to inaccuracy in the zeroing of the detector angle. In (c), the nonzero 'L&K,, has shifted the diffraction pattern so the peaks and Ljnes agree. The goodness of fit is determined by eye.

This technique was used to determine the interlayer spacing of each sample studied at each temperature where a diffraction pattern was recorded. In the case of Figure 9, an excellent determination-to within HL08 A-could be made using the low-resolution data. This is because the data contains many evenly-spaced peaks extending out to high angles. When only a few peaks are visible, such as in the liquid-crystal phase, the measurement is fax less accurate.

(a) b = 56.00 A, 280met = 0.00'

"ppf I I I I

I I I

1 I I I I I I I 1 N l

20 (degrees)

Figure 9: Determining the interlayer spacing of NaPC22. Dashed Iines represent predicted peak positions for the b and 2OOKse, shown. The numbers above the lines are the 'ililler indices of the peaks.

I Interlayer Spacing ( -4)

Table 2: Interlayer spacing at key temperatures during heating and cooling. The relevant temperatures were different for each sarnple.

Y \ I

Results of Analysis

NaPCI2

Na, Mg Samples A plot of interlayer spacing vs. temperature for .ClgPCI8 is shown in Figure 10. -A substantial change in the layer spacing takes place near the transit ion temperatures. bot h heating and cooling. This occurred in

36.9 AI 0.1 28.5 I 1.0 53.1 z t 0.1

Room Temp. 37.60 I 0.09

each of the metal alkylphosphonate sdts we investigated. In our studies. the exact temperatures of the transitions were not determined. but major changes in the interlayer spacing always occurred at temperatures consistent with the transit ion temperatures determined by differential scanning calorimetry [4. 161 and listed in Table 1.

The measured interlayer spacings for al1 samples are listed in Table 2. In the Xa and M g samples. the first transition corresponds with the onset of chah rotation [-Il. The rotation appears to cause an expansion of the Iayee in some cases. a contraction in others. and no change in still other cases. Since an overall contraction can occur. we conclude that the chain rotation has a greater effect on the interlayer spacing than does conventional thermal expansion. However, the factor or factors that distinguish the materials which contract from those which expand during this first transition are not well- understood.

1st Transition

35.38 0.12

The substantial "collapsen of the layers above the main transition temperature is due to the melting of the chains. The chains leave their all-trans conformation and their effective extension off the inorganic layers decreases. Subsequently. the layen pack more tightly together. When cooled, the chains return to a more extended conformation [4] and the layers move apart. In most cases the final interlayer spacing is greater than the initial. Apparently the tilt angle between the chains and the inorganic layer normal is smaiier after the transition than it was before the transition.

Main Transition 24.6 * 0.4

Room Temp.

36.8 3~ 0.4

Figure 10: Interlayer spacing of MgPCls through heating and cooling. Circles represent individual measurements of the spacing. The solid line is a guide to the eye. Dark arrows correspond to the phase transition temperatures listed in Table 1 for heating (J) and cooling (f).

While interlayer spacing measurements were unarnbiguous and extremely precise in the sample's initid phase, finding the spacing after heating and cooling involved a great deal of uncertainty. This was not only because few peaks were visible. but also because several lattice constants fit the data equally well. as seen in Figure 11. There are four peaks clearly visible at t his temperature. and a fifth is likely present in the second peak's shoulder at around 6.5'. While the first peak and shoulder appear to be consistent with a layer spacing of 26.7 A in ( a ) . oone of the other peaks are fit well. Layer spacings tailored to the second and t hird large peaks, in (c) and (e) respect ively. give no better results. We thought perhaps a better fit might be possible using twice one of these candidate layer spacing. Any peak consistent with a spacing of d is also consistent with a spacing of 2d. which gives twice as many peaks. Figures 1 l ( b ) . (d). and ( f ) show that no single lattice constant satisfactorily fit this diffraction pattern.

Ultimately. the spacing in Figure 1 l (6) was chosen as the most likely spacing For two reasons. First. it fit both the largest peak and the shoulder well. Second. a better fit was obtained for ZlaPCZ2 after heating and cooling. (See Figure 6(e).) h spacing of 61.9 .A agreed with al1 of the visible peak positions in that sample. and it was reasonable to expect a spacing of the same order of magnitude in k[gPCl8. It is crucial to point out t hat these values actually represent the Lat t ice constant in the y-direct ion. and not necessarily the lqer spacing. Upon cooling, the layers may not separate by a factor of alrnost two as proposed. but the spacing may remain unchanged while the layers develop an alternating character. If the periodicity in the structure occurs every two layers, rather than every layer. thea the interlayer distance will he d but the lattice constant will be 2d. Clearly, more work is necessary to resolve this issue.

With the Na samples. an additional complicating factor cornes into play: a second interlayer spacing. Easily seen with the high-resolution mode at room temperature, this second set of peaks appears as small shoulders on the main diffraction peaks in the low-resolution mode. Both are shown in Figure 12. Evidently, some fraction of the sample has a smailer interlayer spacing than the rest of the sample. The larger spacing, or "swelling," is believed to be due to the presence of H20 in the inorganic layers. Where possible, the second spacing was measured and the results are listed in Table 3. The interlayer spacings as functions of temperature for NaPCzz are shown in Figure 13. The lâyers have nearly ident ical phase transit ions, and the effect s of t hose phase transitions are independent of whether or not the inorganic layers contain water. The presence of two distinct layer spacings might also help to resolve the indexing problem in MgPCls described above. but no clear value could be infenred from the available data,

10+~- (a) br26.7 A (b) b = 53.4 A

O O 0 - - 0 0 0 0 0 0 0 I 1 3 4 1 3 4 5 6 7 8 - O O O O - - 0 0 0 0 0 0 0

- I I , , I I I

n O (c) b = 30.7 A (d) b =61.4 A aJ - 0 O O O - 0 0 0 0 0 0 0 0 ~ a I - 3 3 J j ? ~ r j 0 7 ~ 9 1

O - - O o O o O O O O 1

I l I I I I I

I I 1 I & I l I I I I I I I I

I 1 I I I I I 1

1 0 + p ; ;

I I I I I I I I I I I I t I I I t I I

I I I I I I I I I 1 1 1 I I I I

20 (degrees)

Fi y r e 1 1: Interlayer spacing determination for 'rIgPCls at 23.4 O C after heating and cooling.

Table 3: Spacing between waterless layers at key temperatures during heating and cooling. The relevant temperatures were diflerent for each sample.

hterlayer Spacing (*A)

NaPCi2 Room Temp. 33.6 10 .36

1st Transition 1 Main Transition 1 Roorn Temp. 27.05 f 0.35 1 22.0 * 1.2 1 26.1 & 2.1

20 (degrees)

Figure 12: Evidence of water-swelling in the majority of the ?laPCi2 sampie. Boldface indices correspond to b = 33.60 A. while those in nomal type correspond to b = 37.60 .-\. The low-resolution intensity has been reduced by a factor of 50.

Figure 13: The two interlayer spacings of NaPC i2 through heating and cooling. Circles and asterisks represent individual measurements of the spacing. The solid and dotted lines are guides to the eye. Dark arrows correspond to the phase transition temperatures listed in Table 1 for heating (4) and cooling (t).

Zn Sample As noted in Section 2.41. the behavior of ZnPCs differs significantly from that of the other materials studied. Its interlayer spacing at mious temperatures is shown in Figure 14. Below the main transition, the spacing increases linearly with temperature. possibly as a result of thermal expansion. -4t the transition, the spacing increases by about 1 .&. The cause of this expansion is unclear. The most likely candidate is a decrease in the angle between the chains and the inorganic layer normal. When cooled. the transition takes place at the same temperature as on heating. With further cooling, the spacing seems to exhibit exactly the same behavior as before it was heated. In this material. then, the chains return to the same configuration in which thry originaily started.

2.4.3 Unit Ce11 Dimensions and Space Group at Room Tempera- ture

Analysis Techniques To find the angles of the unit cell. a. 3. and 74. and the unit ce11 dimensions along the inorganic layers. a and c. the cornputer progam described in Section 2.4.2 was expanded. This primarily involved changing equation (1) to make it compatible with a triclinic unit ce11 [lJ].

w here

abcdl - cos2 o: - cos2 3 - cos' y + 2 cos a cos 3 cos y.

6'2 sin2 a. a2c? sin2 3. a2b2 sin2 y.

abc2(cos R COS 3 - COS Y). u2bc(cos SCOS - COS a),

ab2c(cos y cos CI - cos 3) .

The values reported in Table 2 are appropriate for 6 in an orthorhombic unit cell. More generally. they correspond to the quantity &. Those values determine one of the six parameters of each material.

Once the (OkO) peaks had been indexed, the best course of action for fitting this sort of data was to initidly assume an ort horhombic unit ce11 ( Le. set a = B = 7 = 90'). Next, the values of a and c were roughly obtained by assuming that the Lowest-angle unindexed peaks were the (110) and (01 1). Normally, one would index those peaks as (100) and ( O O l ) , but those two reflections

Temperature

Figure 14: Interlayer spacing of ZnPCs through heating and cooling. Circles represent individual measurements of the spacing. The solid line is a guide to

the eye. Dark mows correspond to the phase transition temperatures listed in Table 1 for heating (4) and cooling (f ).

IO 1 0 I l tD IO II OOOOOt O t O001 01 II I l I I I I l I I I I II IIIU I I I I

I I I I I I l I I I I I I I I l I I I I I I I J I I l 1 I I I I I l I I t I I I I I I I l I I I I I I l I I

5

Figure 15: Peak indexing for .iaPC12. a = S.30 A. b = 37.60 A. c = 6.05 .A. a = J = y = XI0. The upper curve is from the Law-resolution mode. wit h the intensity reduced by a factor of 50. The lower curve is from the high-resolution mode. Only indices consisitent with the space group Prnn?, are shown.

are forbidden for space group Prn112~. Finally. a. 3. and y were varied until the predicted peak positions at higher angles agreed with the rneasured peak positions. Without some a priori knowledge of which peaks will appear and which will not. this method left considerable room for interpretation with regard to when the proper fit was achieved.

If' there was both high-resolution and Iow-resolution data available for a particular sarnple. the peak positions generated by the computer program were made consistent with bot h. The high-resolution data provided constraints on the precise positions of the peaks, and showed the presence of closely spaced peaks, al1 of which had to be separately predicted by the computer program. The low-resolution data showed even very dim peaks, al1 of which had to be accounted for as weH.

Results of Analysis Non-(OkO) peaks were seen only in NaPCI2, ZnPC8. and MgPCla. High-resolution scans were performed for the first two. The indexing for NaPCi2 is shown in Figure 15. Notice that the high-resolution mode is clearly able to distinguish four peaks around 22 degrees which are blurred together in the low-resolution mode. hlso notice that the low-resolution mode

Table 4: Unit ce11 dimensions and angles of metal-alkylphosphonate salts at room temperature as measured by low-resolution and high-resolution S-ray powder diffraction.

detects peaks at around L0.9" and 12.8" which are not obviour in t h e high- resolution mode. The lines match the data well when the parameters listed in the caption of Figure 15 are used. The fit is most problematic with respect to the peak at ??.O0. That peak seems to be at too high an angle to be the (220). but at too low an angle to be the (Oïl). Also. the high-resolution data sug- gests t hat t here might be peaks at around L3.2. 16.9. and 19.0!i0. The count ing statist ics in t hese regions are not sufficient to distingush these candidates from the measurement uncertainty, however. The low-resolution measurement continued to higher angles than shown in Figure 15. and was consistent with the same unit ceil parameters.

The diffraction pattern of ZnPCs proved more difficult to index. as can be seen in Figure 16. Most of the difficulty stems from the low signal-to-noise ratio of the high-resolution mode. making unclear where peaks occur and where they do not. Atternpts to index the patterns using an orthorhombic unit ce11 resulted in many unmatched peaks. so the CI and y angles were adjusted until reasonable agreement was found. The many dashed lines in Figure 16 suggest t hat the indexing scheme shown is not necessarily the only one possible. Wit h five adjustable parameters. it is impossible to rule out every ot her set of' unit ce11 dimensions and angles. However. we can confidently conclude that ZnPCa is not orthorhombic, and consequently does not belong to space goup Prnr&. The other samples. however, produce diffraction patterns which are consistent with that space group.

NaPCI2 ZnPCR

f l (degrees) 1 y (degrees)

Table 4 summarizes the results of our measurements of unit ce11 dimensions and angles.

c ( A ) 6.05 3.85

90 90

2.4.4 Chain Orientation and In-Plane Structure at Room Temper- ature

a ( A ) 8.30 4.54

a (degrees) 90 89.0

90 88.7

Analysis Techniques It is interesting to compare the interlayer spacings of the materials studied with the spacings one might predict for a structure where the c h a h are perpendicular to the inorganic layers. but are not

b (A) 37.60 14.73

26 28 30 32 28 (degrees)

Figure 16: Indexing of ZnPCs; a = 4.53 A, 6 = 24.73 .A. c = 3.85 A, a = 89.0". 13 = 90.0°, and y = 88.7O. The upper curve is in the low-resolution mode. with the intensity reduced by a factor of 150. The lower curve is in the high- resolution mode.

Table 5: Results of interlayer spacing calculation for noninterdigitated chains oriented perpendicular to the inorganic layers.

NaPCi2 NaPC18

interdigitated-that is. chains attached to one layer do not stick in between

chains attached to the next layer. We can calculate the c h a h length by using the widely accepted values of 1-54 A and 112" for the C-C bond length and the C-C-C bond angle. respectively (81. Because the chains are in the all-trans conformation, each C-C bond adds 1.54 sin (F) = 1.28 .A to the length of

the chah. Cao et al. [8] measured the inorganic Iayer thickness to be - i -4 in similar materials. so we can add that to our estimate. Finally. the CH3 endgroups have some finite size as well. which we will estimate to be -. 2 A. Putting these numbers together. we compare in Table 5 the calculated spacings for each sample with the measured spacings from Section 2.4.2. In every case. the spacing is measured to be less than calculated. This means t hat the chains are oriented in one of two ways: either they are interdigitated or they are not perpendicular to the inorganic Iayers.

To determine which is the case, we need a mode1 which predicts the diffraction peak intensities. If we restrict ourselves to looking at only the (OkO) peaks (the only ones we conclusively indexed), our model can involve only the direction perpendicular to the inorganic layers. the y-direction. We model the electron density, p ( y ), as the sum of a few square waves. as shown in Figure 17. CVe choose square waves because t hey are easy to Fourier transfom. The electron density is highest at the positions of the metal atoms. slightly Lower in the rest of the inorganic layers, and considerably lower in the chains. The major difference between the two configurations is the central region in which the chains attached to neighboring inorganic layers meet each other. In the interdigitated configuration. the carbon atoms in this region are packed more tightly, and the electron density rises. In the tilted configuration, the central region contains no carbon atorns, only hydrogen, so the electron density drops.

1 chah length ( A ) 14.0 21.7

Thus these two models are the sums of three different square waves. This is specified further in Figure 18. We choose to define dl of our electron density values with respect to the chains' electron density (between B and C). The

calculated spacing ( A ) 39 54

measured spacing ( A ) 37.6 46.1

C' +- electron density

- electron densHy

Figure 17: One-dimensional models of the electron density as a function of position in an alkylphosphonate salt for the interdigitated ( t o p ) and tilted ( bottom) configurations.

Figure 18: Half-period of the one-dimensional mode1 of the interdigitated configuration's electron density. The tilted configuration is ident ical except t hat p, falls below the axis.

Fourier transform of p ( y ) . p ( s ) . is then

A constant offset in p ( y ) , such as our baseline electron density. merely adds a delta function. J(s), to p ( s ) . We ignore the delta function since we do not look at s = O, only at values of s where (OkO) diffraction peaks occur. W e can simplify p ( s ) by noting that peaks are only found at s = = sk. where k is a nonzero integer. Plugging this in, we get

'" [ O ( i) + (sin (iTg) - sin (tr;)) - sin ( k r g ) ] 7 pk = -po sin k;r- kn

where A, B, C, p,, ph, and p, are defined in Figure 18. The intensity of the (OkO) diffraction peak, Ik is proportional to pf, so our final expression for the

intensity is,

Pc - (ir;) + (sin (irn;) - sin (kx : ) ) - ; sin ( k i g ) ] ' - (2 )

Yote that this depends on only five parameters: 6' E, $$, h. and fi. We Pa

cm fit these parameters to the measured intensity pattern. If 5 is found to be positive, then the material is in the interdigitated configuration. If it is negative, the material is in the tilted configuration.

In materials which producr visible diffraction peaks from non-(OkO) planes. the one-dimensional mode1 can never Fully reproduce the diffraction pattern. For these materials. use of the computer program. bragg. is necessary. The input to bragg consists of the following:

a dimensions and angles of the unit ce11

a positions of atoms in the unit ce11

symmetry elements of the relevant space group

form factors of the atoms

a isotropic thermal parameters of the atoms

O X-ray wavelengt h.

The program t hen calculates 28. the structure factor densi ty (proport ional to the intensity). and multiplicity of each reflection. For a given structure. ive can compare the calculated intensity pattern to the measured pattern and decide whether the material has that stmcture,

The atomic positions ive used in bragg were drawn from two different sources. The atoms in the inorganic layers and the first C atom in the chains were positioned according to the results of Cao et al. [8] for the inorganic layen in Mn(O3PCd!I5) HzO. Of course? we replaceci the Mn atoms by the metal appropriate to the material being simulated. hnother computer program read in a tilt angle between the chains and the layer normal and calculated the locations of the remaining C atoms in the dl-trans chains. The program determined these positions by using the C-C bond length and the C-C-C bond angle listed above. The locations of H atoms were not input to bragg because hydrogen does not appreciably scatter X rays.

O 2 1 2 1 O 0201 O E O P 01 3û2 1 3 3 QI13 4 E r 4 42 O01 O O I RIZ1 O 1 2 0 tZ

Figure 19: Cornparison between bragg output (vertical [ines) and measurement [dl (circles) of the diffraction peak intensities for Zn(03PCH3) H-O. Both are scaled to set the (010) peak intensity = LOO.

In order to make sure it was valid to use the inorganic layer structure from another class of SAM materials. we tested it against the powder diffraction peak intensities which Cao et al. [8] reported for the zinc alkylphosphonate salt. Zn(03PCH3) H 2 0 . This material is an ideal choice for such a test since it effectively has chains of zero length (no CH2 units). As can be seen in Figure 19. the results from bragg and the measured peak intensities agreed fairly well when the layer thickness was increased to 8.20 A frorn Cao's original value of 6.95 -4. While not all of the intensities match precisely. the general trends are sirnilar. We theo used this mode1 of the inorganic layer structure to make cornparisons with our own difiaction measurements.

Results of Analysis The best fit of the one-dimensional mode1 to the room- temperature NaPCls diffraction pattern is shown in Figure 20. The diffraction pattern seems to have an alternathg character to it: up to (0?0), the odd- numbered peaks are more intense than the even-numbered peaks: starting wit h

1 I I 1 I l 1 I I 1 I I I 1 1 I O 20 30

20 (degrees)

Figure 20: Calculated peak intensities (circles) from the one-dimensional mode1 of Figures 17 and 18. and the measured diffraction pattern of NaPC la

(line). 5 = 0.021. = 0.195. c = OS65. = 0.20, and h = -0.14. D D Po

(O8O), even-numbered peaks are more intense t han odd-numbered peaks. This aspect is perhaps the most important in resolving whether the chains are tilted or interdigitated. As for the fit, it reproduces the data faithfully up to (0160), where it breaks down. At this point, the fit gives even peaks once again smaller than odd peaks. Clearly. this is not the case in the data. but the reason why is not well understood,

It was mainly the parameter which determined how the peaks alternated. since 5 was chosen to give a periodicity on the order of twice the angular distance between consecutive diffraction peaks. For > 0. (020) was more

Pu

intense than (030 j. For < O. (020) was less intense than (090j. in agreement with the data-therefore the electron density is Iess at the midpoint between inorganic layers t han it is in the chains. This means t hat the chains are tilted. The alternating pattern was also seen in NaPCi2. ?laPC22. and hlgPCL8 data. Al1 were found to be in the tilted configuration. Yo alternating pattern could be seen in ZnPCa. so the mode1 is not sufficiently detailed enough to reveal the chain orientation in this case.

The proposed structure of MgPC18 for a tilt angle of 52' (selected from Reference [Y]) was entered into 6ragg, and the results are s h o w in Figure 21. It is obvious from Figure 21 that the calculation does not agree wit h the data. At low angles. the alternating intensity pattern is not reproduced well. Large (110) and (120) peaks are predicted. but are only barely visible in the data. Also signifiant ly overestimated are the intensities of (200) and ( 2 10). The large measured peaks around 20" are not intense according to the calculation. As a whole. it appears that the calculated intensity envelope decreases more quickly than in the data. and rises again at different angles. We conclude. then. that our proposed structure is not a good mode1 of the sample's structure.

The discrepancies could have several causes. First. the results from bragg depend considerably on the d u e s of a. and c. Perhaps our peak indexing. and hence the dimensions of the unit ce11 we found. were mistaken, However. it is impossible to determine from this data whether any non-(0k0) peaks are present at angles lower than LS0, where the first visible non-(0k0) peak sits. limiting our ability to assign a and c unambiguously. Second. the sample structure may not have the periodicity in the x-direction which leads to such strong (h10) reflections. It was assumed that dl of the C atoms in the chains sat at the same x-coordinate, due to the symmetries in a P m d l unit ce11 [SI. If this was not the case? then perhaps other (hkO) peaks would be more intense. Such a condition would imply that the sample breaks some of those symmetries. Third. our layer thickness may have been incorrect. Varying the thickness did adjust the envelopel but it was impossible to find an envelope

20 (degrees)

Figure 21: Diffraction peaks predicted by bragg (vertical f ines) for !vIgPC18. and the measured diffraction pattern (solid l ine) . The bragg output is scaled so the intensity of (020) agrees with the measurement .

where the (070) peak was as intense as in the data without the (080) being equally as inteuse-in clear contradiction to the measurement. Fourt h, the tilt angle we used may not have been appropriate for our sarnple. This affected the alternating pattern of the (Ok0) peaks. but a tilt angle could not be found which reproduced the pattern seen in the data. In al1 Likelihood. it is a combi- nation of the above parameters which require adjustment in order to produce some agreement with the measurement. One or more of them will need to be determined through independent means before this technique can give reliable values for the ot hem.

2.5 Ideas for F'uture Studies The work described above has demonstrated the usefiilness of S-ray pow-

der diffraction techniques for studying met al alkylphosphonate salts. and has opened up several directions in which t hese studies could be continued. Per- haps most obviously, these techniques can be used to determine the interlayer spacing and structural behavior of phase transitions in other alkylphosphonate salts of varying chain Length and metallic composition. It would be especially interesting to see whether longer-chain Zn compounds melt in the same way as did the Na and M g compounds we studied. This would clarify whether the Zn atoms or the short chains are responsible for the unusual behavior of ZnPCa.

Another interesting study would be to measure the interplanar spacing of one cornpound as a function of the heating and cooling rate. The most likely effect would be on the unit ce11 dimensions after cooling. The interlayer spacing may be d e c t e d by the cooling rate since slower cooling might allow the chains CO return more completely to t heir original all- trans conformation. or move to a higher tilt angle. .Uso. the in-plane structure might be affected as well. Specifically. the sharpness of the high-angle peaks, such as that at around 2l.Y in Figure 6 ( e ) . might depend on the rate of cooling. The sharpness of this peak is an indicator of the crystallinity of the inorganic layers.

Lastly. and perhaps most importantly, future studies of this sort need not sufter from the limitations of the high- and low-resolution modes of the diffractometer. An intermediate-resolution mode-one with a higher signal-tenoise ratio than the high-resolution mode and more angular resolving power than the low-resolution mode-would be ided. Such a mode c m be achieved by using either the germanium monochromator with the graphite analyzer or the graphite monochromator with the germanium analyzer. The liquid crystd phases of the alkylphosphonate salts were not st udied wit h the high-resolution mode due to prohibitively s m d signal. One advantage of the intemediate- resolution mode would be its ability to better probe the alkylphosphonate s d t s at higher temperatures.

Figure 22: Schematic diagram of an all-trans alkanethiol chain with seven CH2 units.

3 Alkanet hiolate-Capped Gold Nanoclusters: Small- Angle Scat tering

3.1 Background and Perspective

3.1.1 Description of Known Structure

.ilkanethi01 chains, such as that shown in Figure 22. are similar to alkylphosphonates in that they are chains of CH2 terminated on one end by a CH3 molecule. On the ot her end a sulfur atom is present. rat her than phosphorous as in alkylphosphonates. In a solution containing gold. the sulfur atoms adsorb ont0 nucleating gold clusters. Eventually, the surfaces of t he clusters are compietely covered with sulfur atoms. and the clusters cease to grorv. Since the sulfur atoms are bound to the chains and chains do not Form bonds with each other. a monolayer of akanethiolate forms on the cluster surface. The newly-formed material behaves as a colloidal suspension of gold in dkanethi- olate [li].

At room temperature. nuclear magnetic resonance ( N M R ) studies have shown that a11 chains in these materials are adsorbed to clusters. that the vast majority of the chains are in an all-tram configuration [lY. 19. 201. and that the chains rotate about their main axis (51. Transmission electron mi- croscopy (TEM) indicates that the clusters are not organized into a regular, periodic structure but do tend to be rougly the same size and are separated by uniform distances from other clusters [M. 61. The sizes c m be controlled bu manipulat ing the gold-to-thiol ratio in the initial solut ion ['il]. The separation of neighboring clusters appears to be small enough that the chains must be interdigitated somehow. The clusters are roughly spherical, but are believed to be faceted, with groups of chains packing on each face as they do on larger flat surfaces. These groups tend to interdigitate wit h other groups. but not in- dividually chain-by-chain (see [5] and references therein). Figure 23 combines these features to give a picture of a typical set of alkanethiolate-capped gold clusters.

Au Nanocluster

All-tram Chain

Chain with gauche Defects

Figure 23: Two-dimensional representation of the packing and chain orientation in alkanethiolate-capped gold nanocliisters.

3.1.2 Potential Applications

The spherical geometry of the monolayers gives a higher surface area than a planar coiifiguration woctld. This makes these materials ideal for catalysis. when other functional groups are put in place of the CH3 group at the end of each chain. They are also suitable for applications in chernical sensing. lubrication. Wear protection. and corrosion prevention (-. 31. The electronic properties of these materials are also interesting due to the controllable. uniform size of the clusters. For instance. the clusters can be made small enough to exhibit quantum confinement of electrons [22. 171. Such structures are re- ferred to as. *quantum dots.' More generally. if semiconductors could be used instead of gold. one could Fabricate rnolecular-scde elect ronic devices w hich wotild be several orders of magnitude smaller in size than currently available devices [l].

3.2 Applications of Srnail-Angle Scat tering

The physics behind scattering at smail angles is identical to that of difhac- tion at large angles: the scattered X-ray intensity distribution as a function of angle depends on the square of the fourier transform of the electron density as a function of position. At large angles, s m d length scales are probed. At s m d angles, large length scdes are probed p23, 241. Smd-angle scattering, therefore, contains information about the largescale electron density of the

material through which the beam passes.

There are five main structural aspects which significantly influeiice the electron density of the materials we studied:

a Average Nanocluster Size

a Average Intercluster Spacing

a Nanocluster Size Distribution

Intercluster Spacing Distribution

O Nanocluster Shape.

Since the (electron) density in the clusters is much greater than in the chains. the material is made up of alternating regions of high and low density. The sizes of these regions are determined by the cluster size and intercluster spacing values. The low-density chains do not scatter .Y rays appreciably. so only the clusters contribute to the signal.

At zero degrees. scat tering from the ent ire sample interferes const ruct i vely making the intensity high. In practice. this signal is hidden beaeat h the transmitted bearn. so it is not directly measurable. At a certain angle. the intensity will drop to zero. due to destructive interference between beams scat tered by electrons on opposite sides of a cluster. This angle is determined by the nanocluster size. At a smaller angle, a drop in intensity is also found due to destructive interference of scattered beams originating in neighboring clusters. This destructive interference is not total because a cluster's neighbors form an incomplete spherical shell around it. The angle of this minimum is deterrnined by the average distance between two neighboring clusters. SAXS st udies have previously been used to determine nanocluster sizes. but not the intercluster spacings [6].

In our samples. of course. the nanoclusters are not al1 identical in size. nor is the intercluster distance uniform everywhere. For each cluster size and intercluster distance present in a sample. the two minima described above will appear at a different angle. The measured scattering pattern will be a sum of the individual scattering patterns produced by al1 the clusters and their respective neighbors. This will effectively *smearv the scattering pattern. making its features less sharp. Such a srnearing effect will also occur if the clusters are not perfectly spherical, since the diameter will Vary throughout a cluster. The amount of srnearing seen in the pattern, then, is a measure of the variability in the cluster diameter (either arnong different clusters or at different points on the same cluster) as well as vaxiability in the intercluster spacing.

40

X-Ray Tube X-Ray Beam Sample - Collimating Slits Detector Monochromator, Analyzer Crystals ( Fkht Tube

Figure 24: Schematic diagram of the diffractometer used for small-angle scattering measurernerits. viewed from above. Components are not drawn to scale.

Small-angle scattering is not the only way we can measure the average nanocluster size in Our samples. High-angle diffraction peaks also contain that information. The ideal diffraction peak from an infinitely large crystal is infinitely sharp. One from a crystal of lirnited size bas a finite width (151. &a- suring the widths of the diffraction peaks is one way to verify the resiilts of the small-angle scattering measurement.

In addition to rneasuring structural characteristics. these small-angle scattering studies were undertaken as a preliminary assessrnent of how appropriate the use of k a y Intensity Fluctuation Spectroscopy (KIFS) might be with these materials. XIFS uses the small-angle scat tering of a coherent X-ray beam to probe equilibrium dynamics on a molecular level r25]. This technique could provide information on the Brownian motion and diffusion of the gold nan- oclusten, but only if the nanoclusters produce a st rong scattering signal. Our studies, using an incoherent beam, provided an order-of-magnitude est imate of the scattering signal we might expect to see in XIFS.

3.3 Experimentai Apparat us

The apparatus used is shown in Figure '24, and was in alrnost al1 respects identical to the high-resolution powder diffractometer described in Section 2.3.1. The main difference was that small-angle scattering measurements were done

in the transmission geometry rather than the reflection geometry used for the powder diffraction measurements. Samples were deposited on Kapton and mounted on an durnimm frame. which was then placed in the sarnple holder described in Section 2.3.1. This allowed the beam to pass through the relatively transparent Kapton and into the sample.

3.3.1 Transmission Geometry

In the transmission geometry, the beam penetrates completely t hrough the sample. and the resulting intensity distribution is measured as a function of angle. The sarnple is kept in the same position while the detector moves over a range of scattering angles. The transmission geometry dlows scanning to much lower angles t han the reflection geometry-even t hrough the direct. transmit ted beam at 0'. Such a rneasurement must be undertaken with caution. though. to ensure that the intense transmitted beam does not damage the detector.

In the reflection geornetry. at very low angles the sample sees only a small region of the incident beam. but in the transmission geomet ry the ent ire beam interacts with the sample regardless of where the detector is. This increases the nurnber of photons interacting with the sample and hence the number of scattered photons detectable at very low angles. In the transmission geomet ry. the sample is often positioned so that its surface is perpendicular to the beam. as shown in Figure 24. In this case. a minimum sample volume is in the beam. To increase the volume scattering the beam. and thereby the amount of scattering signal. the sample can be turned so its surface is at a smaller angle to the beam. This effectively increases the sample thickness.

3.3.2 Minimizing Background Scattering

In the ideai small-angle X-ray scattering ( S A S ) experiment. the only S rays which are detected arise from scattering in the sample. In practice. a substmtial amount of background signal is also detected. The background arises from the portion of the bearn which passes unabsorbed and unscattered t hrough the sample. as well as from scat tering off of ot her elements in the flight path. If too much background is present, its noise drowns the relatively small scattering signal ob tainable wit h our apparat us. To minimize it . we carefully positioned the three sets of dits Iabeled A, B, and C in Figure 24. The dits also con be used to remove the Cu Ka, component of the beam, making it more monochromatic. In addition? they collimate the beam, reducing its divergence as seen by the sample.

It is common to use dits in SAXS in the following way [15]: Close one set of slits into the beam so as to limit its size and/or divergence. This produces

Figure 25: Profiles of Cu Ii,, (darker line) and K,, ( l ighter line ). The width of the dit C opening was 0.1 mm.

a significant amount of unwanted scattering, which can be removed by using a second set of slits. Place this second set downstream from the first. and close them down to. but not actually in contact with, t h e direct beam. The farther downstream the second slits are placed. the more effective t hey will be in removing the diverging scat tered beam.

The dits B and C were intended to be used in exactly this way. However. it was found that slit B could not remove the Ii,, part of the beam without also cutting away a substantial fraction of the desired K,, cornponent. Since the bragg angles of K,, and K,, are not identical, they diverge as they leave the rnonochromator. However, the beams are fairly wide and their angular sepmation is very small, so at B they overlap entirely. This is illustrated in Figure 25, which shows the beam profiles as measured at C, where. despite having traveled 77 cm downstream from BT the two beams still overlap almost entirely. The profles were measured by positioning the detector in the K,, beam ( O 0 ) , closing the slits C d o m to 0.1 mm, and scanning the slits across the beam, then repeating with the detector at the position of the Ka, beam ( -0.065O ).

It was decided. then. to use slits A to reduce the size of the beam. slits B to remove the scattering off of dits .A, and slits C to remove the now-less- overlapping K,, component. This made for a significant decrease in the beam intensity incident on the sample and created a modest background of scattering from slits C, but the improvement in background removal was substantial. as can be seen in Figure 26. The double peak when the dits are wide open is reduced to a single peak, signifying the removal of the Ii,, signal. and the beam's "shouldersn are cut to lower angles when the dits are used this way. Interest ingb the shoulders are not icably asymmetric. being higher at negat ive angles. The source of the asymmetric part of the scattering was found not to be the slits. but in fact the analyzcr crystal. When the detector and analyzer are rnoved in the negative direction, they reach a point where the front edge of the crystal is at 0' and hit by the direct beam. Some of the beam is scattered from this edge into the detector. providing the extra shoulder at negative angles. .-\ similar shoulder does not appear at the positive angles because the back edge of the analyzer crystal is shieided from the direct beam by the Pb sli t descri bed in Section '3.3.1.

3.3.3 Resolution-Lirniting Factors

The incident beam size also plays a role in the scattering pattern produced by the sample. since different parts of the illurninated region of the sample will be at slightly different angles to the detector. This makes any sharp features in the scattering pattern less well-defined. If the sample is turned so its surface is not perpendicular to the beam. as suggested in Section 3.3.1. this smearing will be asymmetric-that is. features at positive angles will be sharper than at the same negative angles or vice versa.

Another aspect of the apparatus which limits the sharpness of the measured scattering pattern is the detector itself. Since the detector has a finite area. it lets in scattering over a range of angles. This range is reduced considerably in the scattering plane through the use of the analyzer, but it still remains quite large in the direction perpendicular to the scattering plane. It is necessary to keep these apparatus-induced effects in mind when analyzing SAXS data.

3.4.1 Nanocluster Size

Analysis Techniques The average nanocluster radius was found from the peak widths of low-resolution, high-angle X-ray powder diffraction data. This was done by fitting each peak to a Lorentzian lineshape of the form?

i! - siits f ù ~ y open : l i ' , - dits partially closed I l ! 1

28 (degrees)

Figure 26: The incident beam with no sample present when al1 dits were wide open (lighter fine) and when closed to minimize background scattering and Cu K,, (darker tine).

where 10 and w are related to the peak intensity and widt h, respectively, and

The Scherrer formula [lj]. 0.9X

t = - Bcosûs '

relates the particle size. t, to the full widt h of the peak at half mai-' ilmum. B. W e can solve for B in terrns of W . noting that the balf-maxima of the Lorentzian occur at q = go k W . Thus B is simply equal to 2w. The Bragg angle. d b , is related to qo by the following:

Ba = sin-' (2) We can then perform a least-squares fit with only lo and u* as adjustable parameters and calculate the nanocluster diameter. t . from the value of W .

The diffraction pattern we actually rneasure can be treated as the sum of several such lineshapes. each with their own Io and W .

Resuits of Analysis The powder diffraction data for Cas - Au is displayed in Figure 27. Five Lorentzian-like peaks appear at the angles characteristic of the FCC gold structure. signifying that the atoms in our nanoclusters are packed in gold's typical crystalline structure. There are also ot her feat ures in our diffraction pattern which are especially prevalent at the Lower angles. These features uise due to scattering from the Iiapton on which our sample is mounted. W e added to our fitting function a sixth. broader Lorentzian plus an arbitrarily selected funct ion of the form. ~ e - ~ ? + ~ + H. Here D. F, G. and H are al1 adjustable parameters. These were included so as to subtract out the additional features and make the peak fitting more accurate.

The fit resuits are summarized in Table 6. The precision of this type of cluster radius measurement is not particularly high. as evidenced by the scatter in t; the Kapton-induced background limits the certainty of our fits. Another source of error is the implicit assumption t hat the clusters all possess identical radii. In actuality, the clusters in the sample follow some size distribution. Each cluster of a different size creates a diffraction pattern with different peak widths, and we measure the sum of dl of those patterns. The Lorentzians fit weil enough to indicate a fairly n m o w size distribution for this sample. CVe con see that almost d of the particles have a radius between 25 and 30 A.

Figure 27: Diffraction pattern of CsS - Au. The solid line is a least-squares fit to five Lorentzians and a Kapton background as discussed in the text.

[ 20, (degrees) 1 ( h k l ) 1 w (A-') ( t ( A ) ]

I Average Radius I 27.0 A I

Table 6: Determination of the C8S - Au nanociuster size from diffraction peak widths.

" 10 20 30 40 50 60 70 1 80

28 (degrees)

Figure 28: Diffraction pattern of Ci& - Au. The solid line is a least-squares fit to seven Lorentzians and a Iiapton background as discussed in the text.

I large clusters I small clusters 1

Table 7: Determination of the Cl8s - AU nanocluster size from diffraction peak widths. At (002), only a sharp peak could be seen, so no rneasurement of the smaller cluster size was made there.

2Ob (degrees) 35.33

.An identical investigation of Cl8S - Au is shown in Figure 28. This data is similar to the previous set in that it consists of the fcc Au peaks atop the

(hkl) (111)

I -

Eiapton scattering. It differs in that there appear to be two independent sets of gold peaks on top of one another: one set of very wide peaks and another of very narrow ones. We infer from this that the sample is made up of two

w (A-') t ( A ) ' -

44.55 64.54 77.90

populations of clusters, small and large. The sizes of both are presented in Table 7. It should be noted that the instrumental resolution. which is on the order of 0.1'. may make a significant contribution to the widt h of the narrower

w (A-') L I

' (002)

(202) (113)

set of peaks. This factor was not taken into account in the calculation of t . so the measured diameter of 130 A should be interpreted as a minimum

t (A) 0.0116

- 0.230 0.315

0.0155 0.00883 0.00962

.Average Radius

possible radius. The actual size may be sornewhat larger. TEM studies of

182 320 294

this material [5] gave an average ciuster diameter of 22.4 .A. which is oot close to either of the values we rneasured. This difference is not Fully understood. but is likely due to variations in the sample preparation methods. In general. cluster dimeters in the range of 15 to 200 .A have been reported pl]. so the values we measured are not unreasonable.

244 1 0.176

6.23 .&

-

12.3 8.97

130 A

ÇVe would not be able to make separate rneasurernents of the two different cluster &es if not for the fact that they are so disparate in value. Were the two populations more alike in size, the sharp and wide peaks would not be so clearly distinguishable from one another. The huge difference in sizes raises the question of how the two populations are distributed in the sample. Are the two types of clusters mixed together throughout, or does the sample have one region of small clusters and another region of large ones? To answer this, we cut down the size of the Xray beam so that it illuminatedonly a fraction of the sample, and measured the diffraction with the beam on six different sections. The results are presented in Figure 29, and show the two populations to be separated. In ( a ) and (f ), the beam was located on the outside edges of the sample, and there we find only large particles (narrow peaks). In (6) through (4, the beam was in the center of the sample, where only s m d particles (wide

16.1 J

28 (degrees)

Figure 29: Diffraction patterns from 6 different regions of the - AU Sam- ple.

peaks) are found. In (e )? the beam is apparent- at the interface between the two regions. The two sets of clusters must have separated when the sample was deposited on the Kapton.

The nanocluster size cm also be found with small-angle S-ray scattering. The results of such a study for both samples will be discussed in the next section.

3.4.2 Intercluster Spacing

Analysis Techniques In order to determine the intercluster distance of each sarnple. we performed a least-squares fit of a calculated small-angle scattering intensity to the measured scattering. The scattering intensity as a Function of the scattering angle. 20. is given by [23]

sin (qr)

Qr 1' (where q = $ sin (y) ), provided that the electron density is spherically symmetric-that is. p(r) = p(r ) .

To salve for I ( 2 0 ) . then. we must know the form of p(r ) . While p ( r ) is not actually spherically symmetric. and while it is impossible to know p(r ) exactly. we can get satisfactory results by using the approximation.

This is shown schematicaI1y in Figure 30. R is the cluster radius and L is the effective extension of the chains off the cluster. The distance between the centers of two neighboring clusters is 2 L + ZR. The origin is placed at the center of a cluster. The Au electron density is quite high inside the cluster. and is much srnaller in the chains. Thus it drops substantially at a distance R from the origin. The low-density region, where there are chains but no clusters. extends to the surfaces of the nearest neighbors. which are al1 approrimated to be at the same distance. 2L + R. The spherical shell containing the nearest neighbors has a higher-than-average electron density. but is not as high as the pure Au density. p l . The rest of the sample, at a distance beyond 2L + 3R. is assumed to be at the average electron density of the material.

Figure 30: The form of p ( r ) used in calculating the small-angle scattering intensity. ( a ) A simplistic model for the arrangement of the clusters and chains. ( 6) The sphericdy averaged electron density for t bis model.

üsing this form of p ( r ) gives

SOL d r P P ( r ) sin (qr) -

- s i n ( q ~ ) - Rcos(qR) 1 Is in ( q ( 2 ~ + J R ) ) - ( 2 L + :IR) cos ( q ( 2 L + 3 R ) )

We can use this result in Equation 3 above. -4s in Section 2.4.4. we can define al1 of our electron densities relative to 7 by adding a delta funct ion at y = 0. an angle at which we do not measure. For the purposes of this calculation. p is taken to be equal to the average electron density of one cluster and its associated chains. With that in rnind, we can use the volume fractions of the clusters and chains to find the values of pz and p~ in terms of p l . R. and L. It turns out that

R3

and if we assume hexagonal close-packing, so that each cluster has 12 nearest neighbors.

7R3 + 6R2 L - 6RL2 - 6L3 13R3+24RZL+ 12RL2

Another factor to account for is the finite s i x of the detector, Because the detector covers a small but non-negligible range of scattering angles. the intensity distribution we measure is in fact a -smeared7 version of the actual intensity distri but ion. .-\ccordingly, the calculated scattering intensities should be smeared as well. For sirnplicity. we accounted for the detector's extent in one direction only. If the detector h a o height, h. in the y-direction and is centered at y = O. then the measured intensity is

We assume also that the incident beam is at a height y = O. so

When the detector is positioned at a distance, dd,, from the sample and at an angle in the x-r plane, 20, from the incident beam direct ion,

for small scattering angles, 4. This integral was calculated numerically, and since the integrand diverges at Q = 20, a change of variables was necessary.

where a = cos-' (y ) . A cornputer program uçed this equation to calculate Im,,,d(20) for the purpose of comparing to the data. The equation depends on only three adjustable parameters: p l , R, and L. along with the fixed pararn- eters, h. dder9 and A. Two other adjustable parameters are added to accoiint for irn precisions in the experimental apparat us: 2BoflSet, to adjust for misalignmen t of the detector. and Io&,, to reproduce the -da&" signal registered when n o X-ray photons are entering the detector.

To put the data in a f o m where it could be compared with the calculation. we needed to separate the transmitted and scattered beams in our measurement. To find the scattered beam intensity, we recorded the intensity distribution with and without the sample present. as shown in Figure 31. and then subttacted the latter from the former. [t c m be seen in Figure 31 that at the lowest angles. the two curves are identical. This is because the very intense transmitted beam dwarfs any effects of absorption or scattering at these angles. Subsequently. ail of the scattering information is lost in this region. Luckily, where the transmitted beam is not present. the scattering signal stands out clearly above the background.

Results of Analysis The best fit results for the background-subtracted CsS - Au data are shown in Figure 32. The fit gives a cluster radius of 27.1 .A. in good agreement with the value of 27.0 .& determined from the diffraction measurements presented in Section 3.4.1. With L = 28.2 .k in the fit. the intercluster spacing is 2 L + 2R = 55.3 A. The data shown in Figure 31 were collected with the sarnple placed with its surface at a low angle (- 5') to the incident bearn. so as to maximize the area of the sample illuminated by the beam. It was hoped that this would enhance the scattering, but the signal was unchanged from a measurement with the sample oriented perpendicular to the beam. The only difference was a slight asymmetry in the scattering which can be seen between -1" and 1" in Figure 31. where the scattering is higher a t negative angles than at positive angles. This asymmetry, which can be predicted through geometrical arguments given the angle between the sample surface and the incident beam, was not seen in the data when the surface was perpendicular to the beam. That data was fit with nearly identical parameters, R = 25.8 and L = 29.0, for an intercluster distance of 54.8 -4.

20 (degrees)

Figure 31: SrnaIl-angle scattering measurement of CsS - Au ( solid line ) and a similar measurement with no sample present for the purpose of background subtraction (iighter line).

28 (degrees)

Figure 32: Small-angle scattering of Cas - Au. The solid line is a least-squares fit to the data points, with pl = 1.90 x IO-^. R = 27.1. L = '18.2. 'l$,nse, = 0.030, and ioffSet = 0.029.

In order to account for the two separate populations of clusters in the CI8s - Au sampie. the fitting program was expanded to allow for a second set of p l , R. and L parameters. The results. with the populations shown inde- pendently and together, are presented in Figure 33. The measured radius of the larger clusters. 130 a by powder diffraction in Section 3.4.1. is somewhat greater than the value of 115 A found by fitting the ShXS data. Furthermore. the smaller clusters are found to have a radius of 7.96 .i with this technique and a radius of 6.21 A with the previous. The cause of the discrepances is uncertain. The intercluster spacings of the small and large clusters are found to be 37.7 and 218 -4. respectively.

It appears. then. that longer chains do not necessarily separate the clusters more than shorter ones. since Cl& - Au had L z 9 A while Cas - Au had L x 29 .A. The chains in Cl& - Au may cootain more gauche defects. and hence are not as straight as the chains in Cas - Au. Another possibility is that the chains on one cluster in Cl& - Au are more completely interdigitated with the chains on another cluster than they are in Cas - Au. The relative concent rat ion of gold to alkanet hioiate during sample preparat ion. a condition which is known to affect R ['21]. may dictate the extent to which the cluster surfaces are separated from each other by the chains. .AISO. the material on which the sample is deposited-Kapton. in our case-may affect the intercluster spacing.

While the fits in Figures 32 and 33 are sat isfactory, t hey are far from perfect . This raises the question of how useful it was to include the effects of the finite height of the detector as described above. To answer this. the scattering intensity calculation was performed without the smearing taken into account. This is shom in Figure 34. Clearly. the fit in Figure 32 is vastly superior. It appears that the fits could be made even better by including more factors such as the finite width of the detector and the finite height and width of the incident beam. Each addi t ional correct ion requires anot her integrat ion and as such begins to tax the limits of available computing power.

3.4.3 Nanocluster Shape and Size Distribution

Aside from separating the Ci$ - Au clusters into two general groups wit h very different radii, no information about the cluster size distribution could be obtained for eit her sample from the srnail-angle scat tering measurements we made. nor could any information about the cluster shape. To include a treatment of t hese characteristics in our data analysis, we would have to use a more complicated form than the one given by Equation (4) and depicted in Figure 30(b) for the electron density. The primary change would be in removing the discontinuities at R, 2L + R, and 2L + 3R. The electron density

28 (degrees)

Figure 33: Smd-angle scattering of ClsS - Au. Solid Iines are least-squares fits to the data points. ( a ) pl = 1.21 x IO-', R = 7.96, L = 10.9. (6) pl = 1.18 x IO-', R = 115, L = 8.50. ( c ) The sum of ( a ) and (6). For aI1, 2OoSer = 0.019, = 6.53 x IO4.

28 (degrees)

Figure 34: Small-angle scattering of CsS - Au without finite-size detector cor- rection in calculation (solid f ine ) . Parameters used are listed in the caption of Figure 32.

should really fa11 or rise continuously, at a rate determined by the cluster shape. the size distribution of the clusters, and the density distribution of the chains off the cluster surface. It is unlikely that the integral of such a function, which is the main component of the scattering intensity calculation. could be performed analytically. While a numerial solution is in principle possible, it is excessively resource-intensive. A sufficient ly realist ic p( r ) would li kely srnear the scattering pattern more than the one used here, so it would be necessary to first account for al1 smearing due to the detector size and the incident bearn size as mentioned in Section 3.4.2. Such a process is infeasible not only due to its corn pleri ty. but also because our measurements lacked a signal-to-noise ratio sufficient for dist inguishing between different shapes or size distributions.

3.5 Ideas for F'uture Studies

..\ few simple improvements could boost the weak scattering signal we measured. Future studies should use samples with a greater thickness so more of the incident beam is scattered. Background scattering could he reduced by placing a di t just in front of the analyser crystal's leading edge. While t his slit would undoubtedly scatter the direct beam just as much. the fraction of that scattering which actually reached the detector would be greatly reduceci. This would allow for studies at lower angles t han current ly possible. where the signal intensity should be even greater.

Future investigations of these materials could include a more thorough sur- vey of the cluster size and spacing for a variety of chain lengths. as well as a study of these two properties' dependences on conditions such as temperature or preparation met hod. With the more powerful analysis techniques descri bed in Section 3.4.3. along with increased scattering signal, these studies could also include shape and size distribution determinations. Since the scattering signal is clearly distinguishable from the background with our apparatus. these materials are good candidates for XIFS studies (described in Section 3.1 2 ) using a synchrotron source.

4 Conclusion Feasibility of Techniques We have seen that a great deal of useful structual information c m be gleaned from variabletemperat ure powder diffraction and small-angle scattering studies of self-assembled monolayers. More precisely. these techniques give insight into the structure and behavior of the surfaces on which the monolayers ase adsorbed. Combined with the results of other types of probes, a reasonably det ailed description of the configurations and behavior of the chains which comprise the monolayers can be developed. With some

minor refinements, the Y-ray techniques we used can and should be applied to other materials of the same sort.

Information About Materials In the metal alkylphosphonate salts. we saw that the chains reside in a tilted configuration at room temperature. We determined that Na samples exhibited two interlayer distances. one where water was present in the inorganic layers and a smaller one where it was not. We also found evidence that at room temperature. ZnPCs does not have an orthorhombic unit cell. and that the structure proposed for MgPC18 does not lead to the rneasured powder diffraction pattern.

When heated. we found that the interlayer distance in the Na and Mg Sam- ples decreases sharply. It increases again upon cooling but does not return to the original spacing, showing the transitions to be irreversible. The temperatures at which these structural changes took place were consistent with previously reported phase transition temperatures for chain melting. In the high-temperature phase. most of the salts appear to be in a srnectic liquid crystal structure in which the layers' interna1 structure is disordered. .A par- t ial or dering was seen w hen the mat erials were cet urned t O room temperat ure. ZnPCs did not enter a liquid-crystal phase at high temperatures. and its interlayer distance expanded. When cooled. the original structure returned. signifying that the transition in this rnaterial is reversible.

In the alkanet hiolate-capped gold nanoclusters. we were able to measure the average cluster size and intercluster spacing, but the data lacked a sufficient signal-to-noise ratio to find the distributions of sizes and spacings or to verify any models of the nanocluster shape. The Cias - Au sample was found to have two very distinct cluster sizes which differed by a factor of 'O. The srnall clusters were grouped in the center of the sample while the large cliisters were located on the edges. The cause of this unusual disparity in cluser sizes is unknown, but may be related to the manner in which the sarnple was deposited on the holder.

Future Studies The main limitation in our studies was a lack of the nec- e s s q .Y-ray intensity to make precise rneasurements. For powder diffraction. the best solution would be to create an intermediate-resolution mode for the diffractometer, where a more reasonable balance of angular resolut ion and signal-t o-noise could be achieved. in the smd-angle scat t ering, t hicker Sam- ples would lead to greater scattering. One means of boosting the intensities for both techniques would be to use a more powerful source, such as a synchrotron. Studies of the dynamics of the ahethiolate-capped -4u nanoclusters via .Y- ray Intensity Fluctuation Spectroscopy axe recomrnended.

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