Studying Polymer Interfaces Using Neutron Reflection - American

Chapter 4

Downloaded by GEORGETOWN UNIV on February 13, 2017 | http://pubs.acs.org Publication Date: July 30, 1999 | doi: 10.1021/bk-2000-0739.ch004

Studying Polymer Interfaces Using Neutron Reflection 1

2

2

D. G. Bucknall , S. A. Butler , and J. S. Higgins 1

ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxon OX11 OQX, United Kingdom Department of Chemical Engineering, Imperial College, London SW7 2BY, United Kingdom

2

Neutron reflection has been used to study the interfaces between the melt phases of crystallisable polymers as well as real time interdiffusion of polymers and oligomers. Both systems are experimentally demanding and have required the use of specialised cells and data collection procedures. The interfacial widths for a number of polymer systems have been determined and the Flory Huggins interaction parameters obtained. In addition, the interdiffusion process has been followed for a polystyrenepolystyrene system above its T and also for a polystyreneoligostyrene in-situ in real time using very rapid reflectivity scans. g

The interfacial behaviour between the component polymers in blends to a large extent controls the bulk polymer blend characteristics. The understanding of these interfaces is therefore of vital importance. The neutron reflection (NR) technique is ideally suited to study polymer interfaces since it provides a composition profile perpendicular to the interface with a resolution on a sub-nanometer length scale. From self consistent mean-field theory for immiscible homopolymers of infinite molecular weight the interfacial width (w) is is related to the Flory Huggins interaction parameter (χ) by w=(2a)/^[βχ {a is the segment length) [1]. Therefore, simply by measuring the interfacial width it should be possible to extract directly the FloryHuggins χ parameter. In reality the situation is not so simple because thermally

© 2000 American Chemical Society

Cebe et al.; Scattering from Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

57


58 excited capillary waves broaden the interface so that the observed width as determined by NR contains a contribution from two superimposed values, which need to be separated [2]. The broadening effect of these capillary waves is however well understood so that their effect can be calculated and a true estimate of the χ parameter obtained. The interfacial width between crystalline polymers has been measured using NR since many of the most important industrial commodity polymers are semi-crystalline in nature. The surface of crystalline polymers are by their very nature macroscopically rough at room temperature and this has forced measurements to be made in-situ at temperatures above the melt temperatures. For miscible systems the interface between initially separated materials will develop by diffusion mechanisms. The distance over which this diffusion occurs can often mean that several techniques are required to follow the whole process. At longer annealing times the dominant mechanism is often Fickian diffusion, and this has been investigated by techniques able to observe long length scales such as dynamic secondary ion mass spectroscopy (DSIMS) [3-5], nuclear reaction analysis [6-8] or Rutherford back scattering [9,10], These techniques typically have a resolution of approximately 10 nm at best and are therefore not normally suitable for studying the initial stages of the diffusion process where high resolution techniques are required. NR has been widely utilised for the detailed study of interfacial diffusion and a number of studies have tested the early time regime predictions of the reptation theory [11,12]. Most of the NR studies reported in the literature have been performed using high T polymers where the samples are annealed and then quenched to room temperature so as tofreezein the structure and enable a full analysis to be performed. However this method does have limitations for studies involving small molecules where diffusion may occur at room temperature and the interface is no longer static, thus preventing this classical approach to NR measurements. This limitation has to a large extent been overcome by making reflectivity in-situ and in real time [13,14] g

Polymer Interfaces in the Melt Neutron reflection (NR) has been successfully applied to the study of interfaces formed between high molar mass amorphous polymers. Such experiments are normally conducted at room temperature (RT) where the interfacial structure of the samples, after annealing, is frozen in (see for example [15] or [16]). There is considerable interest in the interfacial behaviour of crystalline polymers but, until recently, it has not been possible to study such materials by NR. The difficulty lies in the sample required for reflectivity. Neutron reflectivity samples must be microscopically as well macroscopically flat since at a glancing incident angle a large area is sampled and averaged over by the neutron beam. Whereas thin films of amorphous polymers are naturally flat once spin coated from solution onto optically polished substrates, the formation of crystallites causes such thin films of semi-


59


crystalline polymers to become macroscopically rough (see Figure 1). At RT this surface roughness causes drastic loss of specular reflection, making NR measurements at best very difficult but more likely impossible. The problem is not relieved by simply heating the films above the crystalline melt temperature [17]. Although this has the effect of removing molecular roughness associated with the polymer crystallinity, the surface still suffers from residual long range waviness, which adversely affects the reflectivity profile.

Figure 1; Surface offor a thin layer of d-iPP measured using an α-step profiling instrument at RT, showing the macroscopic roughness of a semi-crystalline polym film (reproduced with permissionfromreference 18.

One solution to overcome these problems is to observe the polymers in the molten state when sandwiched between a polished silicon substrate and a heated trough which contains a bulk layer of one of the polymers [13,19-21]. This produces both molecularly smooth and macroscopically flat samples allowing accurate determination of the interfacial width and profile. A simple heating cell, shown in Figure 2, has been developed which allows such experiments to be carried out. This cell consists of a brass trough into which a plug of hydrogenous polymer is moulded.


60


A silicon wafer, coated with a layer of deuterated polymer, is clamped face down on to the surface of the polymer plug. The cell is heated by means of thermostated cartridge heaters in the brass base and has been designed such that the neutron beam passes through the silicon wafer, with approximately 90 per cent transmission. Thin films of the deuterated semi-crystalline polymers are prepared by spin casting hot solutions of the polymer directly onto the polished silicon substrate.

Figure 2: Schematic illustration showing a section through the polymer heating used for studying crystalline polymer interfaces (reproduced with permission f reference [19]).

The assembled cell is heated to the desired temperature, and aligned before data collection occurs. Although there may be thermal loss from the top surfaces of the cell, it has been found that the polymer within the cell attains and holds the required experimental temperature within approximately 10 minutes of heating. To prevent thermal degradation occurring during the experiment, the whole cell is housed inside an inert atmosphere box with neutron transparent quartz windows front and back. Alignment of the cell is achieved using the neutron beam, so there is always a delay of at least 30 minutes from the point at which the heating is started to when reflectivity data collection begins. All the data reported here have been collected using either the CRISP or SURF reflectometers on the ISIS pulsed neutron source at the Rutherford Appleton Laboratory. These instruments view a liquid hydrogen moderator providing neutrons in a white beam with a wavelength of 0.5-6.5 A. To achieve a large Q range (Q=(4πsin0) /λ ) three different angles are measured for each sample, with the pre-sample collimation slits varied so that at each angle a constant resolution and


61


illuminated area is maintained. Cell calibration, required for the data reduction normalisation factors, is obtained by taking transmission measurements of the Si block. A combination of both non-linear least squares fitting routines and maximum entropy methods have been applied in the reflectivity data analysis [16,22]. Reflectivity measurements using the cell were first performed on a sample of amorphous deuterated polystyrene (dPS) in contact with low density polyethylene (LDPE) at 150C [19]. The characteristics of the polymers are given in Table I. This system had been chosen since it is one of only a few that contain semi-crystalline polymers which have been reported in the literature.

Table I. The characteristics of polymer used in melt interface studies.

M

MJM

dPS

190k

1.08

- linear low density

LDPE HDPEi HDPE LLDPE

44k 156k 58k 150k

5.6 8.2 6.8 1.02

deuterated polypropylene - isotactic - atactic

d-iPP d-aPP

274k 111k

5.5 1.5

Polymer

w

deuterated polystyrene polyethylene - low density - high density

2

n

The interfacial width obtained fromfittingthe dPS-LDPE NR profiles is given in Table II. This measured interfacial width is described by a self-consistent mean-field theory, which is broadened by thermally excited capillary waves [2]. The measured interfacial width is given by Gaussian quadrature addition of the intrinsic (unbroadened by capillary waves) interfacial width, Δ , and the interfacial width associated with the capillary waves, A . This gives:0

c

Δ Δ

where

2 Π +

0

Δ

2

(1)

c

(2)

0

2

{2π/Α ) 0

and

ΔΙ

•Μ {ΐπ

/Ο* +{ΐπ

(3) Α,)* )


62 The capillary wave broadening is therefore dependent on the in-plane coherence length of the neutron, λ « 20μηι, the dispersive capillary length, a = ^7cy ct A , 1

£

d

Q

the Hamaker constant, A, and the interfacial tension γ = avk T^j χ/β Ό

g

(α is the

1

segment length and v* is the monomer volume), and d is the layer thickness. This approach has been applied to evaluate the effects of capillary wave broadening on the dPS-LDPE system [19]. The values of χ and γ obtained (see Table II) have been shown to agree well with the spread of data found in the literature and give considerable confidence in the use of the cell for applications of this method to obtain accurate values of χ and γ for other polymer pairs. 0


0

Table II. NR measured interfacial width, w, Flory Huggins parameter, χ, and interfacial tension, γ . 0

Polymer pair Τ (°C)

w (nm)

X

3.0 ± 0.9

0.14±0.09

2

y (mJm ) 0

9.0 ±2.0

dPS-LDPE

150

diPP-HDPEi

175 200 225

6.0 ± 0.6 7.0 ± 0.7 5.7 ±0.1

(1.6±0.1) x 10 (1.0±0.2)x ΙΟ" (1.9±0.1)x 10"

175

9.9 ±0.1 9.1 ±0.2

(4.4±0.1)x 10" (5.1±0.2)x 10"

daPP - LLDPEi - HDPE 2

2

2

2

3

3

2.68 ± 0.08 2.28 ± 0.03 3.23 ±0.05 1,42 ±0.02 1.52 ±0.03

A majority of the data collected using this cell has been with a polypropylene (PP) - polyethylene (PE) system, using a combination of two PP tacticities and a number of PE's of varying densities from linear low density PE (LLDPE) to high density PE (HDPE) [18,20,21]. Deuterated isotactic PP (diPP) is semi crystalline with a melt temperature of 157°C, while deuterated atactic PP (daPP) is amorphous. The melt temperatures of the LLDPE and HDPE used are 102 and 131 °C, respectively. Reflectivity profilesfromall the systems were obtained at temperatures well above the melt and glass transition temperatures of the polymers. Data from the diPP-HDPEj system have been collected at 175, 200 and 225 °C and the interfaciai widths obtained. The fitting revealed that in some cases the diPP does not fully wet the silicon [21], but the diPP layer was sufficiently thick to prevent complete dewetting


63 from the substrate, and the film homogeneity and interface with the HDPE were believed to be unaffected by this process. By applying Equations 1-3 to the results of thefittedreflectivity data, the values of the measured interfacial width together with the evaluated values of the χ 1

parameter and γ given in Table II were obtained. The interfacial widths measured for daPP-HDPE and daPP-LLDPE are seen to be significantly larger than that for diPP-HDPE , indicating that daPP-PE polymers are more miscible as indicated by the reduction in the calculated χ value. The reason for this increased miscibility is unclear, and is currently under investigation. The similarity in miscibility between daPP with HDPE or LLDPE is expected since the LLDPE is only lightly branched (18 branches per 1000 backbone carbon atoms compared to 3 for the HDPE) and therefore similar to the extent of branching observed in HDPE. Based on the limited number of points measured there does not appear to be any systematic temperature dependence of the interfacial parameters for diPP-HDPEi in the range 175 ≤Τ (°C) ≤ 225, as may have been expected. 0

2


1

Diffusion Studies

Until recently the use of NR to study miscible polymers has been limited to the investigation of diffusion processes that take place well above ambient temperature. Using the reflectometers at ISIS a full reflectivity profile covering a momentum transfer, Q, from approximately 0.007 - 0.6 A requires measurements at 3 incident angles. This typically takes between one to two hours depending on the sample. Any change in the interface or sample composition profile during this measurement time can corrupt the data. Therefore, to measure diffusion processes has conventionally required the polymer structure to be frozen in. For amorphous polymers, where the glass transition temperature (T ) lies well above ambient, this is easily achieved by annealing for a given time above T and then rapidly quenching the sample to RT, before a full reflection profile is collected. This procedure is repeated successively at various annealing times to build up the time dependence of the diffusion process. However, for systems where the interface remains mobile at RT this approach is not adequate and either a quench to below RT must be made to immobilise the system, or in-situ real time reflectivity measurements must be performed. By utilising the high flux available on the SURF reflectometer, a methodology for conducting neutron reflection experiments in real time has been developed in order to study the initial stages of the interdiffusion of polymers. This is achieved by taking reflectivity measurements at the annealing temperature, but restricting the data collection to a limited Q range from one angle [14,18]. Using a white beam of neutron wavelengths, a partial reflectivity profile for the specified incident angle is obtained. Data collection is therefore restricted at the lower limit to the time required to reduce the error in the data points to be adequate enough to enable the features to be observed and be fitted. Rapid data collection is therefore possible and the time taken to collect such partial reflectivity profiles, with adequate statistics to extract interfacial widths, -1

g

g


64 has been reduced to six minutes. By decreasing the incident angle during the experiment the restricted measurement window is progressively moved to low Q ranges, enabling collection of data from different portions of the full reflection profile. This allows only the most significant regions of the reflectivity profile to be measured. The viability of this technique has been demonstrated by investigating the interdiffusion of high molar mass deuterated and hydrogenous polystyrene (hPS and dPSi). Subsequent work has extended this methodology to study the ingress of oligomeric polystyrene (OSt) into deuterated high molar mass polystyrene (dPS ). The characteristics of the polymers used are given in Table III.


2

Table III. The characteristics of the polymers used in real time neutron reflection studies. Polymer deuterated polystyrene

M dPS! dPS OSt hPS

2

oligomeric styrene hydrogenated polystyrene

w

40k 101k 1.11k 49k

MJM

Tg/x:

1.02 1.02 1.1 1.03

84 103 27 104

n

Polymer-Polymer Interdiffusion

The interdiffùsion of polystyrene hPS and dPSi has been studied at 115°C. Since these polymers are immobile at RT it is possible to prepare a bilayer, and measure a full three angle reflectivity profile of the sample before any interdiffùsion occurs. The sample is then placed onto a preheated sample stage and partial reflectivity profiles are measured every six minutes using fixed angle restricted Q window measurements. By incrementally decreasing the angle of incidence it is possible to monitor the decrease of the interference fringe amplitude, which is associated with interdiffusional processes, within the Q window. After annealing for almost four hours, the sample was removed from the heating stage and quenched to RT before finally collecting a full three angle NR profile. A limited set of all the reflectivity profiles are shown in Figure 3.



65

Figure 3: A selection of reflectivity profiles for the hPS-dPSi bilayer measured in time (solid symbols) at 115X1 and at RT (open squares) before and after annea and j respectively). The real time reflectivity profiles were measured at a fixed with 6 minute count times. The mean time for the profiles plotted are 5(b),32 (d), 93 (e), 124(f),155 (g), 186 (h) and 212 (i) minutes. The solid lines are fi assuming a model as described in the text (reproducedfrom reference [14]).


66


Due to the restricted Q range in the data from the real time measurements, interpretation of the NR data is limited to specific models and functional form fits based on the fits to the 'as made' sample. The interfacial widths were determined from the reflectivity data by fitting the profiles with a standard two layer model and assuming a simple Gaussian interfacial profile between the dPS1 and the hPS. The interfacial profile is seen to be symmetric as may be expected for a system where the polymers are of approximately equal molecular weight.

Figure 4: A log-log plot of time dependence of interfacial width of hPS-dPS1 (reproducedfrom reference [14]).

The width of the polymer interface as a function of annealing time is shown in Figure 4 and the magnitude of the interfacial widths especially for the longer annealing times have been confirmed using DSIMS. For times approximately t > 6000s the interfacial width, w, increases with a t dependence on as indicated by the solid line in Figure 4. Assuming that the diffusion coefficient, D, is given by the relationship w= faDt) [11], a value of the diffusion coefficient for this system of D 17

1

= (1.7±0.2) χ 10- cmV is obtained from the gradient of the linear region of a plot of w versus t [14]. This compares favourably with published literature values for PSA


67 dPS interdiffusion coefficients, although is perhaps small given the comparatively moderate molecular weights used here. Given this value of D, the reptation time for these polymers can be calculated using the formula τr =

Nb

Π 1]> where b is

the segment length (= 6.7 A), and Ν is the degree of polymerisation. This gives x (dPSi) = 3223+363 s and Tr(hPS) = 4333±489 s. The time behaviour of the interfacial width for t > τ shows the expected t dependence predicted by Fickian diffusion. The expected t dependence that has been predicted for times in the regime x r < t < x r (where x is the Rouse time [23]) is observed and shown by the solid line in r

/2

Γ

A

R

figure for t < 7000s. The calculated x for these polymers ( τ = dr/d,9 where d R

R

T

is the polymer tube diameter ( d = 57 A [11])) is 215+23 s. The expected change in time dependence at the Rouse time therefore will not be observed in these experiments due to the time resolution of the reflectivity measurements.


T

Small Molecule Diffusion The study of small molecule diffusion into polymers using NR requires a slightly different technical approach compared to polymer-polymer systems (described above), since such diffusion processes can take place at RT. To prevent diffusion occurring before data collection can be instigated the polymer and small molecule penetrant have to remain apart. This has been achieved by designing a cell in which an inverted silicon wafer, coated with the deuterated polymer, is held above but separate from a container filled with the penetrant (see Figure 5). The cell can be heated to the experimental temperature and aligned, before remotely raising the container into contact with the silicon and immediately beginning data collection [14,18]. Using such a cell the interdiffusion of oligomeric styrene (OSt) into high molar mass deuterated polystyrene (dPS ) at 65°C has been studied. The polymer characteristics are given in Table III. As before, fixed angle partial reflectivity profiles have been collected every 6 minutes. As for the real time hPS-dPSi measurements, the incident angle was incrementally reduced with time from 0.8-0.5°, in order to progressively move the window in Q to lower ranges. Like the hPS-dPSi NR data, interpretation has been carried out using constrained models and functional form fits because of the restricted Q range. However, the interfacial profile between OSt and dPS is more complex than the simple polymer-polymer case and could only be modelled using a highly asymmetric interfacial profile, which is qualitatively similar to predictions from Case II diffusion theory [23-26]. The asymmetry in the interfacial profile is modelled by two discontinuous error functions so that the neutron scattering length density is given by: 2

2


68

// x< x then Q


//Λx

Q

then

p(x) = |^ - ^

p(x) = [p^-f

+p

2

(4)

κ-

where erfc(x)-1 - erf(x) and all other variables are defined graphically in Figure 6. This functional form has been confirmed by modelling the data using a bilayer with an interface made up of a number of thin layers. This discontinuous error-functional form is applicable for the early and intermediate annealing times, but begins to break down for longer times (t > 140 minutes) where such a simple model of the diffusion process cannot fully describe the data.

Figure 5: Schematic illustration of the heatable cell used to study small molec ingress into high molecular weight polymers (reproducedfrom reference [18]).



69

Figure 6: Schematic illustration of the discontinuous error functional form used model the 0St-dPS2 data (reproducedfrom reference [18]). These asymmetric interfaciai profiles show that the interfacial width on the dPS side of the interface is much larger and more extended than that on the OSt layer side, creating a profile with a diffuse tail and an otherwise sharp interface. This confirms that the oligomer diffusion into the polymer is much faster than the polymer diffusion in the opposite direction as may be expected from Case II diffusion theory. [27,28] The time dependent behaviour of the error function widths used to describe the scattering length density profile are shown in Figure 7. The width, w/, on the dPS side of the interface, which describes the OSt diffusion into the dPS , appears to form instantaneously in the time resolution of the reflectivity measurements and then gradually increases with time. The error function width, w , which describes the dPS diffusion into the oligomer, is initially much smaller, but also shows an increase with time. The position of the interface is seen to move towards the polymer suggesting that the system has fully swollen before the first measurement, and what is observed in the time scale of these measurements is the dissolution of the polymer. The change in interfacial position x (t = 0)-x (t) shows a t dependence as shown in Figure 8. The total width of the interface at longer times for such asymmetric systems is expected to show a Φ dependence [23], that is related to the small molecule diffusion coefficient by w=D t. In this case the oligomer is the smallest molecule, so taking w=w1+ w , gives a value of D for the OSt in this system at 65°C of 8 (± 1) χ 10cmV [14]. This time dependence relationship holds for the case where time is larger than the small molecule reptation time, T (S), and the polymer chains behave like a transient network swollen by the oligomer chains. This value of the diffusion coefficient would give x (S) equal to 20 seconds. Under these circumstances it is not expected to see the change to different time dependent behaviour at t < x (S) as predicted by theory [23]. 2

2

2

2

0

2

0

s

17

2

s

1

r

T

r



70

Figure 7: The variation of the interfacial width as a function of annealing tim obtainedfrom the discontinuous error functional form of the interfacial profde mo used tofita selection of the reflectivity data obtained for the OSt-dPS syste (reproducedfrom reference [14]). 2



71

Figure 8: Plot of shift in interface, x , as function of square root of time, showing dependence indicated by the solid line through the data (reproduced from refere [18]). 0

Conclusions NR has been demonstrated to be widely applicable technique for detailed studies of polymer interfaces. The requirement for flat and smooth samples has often been thought of as a limitation to the applicability of the technique. This chapter has described some of the work which has been carried out on systems which up to now have not been studied using the NR technique due to problems associated with obtaining adequate samples. The interfacial widths from semi-crystalline polymers have been determined allowing Flory-Huggins χ parameters and interfacial tension values to be extracted by measuring these samples at elevated temperatures well above the crystalline melt temperature. Further to these studies of immiscible systems the kinetics of the early stages of diffusion process has been observed in-situ in real time on miscible systems. Rapid data collection procedures with reflectivity curves obtained every six minutes



72 have been demonstrated on the test system of polystyrene-polystyrene and a square root time dependence on the interfacial width observed. This has allowed a diffusion coefficient to be extracted which is in close agreement with published values for this system. Oligomer-polymer diffusion using this in-situ real time technique has also been observed and the interfacial profile measured as function of time. The asymmetric interfacial profile is in qualitative agreement with Case II diffusion theories where swelling and dissolution of the polymer by the small molecule penetrant occurs. With current neutron sources the times of data collection for each partial reflectivity scan will remain of the order of minutes. However, with the advent of the next generation of high intensity neutron sources being planned or built around the world significant advances can be predicted for these real time measurements. 'Time will telP as the saying goes.

References 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

17. 18.

Helfand, E.; Sapse, A. M . J. Chem. Phys. 1975, 62(4), 1327-1331. Sferrazza, M.; Xiao, C.; Jones, R. A. L.; Bucknall, D. G.; Webster, J.; Penfold, J. Phys. Rev. Lett. 1997, 78(19), 3693-3696. Whitlow, S. J.; Wool, R. P. Macromolecules 1989, 22(6), 2648-2652. Whitlow, S. J.; Wool, R. P. Macromolecules 1991, 24(22), 5926-5938. Agrawal, G.; Wool, R. P.; Dozier, W. D.; Felcher, G. P.; Zhou, J.; Pispas, S.; Mays, J. W.; Russell, T. P. J. Polym. Sci, Part B: Polym. Phys. 1996, 34(17), 2919-2940. Payne, R. S.; Clough, A. S.; Murphy, P.; Mills, P. J. Nucl. Instrum. Methods Phys. Res., Sect. Β 1989, 42(1), 130-134. Reiter, G.; Steiner, U. Journal De Physique II 1991, 1(6), 659-671. Shearmur, T. E.; Clough, A. S.; Drew, D. W.; Vandergrinten, M . G. D.; Jones, R. A. L. Physical Review Ε 1997, 55(4), R3840-R3843. Composto, R. J.; Kramer, Ε. J. J. Mater.Sci.1991, 26(10), 2815-2822. Green, P. F.; Palmstrom, C. J.; Mayer, J. W.; Kramer, E. J. Macromolecules 1985, 18(3), 501-507. Karim, Α.; Mansour, Α.; Felcher, G. P.; Russell, T. P. Phys. Rev. B: Condens. Matter 1990, 42(10), 6846-6849. Kunz, K.; Stamm, M . Macromolecules 1996, 29(7), 2548-2554. Bucknall, D. G.; Butler, S. Α.; Hermes, H. E.; Higgins, J. S. Physica Β 1998, 241, 1071-1073. Bucknall, D. G.; Butler, S. Α.; Higgins, J. S. Macromolecules submitted. Russell, T. P. Material Science Reports 1990, 5, 171. Bucknall, D. G.; Higgins, J. S. Polymers and Surfaces - A Versatile Combination; Hommell, H., Ed.; Recent Research Developments in Polymer Science; Research Signpost: Trivandrum, India, In press. Higgins, J. S.; Oiarzabel, L.; Fernandez, M . L. ISIS Annual Report 1993, II, A156. Bucknall, D. G.; Butler, S. Α.; Higgins, J. S. J. Phys. Chem. Solids submitted.


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19. 20. 21. 22. 23. 24.


25. 26. 27. 28.

Hermes, H. E.; Higgins, J. S.; Bucknall, D. G. Polymer 1997, 38(4), 985-989. Butler, S.; Hermes, H.; Bucknall, D.; Higgins, J. S. Abstracts Of Papers Of The American Chemical Society 1997, 213(Pt2), 476-POLY. Hermes, H. E.; Bucknall, D. G.; Butler, S. Α.; Higgins, J. S. Macromolecular Symposia 1997, 126, 331-342. Sivia, D. S. Data Analysis - A Bayesian Tutorial, Clarendon Press: Oxford, 1996. Brochard-Wyart, F.; de Germes, P. G. Makromol. Chem., Macromol. Symp. 1990, 40(Dec), 167-177. Hui, C. Y.; Wu, K. C.; Lasky, R. C.; Kramer, E. J. J. Appl. Phys. 1987, 61(11), 5129-5136. Hui, C. Y.; Wu, K. C.; Lasky, R. C.; Kramer, E. J. J. Appl. Phys. 1987, 61( 11), 5137-5149. Rossi, G.; Pincus, P. Α.; de Gennes, P. G. Europhys. Lett. 1995, 32(5), 391396. Fernandez, M. L.; Higgins, J. S.; Penfold, J.; Shackleton, C. J. Chem. Soc., Faraday Trans. 1991, 87(13), 2055-2061. Bucknall, D. G.; Fernandez, M . L.; Higgins, J. S. Faraday Discussions 1994, 98, 19-30.


Studying Polymer Interfaces Using Neutron Reflection - American

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