Small angle neutron scattering with nuclear polarization on polymers

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Small angle neutron scattering with nuclear polarization on polymers

H. Glättli, C. Fermon, M. Eisenkremer, M. Pinot

To cite this version:

H. Glättli, C. Fermon, M. Eisenkremer, M. Pinot. Small angle neutron scattering with nuclear polarization on polymers. Journal de Physique, 1989, 50 (17), pp.2375-2387.

�10.1051/jphys:0198900500170237500�. �jpa-00211068�

Small angle ^neutron scattering ^{with nuclear} polarization ^on polymers

H. Glättli (1), ^C. Fermon (1), M. Eisenkremer (1), ^{and M.} Pinot (2)

(1) Service de Physique ^{du Solide et} de Résonance Magnétique, CEN-Saclay, F-91191 Gif-sur- Yvette Cedex, ^France

(2) Laboratoire Léon-Brillouin, CEN-Saclay, F-91191 Gif-sur-Yvette Cedex, ^France

(Reçu ^{le 17 avril} 1989, accepté ^{le 26 mai} 1989)

Résumé.

On

reformulé le concept de variation de contraste due à la polarisation ^nucléaire

dans le cadre de la diffusion de neutrons

petits angles (DNPA)

^des polymères

^solution.

Des signaux ^{de DNPA ont} été obtenus provenant ^du polystyrène

solution dans le toluène solide deutéré. Les noyaux d’hydrogène ^{ont été} polarisés dynamiquement par effet solide. En utilisant

faisceau de neutrons

polarisés, ^le signal de l’échantillon

polarisé

intensité doubler par

polarisation ^des protons ^{de 50 %.}

Abstract.

The concept ^{of contrast} variation due to nuclear polarization has been reformulated with the emphasis

^small angle ^neutron scattering (SANS) ^of polymers in solution. SANS has been performed

solid solutions of polystyrene in deuterated toluene. The hydrogen ^nuclei

have been polarized dynamically by the solid effect. Using

unpolarized ^neutron beam,

nuclear polarization ^{of 50 %} enhanced the intensity of the small angle scattering by

factor of 2 with respect ^to

non-polarized sample.

Classification

Physics ^Abstracts

36.20

61.12E - 61.40K

76.70E

Introduction

Thermal neutron scattering has become an important tool in many parts ^{of condensed matter} research, whether it be physics ^{of the solid and} liquid ^state, chemistry ^or biology. Of the many

interesting properties of thermal neutrons, spin-dependent scattering gives ^a particular ^handle

to obtain results not accessible by other methods. The spin-dependence ^{is of course most}

useful in those cases where some average ^over nuclear spin ^{variables is non-zero. The} simplest example is nuclear Zeeman order, commonly ^{called nuclear} polarization, where the nuclear

magnetic ^{moments are} preferentially aligned along ^{the direction of an} applied ^{field. But in the}

absence of an (effective) ^{external field,} the nuclear moments may also order spontaneously,

driven by ^their dipolar interaction. A review of neutron scattering and nuclear magnetism ^can

be found in references [1, 2]. ^A general treatment, including electronic magnetism, ^has already ^been given in reference [3].

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500170237500

Of all common nuclei, ^the proton ^has by ^{far the} largest spin-dependent scattering. ^{This is}

the main reason why protons have been used in the pioneering experiments ^on Bragg scattering with Zeeman order [4] ^{and with} long range dipolar ^order (nuclear antiferromagnet- ism) [5].

It is a happy coincidence that protons ^{can be} (and ^have been) polarized ^{to a} high degree ⁱⁿ

many substances. This is partly ^{due to} the intrinsic properties ^{of the} proton (large magnetic

moment, spin 1/2) ^{but also to the} vast amount of effort spent by high energy physics

laboratories around the world to produce hydrogen-rich ^and highly polarized proton targets [6].

Since

another happy coincidence

hydrogen ^is everpresent ⁱⁿ organic chemistry ^and

thus in biology, macromolecular structure research seems to be a choice domain to apply polarized proton techniques, ^and since - last coincidence

the high proton polarizations

have been achieved in organic solvents, ^{it seemed most} promising ^to study macromolecules in solution and to use the proton polarization ^{as a} powerful ^{means for contrast} variation in low resolution (small angle) scattering. ^{An ambitious} project along ^{these lines is} under way in Geesthacht and the first results have been obtained on biological macromolecules [7].

Another interesting domain where contrast variation can be helpful ^is polymer ^confor- mation, both in solution or in the melt. To this end we have built an apparatus ^{installed at the} ORPHEE reactor of the Laboratoire Leon Brillouin.

After a short review of the theory ^{of small} angle ^neutron scattering (SANS) adapted ^{to the}

case of polarized ^{nuclei, we will summarize the basic} experimental problems which have to be

solved, describe the essential features of our apparatus, and show the first results on polymers

in (frozen) solutions. Some conclusions and an evaluation of the future outlook of this method will be given ^{at the end.}

Small angle ^neutron scattering by polarized ^nuclei.

The dominant interaction between a neutron (spin s) ^{and a nucleus} (spin I) ^{is a} nuclear force.

The magnitude ^J of the total angular ^{momentum can take two} possible ^{values for slow}

neutrons Jz

^{J + 1/2 to which} correspond ^two b+ ^{and b_ . The total} scattering amplitude ^can

then be expressed ^{as : b}

bo ⁺ bn ^{1 - s with}

The values of bo ^and bn ^{are known for most nuclei} [8]. Some of the values most currently

encountered in organic compounds ^are given in table I.

Table I. - Neutron scattering lengths ^{and N. M. R.} frequencies ^{at 2.5 T} for ^{some nuclei.}

For an assembly of fixed nuclei the scattering ^{cross section is :}

or

Q ^{is the momentum} transfer. For elastic scattering,

À is the neutron wavelength and 0 the full scattering angle.

The average ( ) ^{is taken over the} possible spin ^{states and/or} isotopes.

Small angle ^neutron scattering (SANS) ^{is a} low resolution method. It is not possible ^to

resolve structural details over distances smaller than dmin = 03C0/Qmax ^where Qmax ^{is the}

maximum value accessible in the experiment. ^{The sum over} all nuclei can then be replaced by

sums over averaged volumes small compared ^to d 3i. ^but large compared ^{to the} interatomic distances. By choosing proper volumes, many physical problems ^can be reduced to those of two simple ^{cases :}

- first : identical particles ^{with a} homogeneous scattering length density imbedded in a

homogeneous matrix ;

- second : two types of identical particles ^{in a} homogeneous matrix. At first sight, ^this

looks very restrictive but in fact the two cases include a large ^{number of} problems ^{in SANS.}

For example, polymers in solution belong ^{to the first case. The} particle is then the monomer.

A mixture of polymers, copolymers ^or partially deuterated macromolecules can be treated with the second case.

We assume in the following ^that only ^one kind of nucleus can have a significant polarization. (These ^{nuclei are} protons, ^{in our case, with a} scattering length ^b

bo p + bnp 1 - s). ^This assumption ^{is in} general well satisfied. The contribution from the deuterons is much smaller due to a lower polarisation ^{and a smaller} b.. Its inclusion in the calculation is straightforward but cumbersome.

First case.

We consider Nm ^identical particles characterized by ^a scattering length density ^{b m -} bp +bn P. s.

1

Pm = .1-. i Im ^{is the} polarization ^{vector of the} particle. n ^{is the number of} polarizable

nI

nuclei included in the particle.

bm = n .

b.p/vn ^and bm 0 ^{b’/vm where i sums over} all the nuclei of the particle ^and

i

0

vm is its volume.

The matrix which contains these particles is also characterized by ^a scattering length density

bS - bô ⁺ b’ p, ^s which is defined in the same way ^as b m. The scattering ^{cross section can then}

be written as :

where the sums over m and s are taken over the volume occupied by ^the particles ^{and the}

solution respectively.

By developing ^this equation, ^we obtain sixteen different terms which can be separated ^into

three groups characterized by ^the dependence upon the polarization ^P of the nuclei. We suppose that there are no density fluctuations in the solution, i. e. , the solution is

incompressible.

Then equation (4) ^{can be written as :}

where So (Q) = E ^{exp (- i Q .} (rm - rm’)) ^{is the} scattering ^{function obtained without nuclear}

m, m’

polarization.

Sop(Q) ^{contains four terms :}

with k and f equal ^{to m or s and}

à -

with k and f equal ^{to m or s.}

The three functions So (Q ), Sop(Q), Sp(Q) ^{are in general} different. But if there is no

correlation between the relative orientations of two polarizations Pk and pe and their relative

position (this ^{is the case for} polarized targets where Zeeman order dominates), ^{we can} write,

for example :

Extending ^{the usual} properties ^{of the} spin operators ^{to the} polarisation ^{vector as defined}

above we can write (Pm. s) = (Ps. s)

pP/2 and (Pk. S) (Pl - s))

P 2/4 where p ^{is the}

neutron polarisation ^{and P} the average nuclear polarisation ^{in the} sample ^{and one obtains}

and

The resulting ^coherent differential cross section is

The last equation reminds of the familiar concept ^{of contrast in} isotopic substitution

experiments [9]. Note that the average ^over all the polarization ^{states is made at} the end and

only ^for fully polarized ^neutrons equation (11) ^{becomes a} simple square of the difference of the two scattering length ^densities analogous ^{to the usual case} in absence of nuclear

polarization.

In this first case, the polarization ^can only give ^an enhancement of the signal ^{but it does not} give ^more information about the structure of the particles.

The incoherent contribution can be separated ^{from the sum of} equation (1) in the usual way [1]. For pP ⁺ 1, the dominant contribution is the spin-incoherence, which varies with

polarization ^as

Here N is the number of polarizable ^nuclei (protons) ^{in the} sample.

Let us now take an example ^to evaluate the enhancement : we consider protonated polystyrene, ^{PSH, in a} deuterated solvent, toluene-d. With the use of table 1 and the room

temperature ^{densities and} neglecting ^{the small} spin-dependent scattering ^{of the} deuterons,

one obtains

and

for a polarization ^{of 70 % and non} polarized ^{neutrons, the} signal ^is multiplied by ^{2.5. With} polarized neutrons p = - 1, ^the signal ^is multiplied by ^{5 but we loose at} least half of the incident neutrons.

Second case.

We consider now two kinds of particles, ^{m ant t,} characterized by ^a scattering length density

b m - bô ⁺ b n pm . ^{s and b =} bô + bn p, - ^s respectively. ^These particles ^are inbedded in a

matrix with a scattering length density b’ = bô ⁺ b’ ^{p, - s.} All these values are defined as in the first case.

Under the same assumptions ^as in the first _case, the development ^{of the coherent}

differential cross section gives :

and Stt (Q) = L ^{exp (- i Q .} (rt - rt. ) ) ^{are the usual} scattering ^functions.

t, t’

The different amplitudes Kke ^are calculated as in the first case. We have :

with i = m or t and

Figure ^{1 shows the three} amplitudes ^{as a} function of proton polarization ^{for a} sample consisting ^of equal ^amounts of deuterated and protonated polystyrene (e.g. ^{a block-} copolymer ^with equal lengths of PSH and PSD) ^{in 50 %} deuterated toluene. ^m stands for PSH and t for PSD. The ratios of the three amplitudes change ^with polarization. This makes it in

principle possible ^to separate ^{the three} scattering ^functions Smm (Q ), Stm (Q ) ^and Stt (Q ) ^from

measurements on a single sample ^{at different} polarizations. ^For comparison, ^the signal intensity ^{at zero} polarization is also shown for pure PSH in toluene-d and PSD in toluene-H.

Fig. 1.2013Intensities of SANS from

ternary mixture of equal ^amounts of PSH and PSD in 50 % deuterated toluene, calculated

function of proton polarization ^for

polarized ^{neutron beam,} compared ^to PSH in toluene-d (0) and PSD in toluene-H(x) ^{at P = 0.}

Expérimental requirements.

Although ^the advantage of nuclear polarization ^{for contrast} variation is important, ^{as shown}

in the last section, ^{there is a} price ^to pay which seemed prohibitive ^to everyone except ^the group of Stuhrmann [7]. ^{In order to achieve} high polarizations ^{a number of} conditions have to be met. They ^{can be} separated ^{in two} main groups :

-

the apparatus ^{needed to create} the necessary sample environment ;

-

the conditions ^to be fulfilled by ^the sample ^itself.

THE SAMPLE ENVIRONMENT. - In organic substances, large hydrogen ^nuclear polarizations

have only been obtained by ^the dynamic ^method generally ^{known as} solid effect [10]. ^{It works}

the better, ^the higher ^the applied magnetic field and the lower the temperature ^{of the} sample.

Fields in excess of 2 T and temperatures below 0.5 K are generally required. ^The magnetic

field has to be homogeneous ^to better than - 0.5 mT over the sample ^{volume. A} symmetric split-coil superconducting magnet ^is unsuitable for the use with a polarized ^neutron beam,

since the neutrons would depolarize upon crossing the zero-field region.

The low temperature ^{has to} be maintained continuously in presence of the polarizing

microwave power which dissipates typically ^{0.2 mW/cm3.} The best way ^to achieve this is a

dilution refrigerator. But, ^since 3He is prohibited around the sample ^{due to its enormous}

absorption ^cross section for thermal neutrons, ^the only cooling ^{fluid is} 4He. One needs thus a

dilution refrigerator ^of high cooling power ^at moderate temperatures combined with a heat

exchanger ^{to the} 4He bath, which imbeds the sample ^{in the microwave} cavity. ^{Even below}

0.3 K, the heat conduction in 4He is considerably larger ^{than inside the} sample ^{itself and}

across its boundary. ^{These two main} thermal resistances have to be minimized by increasing

the surface-to-volume ratio of the sample.

In order to optimize the small angle scattering, ^a large sample ^is desired and stringent requirements ^{are put on the nature} and thickness of the material traversed by ^{the neutron}

beam in order to minimize absorption ^and background scattering. ^In addition, ^the

introduction into the microwave cavity ^of samples ^unstable above, say, 100 K has ^to be considered. This causes additional constraints on the design ^{of the} cryostat.

SAMPLE. - The aim of (neutron) ^small angle scattering ^{is the} study of the conformation of macromolecules in solution. One of the necessary properties of the solvent - which has to be verified - is then not to alter this conformation upon freezing. ^{This is most} easily ^achieved by quickly freezing ^the solution into an amorphous, glassy ^state. From research on organic polarized proton target materials it has been found a long time ago that glassy ^{solvents are}

also the most easily polarized. ^{This is one} of the main reasons why experiments ^{on contrast}

variation by dynamic polarization ^of hydrogen could be started with a reasonable hope ^for

success.

As a second requirement, the solvent should contain the « right ^{kind » of} paramagnetic impurities ^{which are} needed for the dynamic polarization. ^Our knowledge ^{of the} details of the

polarization ^{mechanism does not allow to} predict ^what polarization will be reached for ^a given pair solvent-impurities. High polarizations have been reached in the following substances,

used for polarized proton targets : different alcohols and diols with Crv complexes [11],

alcohols doped ^with porphyrexide, ^{a stable free radical} [12], and solid ammonia with free radicals created in situ by irradiation [13]. ^Less successful attempts with combinations of other solvents and other paramagnetic impurities ^{have been} published [6], [14] ^{and it can} safely ^be guessed that many ^more negative results have remained unpublished.

Finally, ^the good combination of solvent and paramagnetic impurity, i. e . the one which

gives ^a high polarization ^{and which conserves} the conformation of the dissolved macro-

molecules, ^{should be} sufficiently homogeneous ^{on the} length scale of interest in order to give

a negligible contribution to the small angle scattering.

Apparatus.

In the following, ^{we will describe the basic} design ^{of our} apparatus, ^which represents ^{one of} the possible ways ^to fulfill the aforementioned general requirements. ^{It was} mainly ^{aimed at} providing ^a survey of the usefulness of dynamic ^nuclear polarization ^{in the} study ^of

conformational statistics of polymers. ^An additional and by ^{no means trivial} boundary

condition was the use of existing equipment ^whenever possible. ^In fact, ^{the main} parts ^{of our} set-up have been taken over from the experiment ^on pseudomagnetism ^{installed at the}

neutron guide ^G5 of the ORPHEE reactor [1, 2].

A graphite monochromator with mosaic spread ^{of 20’ reflects a beam of neutrons with}

À

0.472 nm onto the sample. The 03BB/2 contamination is eliminated by ^a ÎN2 ^{cooled Be-}

filter. Two slit collimators are used to increase the angular resolution down to

6min == ^{0.2 nm-1. The SANS} spectrum ^{is taken} point by point ^{with a} single BF3 detector. The

intensity of the direct beam is 5 x 104 n/CM2/S. The maximum angle accessible to the detector

is limited by ^the magnet ^{coils to ± 7°. This} corresponds ^to Smax

^{1.6 nm-1.}

A 15" electromagnet ^{with a 50 mm} air gap establishes ^a magnetic field of 2.5 T with sufficient homogeneity ^{for a 15 x 15 mm} sample ^{cross section. The} optimum length ^{of a}

deuterated organic sample ^{is 5 mm. The} typical sample volume is then 1.2 cm3. This calls for 0.25 mW microwave power for polarization. ^A perfect ^dilution refrigerator ^can carry away 25 J/mole at 0.2 K. We need thus a circulation rate of at least 120 03BCmole/sec.

From _many solvents, glassy samples may be obtained by freezing droplets deposited ^{with a} syringe ^on liquid nitrogen. ^{In this} way, the diameter of the beads and thus the volume/surface ratio can be controlled. This method of sample preparation ^is routinely ^{used for} polarized proton targets ⁱⁿ high energy physics. ^It calls for means to introduce the beads into the microwave cavity ^{at or at} least close to liquid nitrogen temperatures.

In situ freezing ^{of the} liquid inside the microwave cavity ^was discarded. With toluene, ^we

were unable to obtain clean, homogeneous ^slabs by freezing it in containers. Toluene sticks to

the walls _upon solidifying and its contraction due to the subsequent ^cooldown produced

strains which resulted in multiple cracks and an important ^small angle scattering.

We choose to introduce the beads from the top ^{of the} dewar, through ^a stainless steel tube of 4 mm i.d. which goes straight ^{down into the} cavity and is thus perfectly ^{suitable as the}

70 GHz waveguide. This choice has different consequences :

An obvious disadvantage ^{is the 4He} film, which tends to short-circuit the dilution

refrigerator. ^A partial remedy consists in thermal anchoring ^{of the} waveguide ^{to the still} (working typically ^{at 0.9} K). ^The film circulation delivers -10 mW between the A-point ^and

0.9 K. This is less than the power necessary for the still ^{to ensure} the desired circulation rate.

But, ^{even below 0.9} K, evaporation of the film at the

hot » end and its condensation at the cold end creates a heat load. Its limitation is here the pumping speed ^at the very low vapour pressure. We have measured ^a thermal loss of 1 mW in a 10 cm section of waveguide (4 ^mm i.d.) between 0.75 K and 0.55 K. Insertion of a teflon rod (- ^{3.9 mm} i.d.) reduced this loss to 2 03BCW ^{and to 15} J.LW between 0.9 K and 0.4 K.

Due to the many constraints mentioned above and to which one has to add the limited space available the cryostat ^{is the most critical} part ^{of the} equipment. ^{A schematic} drawing ^of

our dilution refrigerator ^{is shown in} figure 2. From this figure, ^{one sees} clearly ^{some of the} advantages ^{of our} design :

-

the beads are easily introduced from the top of the dewar into a clean cavity. ^{This is} important, since all cold parts ^if exposed ^to air, ^even for short times, ^condense enough

moisture to give ^{rise to small} angle scattering ;

-

there is a possibility ^{to recover the beads} (in ^{case of a valuable} sample) ^at nitrogen temperatures ^without breaking ^{the vacuum of the dilution} refrigerator ;

-

the construction of the cryostat ^is relatively simple ^{due to the} complete separation ^{of the} waveguide-cavity-sample unit from the dilution part. However, the space remaining ^{for the}

dilution refrigerator becomes rather small ;

-

it is possible ^{to introduce a mobile teflon} plunger ^{from the} top of the dewar into the

cavity. ^{As mentioned above such a} plunger is necessary ^to diminish the thermal loss along ^the waveguide between the still and the heat exchanger. ^In addition such a plunger ^allows cavity matching ^{and even} modulation of the microwave modes during polarisation.

Concerning ^{the dilution} refrigerator, ^we may just ^{mention here two not} quite conventional

design ^details.

We used a heat exchanger between 4.2 K and the still together ^{with a} compressor in order to condense the 3He _gas at - 2 bars [15]. ^{This obviates the need to pump on the 4He bath,} extending the time between the transfers to above 24 h. (The ^4He consumption ^{is 0.15} llh).

Such a design ^{needs two flow} impedances ⁱⁿ series, usually placed just above and below the

still. Their ratio is quite critical. If the second impedance ^{is too small,} the gas fraction created

Fig. ^2.

^Schematic drawing of the essential parts ^of

^dilution refrigerator : 1)

^can, 2) enthalpic ^heat exchanger, 3) primary ^flow impedance, 4) still, 5) concentric heat exchanger, 6) secondary ^flow impedance, 7) waveguide, 8) dilution chamber containing, 9) ^sintered silver, 10) cavity (electrolytic Cu), 11) ^NMR coil, 12) ^window (Al foil), 13) ^3He pumping line, 14) ^{3He retum line.}

in the first expansion ^{will not} recondense at the still temperature. ^{If it is too} large, ^{a non} negligible ^amount of gas will be created in the second expansion. ^{In both cases,} the proper

functioning ^{of the low} temperature exchanger ^is impaired. ^{We choose to} place ^{the second} impedance ^inside the upper third of ^a single, concentric heat exchanger, ^{in order to facilitate} construction, ^{to minimize solder} joints ^{and to be less} dependent ^{on the flow} impedance ^ratio (due ^{to a lower} temperature ^at the second expansion).

With the design ^{flow rate of 300} >mole/s, ^the temperature ^{in the 4He filled} cavity ^reaches typically ^{280 mK} in absence of microwave heating, ^{as measured} by ^{a 220 fi} Speer ^carbon

resistor soldered to the cavity ^{walls. The} background ^SANS spectrum ^{of our} apparatus without dewar and with the dewar and empty cavity ⁱⁿ place ^{is shown in} figure ^3.

As will be seen from the results given below, ^our set-up ^{is far from} being ideal. Its

disadvantages ^{are an} unnecessarily high wavelength resolution, resulting ^{in a low beam} intensity together with slow data collection.

The former is inherent in neutron beams diffracted from single crystals while the latter could be improved by ^a position ^{sensitive detector at} the expense of either resolution or

sample ^{area. It was} nevertheless found very convenient ^to have a small angle spectrometer

full time at our disposal ^{for the} feasibility tests, ^{and a} white beam at a guide ^{end was not}

available for this purpose ^at ORPHEE.

Significant improvements ^can be obtained (and ^are planned ^{or under} way) ^{at the} existing

site i. e. with the same neutron beam :

-

the small angle background ^can be lowered by ^a careful choice in materials for the

cryostat tails ;

Fig. ^3.

Background scattering with and without dewar and empty cavity.

-

polarized ^neutrons will allow ^a clearer discrimination of polarization-independent (e.g.

background) scattering. They ^{allow us also to measure the mean nuclear} polarisation ⁱⁿ

addition to the mean square ;

-

the proton polarization should increase at lower temperature. ^An improved design ^of

the dilution refrigerator, ^{with a} larger ^{flow rate and a more efficient thermal} anchoring ^{of the} waveguide above 0.6 K should allow a lower polarizing temperature ^{at the same microwave} power ;

-

a position sensitive detector would not only increase the counting statistics, ^{but also}

eliminate the errors due to a drift in polarization during counting ^time.

Experimental ^results.

The aim of our apparatus being ^the study ^of polymers, ^our first and modest ambition was to

reproduce known results. A textbook example ^{of a linear} polymer ^{in a} good solvent is ^a solution of polystyrene (PSH) in toluene. If quickly frozen down to 78 K, toluene forms a

glass. ^{It is stable} up ^to 130 K where it crystallizes [16]. ^The paramagnetic ^{center which in} general polarizes ^{best is a} Cr-complex (EHBA-CrV) [17]. ^But being ionic it does not dissolve in toluene. Keeping ^{CrV means then} changing the solvent. One of the possible ^{choices is} dimethyl-formamide (DMFA) ^{which dissolves} CrV and which is known as a good solvent for PSH. It is however difficult to obtain glasses from pure DMFA. We tried then mixtures of DMFA and toluene. They ^form easily glasses and dissolve both PSH and EHBA-CrV.

Figure 4 shows the scattering ^{from a} frozen mixture (-1.5mm ^dia. beads) ^{and from a} liquid sample ^{of 90 %} toluene-d and 10 % DMFA with 0.5 % EHBA-CrV. For comparison,

the scattering from beads of _pure toluene-d is also shown. The incoherent scattering ^{due to}

the protons in DMFA has been subtracted. One clearly ^{sees a much} larger ^small angle

contribution of the frozen mixture compared ^{to both the} liquid sample ^{and to} the pure frozen toluene-d. If this large signal ^{is due to} concentration fluctuations, ^{the use} of deuterated DMFA would decrease its amplitude by ^a factor 50. We did not test this due to lack of deuterated DMFA. The residual signal in toluene is very small and comparable ^{to our} background. It seemed then more promising ^{to look for a} paramagnetic impurity ^{soluble in}

toluene. The highest polarizations reported ^so far in toluene (60 ^{% at H}

^{2.5 T and}

T

0.5 K) have been obtained with di-tert-butyl-nitroxide (DTBN) [18].

Fig. ^4.

SANS from mixtures of 90 % toluene-d and 10 % DMFA (---) beads, (-) liquid compared ^to

beads of pure toluene-d (... ).

The SANS of a sample ^{of PSH} (1.5 %) in toluene (99 ^% deuterated) is shown in figure ^{5 for}

three different polarizations, 0, ^{25 % and 40 %. For} Q > ^0.2 nm-1 the signal has been fitted with a Debye function added to a constant background :

with f (x) _ (2/x2) [exp (- x ) - [ + x ].

The fitting parameters ^are given in table II. Within the precision ^{of the} fitting, the radius of

gyration Rg ^{is as} expected independent ^of polarization. PNMR ^{are the} proton polarizations ^as

determined by NMR in the usual way i.e. by comparing ^{the cw} absorption signal ^{with the}

thermal equilibrium signal ^{a 1 K. Due to the small number of} protons, ^the absorption ^{is weak}

Fig. 5. SANS ^from

solution of 1.5 % PSH (M = 34 500 ) ⁱⁿ toluene-d for three different

polarizations.

Table II. - Fitting parameters o f figure ^5.

even at the highest polarizations and corrections for nonlinearities are not necessary.

However, the thermal equilibrium signal ^is accordingly small and any parasitic (non polarizable) protons within the range of the NMR coil will tend to increase it noticeably. ^The

nuclear polarization measured in this way is then ^a lower limit.

Shown in table II are also the root mean square polarizations (p2)1/2 ^{deduced from the}

neutron scattering intensity Io through equation (11). They are systematically higher ^{than the}

NMR values. All errors indicated correspond ^to the statistical accuracy. They cannot account for the discrepancy. In addition to the possible underestimation of PNMR, ^{mentioned above,}

an inhomogeneous polarization ^would systematically ^{lead to} (p2)1/2:> ^{P. A} statistical distribution of polarizations ^{on a} macroscopic scale has been found in the only instance when such a measurement was possible [19].

Conclusion

It has been shown that nuclear (proton) polarization ^{is in} principle ^a powerful way of ^contrast variation in the study ^of polymers in solution. It has also been shown that it is experimentally

feasible to combine nuclear polarization ^{and small} angle scattering ^even though ^{this needs one}

of the most sophisticated sample environments encountered in thermal neutron scattering.

The resulting problems ⁱⁿ reliability, operating ^{cost and} sample throughput will limit the use to particular ^cases where the standard method of contrast variation by isotopic substitution is insufficient. A detailed study of the conformation of block-copolymers ^{is one of the} interesting possibilities, ^as sketched in figure ^1.

For all problems ^on macromolecules in solution, ^{one has to} keep in mind the limitations

already ^{mentioned i.e. an} easily polarizable solvent without small angle scattering in its frozen state and preservation of the macromolecular conformation _upon freezing.

These limitation would not exist with bulk samples ^of macromolecules _e.g. polymer ^blends

where interesting information could be obtained by ^the present ^{method of contrast variation.}

Acknowledgements.

We would like to thank the small angle scattering group of LLB for their advice and guidance during ^{our first} steps ^{in SANS and for} providing ^{us with the suitable} polymers, ^{G. Jannink}

and J. des Cloizeaux for _many enlightening discussions and P. Pari for his help ^and hospitality

during the construction stage of the dilution refrigerator.

References

[1] ABRAGAM A. and GOLDMAN M., Nuclear Magnetism : Order and Disorder (Oxford ^Univ. Press, Clarendon, London and New York) 1982, Chapter ^7.

[2] GLÄTTLI H. and GOLDMAN M., Neutron Scattering, Methods of Experimental Physics, ^{Eds K.}

Sköld and D. L. Price (Academic Press), ^{Vol. 23} (1987) Part C, Chapter ^21.

[3] SCHERMER R. I. and BLUME M., Phys. ^{Rev. 166} (1968) ^554.

[4] ^{HAYTER J.} B., JENKIN G. T. and WHITE J. W., Phys. Rev. Lett. 33 (1974) ^696.

[5] ^ROINEL Y., ^BOUFFARD V., BACCHELLA G. L., ^PINOT M., ^MERIEL P., ^ROUBEAU P., ^AVENEL O.,

GOLDMAN M. and ABRAGAM A., Phys. Rev. Lett. 41 (1978) ^1572.

[6] See e.g. the proceedings ^{of the} workshops

polarized target materials :

2014

SIN-Montana (1986) ^Helv. Phys. ^{Acta 59} (1986) ^{N° 4 ;}

2014

Bad Honnef (1984) ^{Ed. W.} Meyer (Physics Instit. Univ. Bonn, ^{F. R.} G.);

2014

Brookhaven (1982) ^{Ed. G. Bunce, AIP} Conf. ^{Proc. N° 95} (AIP, ^New York) ^{1983 ;}

2014

Abingdon (1980) : Rutherford Laboratory Report ^RL-80-080.

[7] ^{KNOP W.,} NIERHAUS K. H., ^NOWOTNY V., NIINIKOSKI T. 0., KRUMPOLC M., ^{RIEUBLAUD J.} M., RIJLLART A. , SCHARPF O . , ^SCHINK H. J., STUHRMANN H.B. and WAGNER R. , ^Int.

Workshop

Polarized Sources and Targets, ^Helv. Phys. ^{Acta 59} (1986) ^741.

[8] See e.g. the compilation by ^{SEARS V. F., Neutron} Scattering, Methods of Experimental Physics,

Eds. K. Sköld and D. L. Price (Academic Press), ^{Vol. 23} (1986), part A, Appendix.

[9] ^DES CLOIZEAUX J. and JANNINK G., ^Les polymères

^solution (Les Editions de Physique ^F-91944

Les Ulis, France, 1987, Chapter ^VII, Section 2.3.

[10] ABRAGAM A. and GOLDMAN M., ^loc. cit., Chapter ^6.

[11] ^{MASAIKE A., GLATTLI H.,} EZRATTY J. and MALINOVSKI A., Phys. Lett. 30A (1969) 63 ;

DE BOER W. and NIINIKOSKI T. O. , Nucl. Instrum. Methods 114 (1974) ^495.

[12] ^{HILL D.} A., KETTERSON J. B., ^{MILLER R.} C., ^MORETTI A., NIEMANN R. C., WINDMILLER L. R., YOKOSAWA A. and HWANG C. F., Phys. Rev. Lett. 23 (1969) ^460.

[13] NIINIKOSKI T. O. and RIEUBLAND J. M., Phys. Lett. 72A (1979) ^141.

[14] ^{GRUDE K.} and MÜLLER-WARMUTH W., ^Z. Naturforschg. ^24a (1969) ^1532.

[15] ^PARI P. , Thesis C.N.A.M. (Sept. 87).

[16] HILL D. A. and HILL J. J., Argon. ^National Laboratory Report ANL-HEP-PR-81-05.

[17] KRUMPOLC M. and ROCEK J., J. Ann. Chem. Soc. 101 (1979) ^3206.

[18] ^{FERNOW R. C.,} Nucl. Instrum. Methods 159 (1979) ^557.

[19] ^{ABRAGAM A., BACCHELLA} G. L., ^GLÄTTLI H., ^MÉRIEL P., ^PIESVAUX J., PINOT M. and ROUBEAU P., Magn. Reason. Relat. Phenom. Proc. 17th Congr. Ampere, ^{Turku, Finl.} (1972)

p. 1, ^{Ed. V. Hovi} (North-Holland, Amsterdam) ^1973.