Sublimation kinetics of organic molecular crystals

Journal of Crystal Growth 55 (1981) 351—362 North-Holland Publishing Company

351

SUBLIMATION KINETICS OF ORGANIC MOLECULAR CRYSTALS H.K. CAMMENGA, H.-J. PETRICK and F.W. SCHULZE InstirutjhrPhysikalische Chemie, Technische Unieersitdt, Hans-Sommer-Strasse 10, D-3300 Braunschweig, Germany

Received 5 March 1981

In the literature very few reliable data exist for evaporation and condensation coefficients of organic molecular crystals, although these should be very useful to study the influence of conformational change, molecular packing, intermolecular forces, etc., in addition to the effects of surface topography and surface diffusion. In the present publication the evaporation coefficient of cis-azobenzene, trans-azobenzene, benzo-[c]cinnoline, trans-stilbene and phenanthrene is letermined at 0—15% relative undersaturation and is found to be 0.25 except for phenanthrene. This result is discussed in connection with a proposed model of pairwise addition or subtraction of admolecules at the half crystal position.

1. Introduction

geneous

reactions, solid state chemistry, measure-

ments of diffusion coefficients of vapours. The kinetics of phase transformations are of great importance in a variety of processes of theoretical as well as practical interest. Because of their greater simplicity most studies have been devoted to such processes in one-component systems, where one of the phases is gaseous, whereas the understanding of solid liquid and solid solid phase transformations on a molecular basis is still rather poor. During the last decase the groups of Hickman and of Cammenga have given theoretical and experimental evidence that most of the long-standing concepts concerning the kinetics and mechanism of the phase transformation liquid vapour are wrong and have undertaken a revision. A recent monograph comprehensively deals with the theoretical, experimental and practical aspect s of this topic [11. The authors of the present contribution, however,

Industrial applications: Single crystal growth, coating techniques, purification by sublimation, freeze drying, vaporization of components in vacuo or in space, chemical vapour deposition, metallurgy, jet propulsion. Environmental problems: Formation of snow, vaporization from glaciers, wanted or unwanted aerosols, dissipation of pesticides via the vapour phase.

2. Basic theoretical concepts Usually, the kinetics of phase change in terms of mass flux per unit area and time are described by the Hertz—Knudsen----Langmuir equation, derived from the kinetic theory of gases [2,3]

believe that in dealing with the kinetics of phase

transformations solid vapour some inportant aspects have also either been overlooked or dealt with in an incorrect manner. Before proceeding, the following (certainly incomplete) list is considered to demonstrate that the subject is by no means of academic interest only but has a variety of practical implications, e.g. in the fields of: Basic research: Dynamic methods of vapour pressure measurement, nucleation, crystal growth, hetero0022-0248/81 /0000—0000/$02 .50 © 1981 North-Holland

/

\V2/

I l—~-——----~-—I

S dt \2irR/ or, for T’e~T’ ~

=

~

\v’T

—

(1)

\/T’J

‘

\2irRT/ where S is the exposed specimen surface area, M the molar mass of the vapourizing species, R the universal gas constant, p the saturation vapour pressure

I/A. (~anz?nenga£‘t al.

352

/ Sublimation

kinetics of organic molecular crystals

(which often result in a, a,~ I due to rate-determincongruent vaporization or ~ condensation processes ing chemical steps), the molecular steps involved iii solid vapour phase transformation are usually described in terms of the terrace—ledge—kink model (TLK model) extensively discussed in time literature: for reviews on this subject, see e.g. refs. [2—71. Referring to the simplified model of the crystal surface depicted in fig. 1, the molecular steps involved are given in fig. 2. Important sources of ledges are the intersections of edge and screw dislocations with the surface, the crystal edges, and holes

~7326?~

Fig. 1. Schematic representation of a crystai surface: (1) molecule in the surface; (2) molecule at ledge; (3) molecular gap in ledge; (4) molecule in kink (half crystal position); (5) molecule adsorbed on the surface (admoleculc); (6) edge dislocation: (7) screw dislocation.

(‘Lochkeime’) respectively islands formed by twodimensional

nucleation

on

rather

perfect

crystal

planes [6,71. The overall evaporation coefficient a is then given by the product of the a~for the different steps involved

[3.51

alla~.

(2)

T, and p’ the pressure of the vapour of temperature T’ in the corresponding to the surface temperature

vicinity of the surface. It must be emphasized that eqs. (1) and (la) only apply to the regime of molecular flow in the vapour, i.e. for p’ less than approximately 1 Pa, which is normally the range of interest in the sublimation or growth of solids with their low vapour pressures. In the regime of viscous vapour flow, however, eq. (1) or (la) must be suitably modifled [1], a fact, which is almost always overlooked. In eqs. (1) and (la) a is a dimensionless factor, called (net) evaporation coefficient if p > p’ or (net) condensation coefficient if p
jf’

Molecule at ledge 2

if’

2’

In addition to the molecular steps, secondary plienomena may play an important if not a doniinating role, e.g., (I) diffusion on the vapour phase in the presence of gas(es) or restriction to molecular flow~ (2) local surface cooling or heating due to the coupling of mass and heat transfer~ (3) impurities affecting kinetics and surface topography. To minimize the influence of these phenomena during experimental studies one has to work at low residual (inert) gas pressures with highly purified equipment and samples using net rates of less than 2 l0-~g cm 5-mS The topics (2) and (3) will be discussed in more detail below. If, however, any influence of (I )—(3) can be ruled out, most authors believe that surface diffusion of adsorbed molecules (admolecules) is the rate controlling step. lt has been shown be several authors that in this case —

2X5 tanh—= .Yo a2=-—— —

,

(3)

S

Molecule adsorbed on the surface

3

if’

3’

Molecule in the vapour

Fig. 2. Molecular steps in evaporation or condensation according to the terrace—ledge—kink model.

where Yo is the mean distance between parallel ledges and X5 is the mean diffusional path on the surface. Eq. (3) normally leads to two limiting cases: (i) For Yo ~‘ X~it follows that tanh(y0/2X~)—~ 1 so

I/K. Camrnenga et al.

/ Sublimation kinetics of organic tnolecular crystals

that a

~-

of solids in the case a, a~< 1 had not yet been traced correctly.

—

a

2

(4)

2X5/y0

-~

4 I ira~~~ lra5..p kBTln(p’/p) kBT(,P — P’)’ one obtains the so-called parabolic law =

(5)

—

1 dm5

X5kBT/ M

Silt

2iram,lipk2irRT)

\h/2~

‘~2

‘~—

‘

We

then decided to focus our interest on mole-

cular crystals of organic substances, because

and, with screw locations involved, when

Yo

353

6~ ~

-‘

where a is the area occupied by an admolecule, ~i the specific edge energy and kB the Boltzmann constant.

X~application of the L’Hospital rule to eq. (3) leads to a2 -÷ 1, so that one obtains the so-

—

in

addition to the effects of surface topography — the influence of molecular shape (conformation), intermolecular force fields, crystal structure and molecular packing can be studied under comparable experimental conditions in selecting from the abundance of organic compounds. Preliminary results have already been presented

orally on several occasions.

3. Materials

(ii) For y~~

called linear law

—

1 dm~—

(

Sdt

~2irRT!

—

M

\i/2

—

~P

,

(7)

In the present contribution, our results obtained with the organic compounds cis-azobenzene, transazobenzene, benzo [c] -cinnoline, trans-stilbene and phenanthrene are reported. These substances have very nearly the molar mass M~ 180 g mol_m. The

~)‘

structural formulae are given in fig. 3. fig. 4 shows a Hirth and Pound have developed a model of advancing parallel ledges on evaporating surfaces leading to a limiting value of a = a2 = 1/3, which should apply to crystals with simple lattices, e.g. metal or alkali halides [3,6,8]. However, a= 1/3 has not been observed experimentally as a general linuting value in the many experiments conducted by various authors, for compilations, see e.g. [2,3,5,9—13]. Furthermore, there are only a few experiments which gave evidence to a higher order law. Considering the other steps in fig. 2,a it is usually estimated that a1 1. We believe that 3 < 1 is highly improbable because (a) in the evaporation

or condensation

photograph of ball models of the substances in their conformation known from studies of, e.g. electron diffraction of vapours, dipole moments, X-ray diffraction. The substances were highly purified by a sequence of steps using only highly purified equipment and material. Benzo[clcinnoline (9,10-diazaphenanthrene) and cis-azobenzene, which were not commercially available, were synthesized by photochemical methods [16]. In the case of the azobenzenes, several 4C-labelled compounds experiments were made with ‘ also prepared by synthesis [16]. The usual procedure

of liquids, whether

metallic, polar or non-polar, only this step is involved and here a a = 1 [114 15] (b) the molecules leav~

~

Maxwell velocity

On examination of the many compilations of evaporation and condensation coefficients of solids [2,3, 5,9—13] one realizes that for metals a = 1, no matter whether they are single crystals or polycrystalline. The same applies to many but not all molecular crystals. Having in the past found and eliminated many erroneous concepts in liquid vapour phase transition kinetics we suspected several years ago that the effective rate limiting molecular step(s) determining the kinetics of congruent evaporation or growth

H

H

~

~

cis -stilbene

~

trons-stilbene

N—N

~

.-~c:~

phenonthrerie

N-N

0 0

cis - azobenze~ie irons - ozobenzene benzo(c)cinnoline Fig. 3. Structural formulae of the substances studied in this contribution.

3.54

II. ,c..

(i000i

,)~i

t

~l

.Suhliniatvni Am

‘1 ‘,os,nR~

lii

1

u/ar

1 ig. 4. Ph o ioeraph sitosvifl~ball in od~ls I t lie sobs Iarices si tidied. tIpper ross ( 1mm Ic It ii rigi it): L’is—st ilbe ne. Irails—st ilbe me. plic nanthrene. I sos er russ : cis—ai ohen7 ctie. ii an s—al ohm, erie. hen i[ c cinnolimme All mnoleetm les cli oss n in ti leir iiiost ri ha he emmillorin a tim in

for purification \sas then iccivstalliialimmn from p~i~ solvents. chrminlalogiaph\ - ~~ne pinhlcalioll. suhliina— lion. :tuain /otte pulilication undei aruori . ftc

L

mcltinu

p01111 ot each substance litus pumilied v. as usuall\ a few lentli oI :i degree higher than mepmmried imm the litemalule. lime punlv was ana!vied hs d~ nanmic calornnelry and was .~U9.98 mol’ 1171. In inosl tneiils bul

in sonic

~

measurements were pci —

liii medpot ssilh single material civslals. was careluIIs 10111 cases ci\ stdhne used inero\sn the expen—

~

~oIulion liv pi ogi amnied sIo~~ cooling II I. A ivpical sinele Cry stal (trans-a/ohen/ene) is slio~smm in lie. 5.

~

4. Experimental

technique

Ahmmost exclusivels daia mit ~t eported iii the lucia— have been mmhlaincd tiom nteasurcmnents ot the

tule

Iree hg. 5. Single er~stal ol trans-aiohenzene. ~rossn from

hexane solution. Length ahou t I LIII.

n-

e~apo1atomm mate (evaporal in Limum cacunill.

Lammgnmnir expemimnemmt. with p’ (I). I his metbtod. h iss cvci - li as ses era 1 Li isa d’. antages. rh e sal u mali on

/ Sublimation kinetics of organic molecular crystals

H.K. Cammenga et a!. A

c

B

circular effusion hole in the centre, and which was connected to the cell body by a short, thoroughly

polished 3~i— -

- I

- -

--i-

--

1

2

‘

~

,

[j.’ Li

i

3_~ I

p~U

2

3 2

1

1

-

~

ground glass joint. The metal cells had a cap which could be screwed on and the metal foil with

s ~

-

355

4-

I

-

Fig. 6. Cells for rate of evaporation measurements. (A) Glass effusion cell (Duran 50): (1) substance; (2) cell body; (3) ground glass cap; (4) metal foil with orifice. (B) Metal effusion cell (Dural): (1) thread for adjusting screw; (2) cell body; (3) thread for cap; (4) adjusting screw; (5) adjustable cell bottom; (6) metal foil with orifice; (7) PTFE washers; (8) cap with thread; (9) manipulating rod. (C) Metal cell for free evaporation: (1) thread for adjusting screw; (2) cell body; (~) thread for auxiliary cylinder guiding a piston for pressing tablets (not shown); (4) adjusting screw; (5) adjustable

piston; (6) manipulating rod.

vapour pressure must be accurately known or has to be determined. surface cooling due and to evaporation and toUnknown radiation may be considerable may lead to data of doubtful significance. In addition, a can only be studied for the case of complete undersaturation but not close to equilibrium, where the principle of microscopic reversibility holds best and where a decrease of a according to the ILK model is expected. We thus decided to undertake free evaporation experiments as well as measurements at low undersaturation. The measurements at low vapour undersaturation were performed by a suitable variation of the Knudsen effusion method. The procedure has already previously been tested and successfully used by us in evaporation studies of liquids with low volatility at low undersaturation and is described in ref. [19], to which reference should be made for more details. The substance under investigation (either polycrystals, single crystals, compressed tablets, etc.) was placed in cyclindrical cells of cross sectional area S made from glass (Duran 50) or from aluminium alloy (Dural). For effusion measurements the cells had an interchangable cap, which carried the

the effusion hole was pressed onto the cell body while lying between two polished teflon gaskets, see

fig. 6. The distance from sample surface to the foil with the effusion hole is made equal to the cell inner diameter, as requested by theory [19]. By using various combinations of orifices of effective area WA and cells of area S the ratio WA/S could be varied from 5.0 X 10~ to 5.4 X 102. Here, W is the calculated penetration probability of the orifice (Clausing factor) and in our cases is always close to unity. The cells containing the sample were carefully .

.

weighed on a microbalance and positioned in an apparatus with the cell orifice opposite to a silvered condenser. The whole system was kept at constant temperature by two consecutive thermostats. To start a measurement, the air was quickly pumped out and .

a high vacuum maintained for a period of 3 to 40 h, while the vapour effusing from the hole was quantitatively collected on the condenser continuously refilled with liquid nitrogen. After the experiment, 14C-labelled the cell was the again weighed. In the case by of scintillation compounds mass was determined counting of the dissolved condensate, which was more accurate than weighing if the mass effused was less than about 1 mg [161. In performing a series of measurements at constant temperature with various combinations of cells and orifices the apparent pressure p’ was calculated from the measured quantities by 1/2

p

me I2irRT~ =

~

(—i---)

(8)

where me is the mass effused in time t. It has been shown previously that a can be determined from a plot of p’ as a function of WAp’/S according to the equation 1 WAp’ p’ p — — —~--, (9) a’ 1’ S derived from a balance of the molecular fluxes [19]. The meaning of ‘y is explained in section 5. If a’y ‘‘ constant it may be determined from the slope of the secant between the intercept P and the point in

356

ILK. Camnmnenga

Ct al

/ Sublimation

kinetics of organic molecular crystals

question. If a’y = constant one obtaines a straight line with the slope —hay. T’he relative understaturation in any point is given by =

p

I WA —

‘ .

(9a)

p ayS

In our evaporation rneasurentents with the effusion reported here the relative vapour undersaturation reached from about 0.2 to 17%. Measurements of the free evaporation rate were performed with metal cells also shown in fig. 6. The pure substance to be studied was pressed into the cells by a tightly fitting piston and a briquetting machine to form a disk which was then lifted by rising the adjustable cell bottom until the sample surlace was at the same level as the cell rim. Thus the cell walls did not form an inipedance to evaporating molecules, which leads to apparent low a-data as in many other investigations. Apparatus and procedure for the free evaporation measurements were analogous to those described above [141. In ~onie cases several consecutive evaporation measurements were mnade with the same sample surface, which was readjusted from time to time to its original position to compensate for the small recession of the surface. technique

In addition to the effusion measurements at constant temperature but varied undersaturation for each of the substances a series of measurements was al constant understaturation (fixed cell geometry) hut at various temperatures. These data were used to calculate the enthalpy and standard performed

entropy change on sublimation, the first of which is given in table 2.

5. Results of sublimation rate measurements and their interpretation The results of about 100 measurenients on the sublimation rate of cis-azoberizene, trans-azobenzene, benzo[c]cinnoline, trans-stilbene and phenanthrene made at low undersaturations are plotted in fig. 7 according to eq. (9) as explained in section 4. Straight lines have been fitted to the data by least squares calculation. Table I compiles the data measured for the substances. As can be seen from table 2, the enthalpy of sublimation (very closely the lattice energy [20]) varies only by about 5% among the substances. Within error limits, a is very close to 1/4 except for phenanthrene, for which it is close to 1/2. y is the

~

106(WA/Sp’ )/Pe. Fig. 7. Plot of the experimental data according to eq. (9). [morn top to bottom: phcnanthrene, benzo[c}cinnoline, trans-azobenzene, trans-stilbenc, cis-azobenzene.

H.K. Cammenga et a!. / Sublimation kinetics of organic molecular crystals

Table 1 l)ata of evaporation rate measurements

Cis-azobenzenc Trans-azobenzene Benzolclcinnoline Trans-stilbene Phenanthrene

)lO 303.45 1.616 303.45 2.066 350.79 2.141 323.65 1.904 319.39 2.402

22 26 12 14 14

1.0

0.26 ±0.03 0.22 ±0.02 0.26 ±0.03 0.22 ± 0.02 0.51 ±0.14

degree of surface roughness and is a function of a itself [21,22]. Generally, 1 ~ y ~ 1.36 [191 and in our case y is very close to unity. ay may be aptly called an effective net evaporation coefficient. In addition to ay and zV-I~table 2 lists also the space group, the number of molecules in the unit cell of the lattice and the dipole moment, As long as only highly purified samples were considered, an influence of preparation could not be detected. Polycrystalline material obtained from the vapour, from the melt or from different solvents lead to identical values of a. Large single crystals of suitable size placed in the effusion cells or samples pressed into the effusion cells showed very nearly the same results as polycrystalline material. The same applied to material which was fused in the cells and allowed to re-solidify, For phenanthrene, a series of free evaporation experiments was also conducted and evaluated after

I\2irRT/ M \i/2

Phenanthrene

a~

~

o is the number of measurements, T the temperature of the measurements (IPTS-68), p the saturated vapour pressure at T, and a-y the net effective evaporation coefficient.

5I din5 dt

357

(10)

0.2

0

20

1K

~

Fig. 8. The apparent evaporation coefficient aT due to surface cooling by ~Talone. T 0 = temperature of measurement.

easily give rise to erroneous results than those with the modified effusion technique. In free evaporation the mass flux from the surface may be 10 to 500 times higher than at low undersaturation. This often causes a considerable cooling of the surface due to the removal of the heat of evaporation [1,231. Additionally, radiation may cause a drop in surface temperature. Both effects are small with metals with their high thermal conductivity and low emission coeffi. dent; thus for metals a < I due to surface temperature drop does hardly occur. If the surface is cooler by ~T than the temperature T0 measured in the experiment, then the apparent aT solely due to surface cooling can be calculated by application of eq. (10) for the temperatures (T0 and T0 — ~ and the simplified Clausing—Clapeyron equation to be aT

‘

2

I

Ii I ——----I ~T\”

\

To

z~H~ ~T \ RT 0 (T0 ~fl/

expI—---~—-~---————I .

/

\

(11)

—

i.e. eq. (Ia) with p’

=

0. Such measurements can more

With this equation aT for phenanthrene at T0

Table 2

Molecular and lattice parameters of the substances investigated Substance

~J1~ 1) (kj mol

Cis-azobcnzene Trans-azobenzene

0.26 0.22

92.92 93.84

Benzolclcinnoline Phenanthrene Trans-slilbene

0.26 0.51 0.22

101.68 90.77 101.10

~

~.s (D)

tree pairselectron

4

3.0

+

4 4 2

0 4.1 0 0

+ o +

Space group

Pbcn P2 1/a P21/c 2m/a ~2m P

o

is the enthalpy of sublimation, N~the number of molecules in the unit cell, and M the dipole moment (in Debyc units).

=

358

IlK. (]anmrnenga et al

__________________

/ Sublimation

/

kinetics of organic molecular crystals

“equivalent conducting layer” ci was calculated for various aT for a typical evaporation rate measurement

at low and at full understaturation. The respective curves are given in fig. 9. For our measurements on

~/ ‘~ 0

0

.

05

0 - i

0

phenanthrene yielding a = 0.5

51

AT/K

0

AT/K

Fig. 9. Equivalent heat conduction layer in phenanthrene versus surface cooling for typical experimental conditions, Left: at slow evaporation rate (effusion technique), right: at free evaporation rate.

319.39 K (our temperature of measurement, where p = 0.2402 Pa) has been calculated for various values of ~T using the measured ~H 5 = 90.77 kJ mol* In fig. 8 aT as a function of ~T is shown. If now the simplifying assumption is made that the heat of subtiniation is only conducted perpendicular to the so face (the assumption of adiabatic walls would be the lower bound) under stationary conditions, the thickness d of the conducting substance layer may be obtained with the aid of the Fourier heat conduction equation: A~

d

1dm5 1)_i sithi

(12)

1 K-1 for phenanthrene this Using A 0.25 W m _______________________________________________

0.5

a ~ o

Ice Benzene Th~oPhene Nophtholeee

=

aT would require a

corresponding surface used experimentally. temperature to d values decrease Thus in (fig. our of9)experiments ~Tmuch6.4 higher K (fig. surface than 8) cooling cannot be made responsible for a < 1. For substances of high volatility, however, surface cooling is one of the ti~ajorreasons for a < 1 . e.g. with many liquids formerly believed to have low evaporation coefficients [1]. But also in the case of moderately volatile solids the drop in surface teniperature may cause a considerable dependency of the a-data measured on the actual heat demand at the evaporating surface. As an example the results of Nitsch and Viardot on ice and on solid benzene, thiophene and naphtalene may be considered [241. The a-data reported by these authors are plotted as a function of the heat flux to the surface a, calculated by us from their data, in fig. 10. On comparing tIns figure with fig. 8, a striking similarity of the curves is evident. All the a versus q curves can be extrapolated to a = I for q —~ 0. We thus can otTer a much simpler explanation for the behaviour of a in this case as Nitsch and Viardot themselves, who have recourse to a lengthy and doubtful theoretical explanation. source offlow low data for a may a tionAnother of and molecular between the be evaporating surface the condenser, as Burrows and others have pointed out [25—281. Following these lines Cammenga has, e.g., recalculated the data of Kramers and Stemerding [29] on the evaporation rate of ice at low temperatures and could demonstrate that their result a< 1 is changed to a= 1.0 ±0.05, if allowance is made for the considerable restriction to free niolecular flow in their experiments [1,11]. A very frequent, though seldomly realized, problem in evaporation rate measurements is the effect of impurities. This is a greater problem with organic solids than with metals or inorganic solids, since these mostly can be annealed in a high vacuum, which causes the impurities to evaporate or/and to

0 0

so

____

ow

so

Fig. 10. Evaporation coefficients, measured by Nitsch and

Viardot [241, as a function of the heat flux to the evaporating surface, calculated from their data,

diffuse into the sample bulk. Even if highly purified samples are used, trace impurities of low volatility may become enriched at the surface and finally may cause a reduction in evaporation rate. Such behaviour

359

was in fact observed by us, when traces of hydrazobenzene in azobenzene or of benzidine in benzo[c]cinnoline were still present as by-products from synthesis. In some cases, which will not be considered here, e.g. with caffeine or hexamethylenetetramine d 12, the contaminants were not identified; but prior to all our experiments greatest effort was made to remove them by various — often laborious — purification techniques. Great care was taken in storage and handling to avoid re-contamination. Nevertheless, if a sample is used for several conse cutive measurements each with a high specific mass loss (mass loss per area), enrichment of impurities may cause an apparent drop in a as demonstrated for phenanthrene in fig. 11. lt is seen that the data may be extrapolated to a = 0.5, the same value as obtained from the measurement with the modified effusion technique. We suspect that the data of many authors, who used substances of doubtful purity, are the lower bounds of a. As has already been mentioned, in our cases the mode of preparation of the sample did not affect a, There was no detectable influence of defect density and surface topography on a. In addition to the rateof-evaporation nseasurements numerous microscopic observations on (001) single crystal faces were made in a specially constructed evaporation chamber [181. This evaporation chamber was made from glass and could be carefully thermostated. The crystal was held on an adjustable ball joint attached to a copper

— —

a

_________ _____________________________________

-________________________

20 ~im

________________

Fig. 12. Steps which originated at the edge of a trans-azobenzene single crystal.

capillary. A fine thermocouple inside the capillary reached to the ball joint and enabled measurement of the crystal temperature. The evaporation chamber was mounted on the stage of a high-resolution microscope equipped with Linnik interferometer (Michelson type), spectral lamp and camera. Because of their low surface reflectivity observation and photography of dynamic processes on surfaces of organic crystals are much more difficult than with crystals of metals and inorganic compounds. Trans-azobenzene crystals grown from n-hexane solution in a special growth apparatus [18] showed perfectly smooth (001) faces prior to evaporation. In the beginning of evaporation.

0:t~~

0

_

100

200

300

a,

a

400

—

50p.rn

—,

Fig. 11. Evaporation coefficient of phenanthrene for repeated evaporation of the same sample as a function of the total mass loss per surface area: (x) effusion technique; (°) free evaporation, continued,

l’ig. 13. Surl’ace of a trans-azobenzene single crystal. Short IR irradiation during evaporation initiates circular etch-pits, which act as a source of macroscopic ledges of 0.05—0.2 pm height during subsequent evaporation.

361)

IlK. Caminanga et at.

/ Sublnnanon kOu’ties ni orga,uc molecular

en-staR

the crystal edges were the main source for ledge formation, fig. 12. Short thermal etching by radiation heat and subsequent evaporation of pure crystals produces the pattern shown in fig. 13 showing almost circular holes (enlarged “Lochkeime”). which act as a source of macroscopic ledges of 0.05—0.2 jam height. Fig. 14 shows a surface after extended evaporation and it is seen that ridges remain on the crystal surface. This is a consequence of residual impurities. On fig. 15 the (001) topography of a trans-azobenzene crystal growls from ethanol is shown after evaporation at ~l0%relative understaturation. The contours arc more angular than in the case shown in fIg. 13. In several cases equidistant ledges of ~I nns height and width v 0 1 5 irn could be observed to move across the surface. (The calculated height of monomolecular ledges is 0.72 ntis.) A few degrees below the melting point (685°C for trans-azobeniene) a quasi-liquid film formed on the surface and the macroscopic ledges became rounded and wave-like while the monomolecular ledges became invisible, Rising or lowering the temperature let the quasiliquid layer either appear or disappear in a reproducible manner, We now would like to strengthen again that surface topography, surface cooling, impurities, vapour diffusion or flow restriction are not responsible for our values a < I - In the present case dipole moments resultine from the presence of asymmetrically dist i ibnted electron pairs show no detec table influence m a and on the lat tL’c eneigs - ci. table 2. We have the following explanation lot the a-data

_ __

_

_

Ic. 14. ‘I rans-a,.atien,.ene cr5 stat surf,ice ~t icr extended free evaporation. ( ‘entre shows a ci 31Cr surrounded by ridges,

501.im lig. 15. Trans-azobenzene (grown form ethanol solution) crystal surt’ace after evaporation at 10% relative undersatura-

tion.

observed by us: It is nowadays accepted that mole-

cular close packmg is the main constructional principle for organic molecular crystals and also to a great extent determines their physical properties. it no hydrogen bonds are involved 1201. The substances discussed in this paper have almost the saute lattice energy (cf. table 2). Their space group is very similar. For crystal structures and molecular cont’orutations see refs. [31 ---33j for cis-a/obenzene. refs. [31 .34. 351 for trans-azobenzene. refs. [36,371 for henLotcicinnohne and ret’s. [38 --42 I for traris-stilbene. tJnt’ortunately. eis-stilbene is a liquid in the range of interest here: our preliminary measurements with the pure substance yield the temperature ol fusion at —20°C. Despite the many similarities between these

PQ9It~~\

:~\\

\-~

1-ig. 16. Schematic representation of the mechanism of pairwise addition of molecules to the kink position.

H.K. Caminenga et al. /Subliination kinetics of organic molecular crystals

compounds, there is, however, a distinctive difference in molecular packing between phenanthrene and the other compounds. Whereas phenanthrene contains only molecules of one conformation in its lattice [30]. the lattices of the other crystals are each made up of two classes of molecules with a slightly different molecular conformation, so that the unit cell contains two of the one kind and two of the other. We assume that molecules can only occupy or leave these two kinds of lattice position pair-wise. This leads to a success-probability of 1/4, which we may identify with the observed evaporation coefficient of a 0.25 ±0.02, cf. table 2. Fig. 16 gives a simplifying sketch of this hypothesis. There is, however, cvidence from quite different sources that the model proposed here deserves at least sortie consideration. It has been shown by spectroscopic measurements that molecules as presented here, e.g. benzo[c]cinnoline, undergo dimerization even in dilute solution of nonpolar solvents [36]. Frank, Myasnikova and Kitaigorodski [43] have demonsdrated in an elegant experiment on mixed crystals of trans-stilbene/ diphenylmercury that the two crystallographic sites in the trans-stilbene lattice are not equivalent with respect to substitution by diphenylmercury. There is still another information concerning the suspected co-operative mechanism involving two molecules. Cis-azobenzene is thermodynamically unstable and upon thermal or photochemical activation reconverts to the stable trans-isomer. We have investigated the kinetics of this cis —~ trans-isomerization in the melt and above and below the eutectic temperature of cis- and trans-azobenzene [44,45] - In the nielt the kinetics were of first order whereas from the crystal above the eutectic point it followed the law of Prout amsd Tompkins. It was observed that the enthalpy of activation for isomerization above the eutectic point (40.6°C) was very nearly twice the value found for the melt (above 71.6°C), as if two molecules had to be activated simultaneously. In addition to the substances discussed in this paper a few sound investigations may be found in the literature with results a < I for some organic molecular crystals. The results for camphor [46—48], thymol [48], 13-caffeine [49] and hexamethylentetramine [11,19,50—53] resulting in a < I cannot solely be interpreted as caused by artifacts or surface diffusiomi kinetics and should deserve future reinvestigation.

361

6. Summary and conclusions It has been tried to demonstrate that the influence of surface topography on the magnitude of evaporation or condensation coefficients is usually small if not negligible at all, unless one deals with crystals of the highest perfection. This is in contradiction with most of the previous statements in the literature. As in the case of evaporation kinetics of liquids, the influence of secondary phenomena as diffusion in the vapour phase, restriction to free molecular flow, cooling or heating of the surface (and a resulting uncertainty of the surface temperature) and impurity effects is generally greatly underestimated. All these artifacts tend to diminish the evaporation coefficients so that literature data often should be considered as the lower bound, We believe that in cases a, a~< I one should pay more attention to the effects of molecular conformation and bond lengths and their change in going from the low density vapour (no intermolecular Van der Waals forces acting) to the molecular packing in the crystal, which is dominated by the intermolecular forces and molecular shape. In the present state of the subject we have no nieans for quantitatively predicting the evaporation coefficient of (inorganic or organic) molecular crystals. In many but obviously not in all cases a, a~= 1. As in many fields of science there is a variety of (often more than doubtful) theories and a considerable lack of reliable experimental data, on which sound theories can be based. To form such a basis, it would be highly desirable to continue to perform measurements of a, a~(excluding any artifacts as thoroughly as possible) over the whole range of saturation for a series of carefully chosen compounds, which form molecular crystals. At low undersaturation, an exchange method involving radioactivetracer-labelled substances with normal substances should be most satisfactory, although it is not easy in its application as we know from our own experience [16].

Acknowledgements The authors like to express their thanks for experimental assistance in parts of the present work to their former collaborators F. Behrens, D. Schreiber and J.

H.K. Carnmenga et al. / Sublimation kinetics of organic molecular er~stals

362

Tries. The authors enjoyed several stimulating discussions of the subject with Drs. C.G. de Kruif and J.C. van Miltenburg of the General Chemistry Laboratory, State University of Utrecht, The Netherlands. Fmnancial support of this work by Deutsche Forschungsgemeinschaft (Bonn--Bad Godesberg), by Fonds zur versthrkten Forderung der wissenschaftlichen Forschung in Niedersachsen and by Fonds der Chemischen Industrie (Frankfurt/Mamn) is gratefully acknowledged.

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