Size and surface effects on phase transitions

Volume 44, number

CHEMICAL

2

1 December

PHYSICS LETTERS

1976

SIZE AND SURFACE EFFECTS ON PHASE TRANSITIONS* D. ARMITAGE**

and F.P. PRICE*

PoIymcr Science and Engineering, University of Massachusetts. Amherst, Massachusetts 01002, USA Rcccived

3 August 1976

Size effects on liquid crystal phdsc transitions are investigated by scanning calorimetry of samples absorbed in porous silica. l*or pore diameter of order 100 A, the liquid crystal transition dcprcssions arc of order O.l”C and the solid mcLting points of order 10°C.

Thermodynamic properties are generally derived in the “ thermodynamic limit” of an infinite system. As the size of the system is progressively reduced to microscopic dimensions, eventually the properties characteristic of the large system will no longer hold [l-6]. Nucleation is an example of size-dependent behavior. A phase transition via nucleation and growth begins in a microscopic region; therefore it is the properties of a microscopic system which determine the undercooling of the transition temperature [1,2]. We report here a simple experimental technique for the systematic study of size and surface effects on a wide variety of phase transition phenomena. The method is based on the use of porous silica of controlled pore size [7,8], available commercially under the name Porasil [9] f . This is a powder of 100 I_Lparticle size with a choice of six pore sizes covering the range of 100-l 500 a diameter. Any material which wets silica will be attracted into the pores and exist in a finely divided state of known dimension. The transition tem* Work supported

by a grant from the National

Heart and

Lung Institute.

of Biophysics, Boston University Medical Center, Boston, Massachusetts, where part of this work was complctcd. * With regret the untimely death of Professor F.P. Price is noted. f’ Pechincy-St. Gobain (France), Waters Associates (Massachusetts). Particle size: 100 12; pore size: A < 100 A. B = 100-200 A, C = 200-400 A, E = 800-1500 A, F > 1500 A. Surface deactivation treatment by ammonium chloride.

**

Present address: Department

perature and enthalpy of such a sample are measured by scanning calorimetry using the Perkin-Elmer DSC 2. The experimental procedure is to bake the PorasiI in an aluminum

sample

pan at 150°C for one hour in

the dry nitrogen atmosphere of the DSC. This is a prccaution against surface contamination, although the material is clean as supplied. Any contamination or chemical degradation will depress the transition temperature, and may dominate the observation. Where possible, deactivated Porasil is used as a precaution against chemical degradation. A few mg of sample are added to the Porasi!, without removing it from the DSC, and the temperature is then raised to the melt region. The sample is seen to be absorbed by the Porasil and an aluminum sample pan Iid can be added. The temperature is maintained in the molten region for 4 h in order to allow the sampIe to flow into the Porasil. For volatile sampIes such as naphthalene md benzoic acid this time is reduced to a few minutes. In order to broaden our comparison with existing data, the results for naphthalene (NAP) and benzoic acid (BA) are presented along with those for the Liquid crystals choIestery1 myristate (CM), p-azoxyanisoIe (PAA), and 4,4-bis(heptyloxyl)azoxybenzene (KAB). The naphthalene and benzoic acid are Fisher thermometric standards. The cholesteryl myristate, obtained from Eastman, is purified by recrystallization from pentanol and then from acetone. RAB. ako from Eastman, is recrystallized from pentanol and then etha305

nol. PAA from Aldrich is recrystallized as for HAB and then further purified by zone refining. The resulting sample purities as judged by DSC melting thermograms are comparable with those of the thermometric standards, i.e. impurity less that 1 : 103. Fig. 1 shows a DSC thermogram of naphthalene in Porasil B, pore size 100-200 A. There is a broad peak depressed AT below the normal transition. We interpret the depressed transition as that due to material in the pores, while the normal transition is due to material existing between the Porasil particles, which are 100 A in diameter. Size effects are negligible at dimensions > 1 ~1;thus the temperature difference AT between the transitions is a direct measure of the temprature depression caused by the Porasil. AT is measured at constant calorimeter power in order to minimize the error due to sample temperature gradients. The broad melting peak is expected on account of the distribution of pore size. Fig. 2 is a thermogram of the nematic-isotropic transition for PAA in Porasil 200-400 A pore size. This transition is sharply defined and the broader depressed peak can be resolved. We adopt the expression AT = (-acosa + C)bT/rHp,, where ATis the change in transition temperature relative to the normal transition temperature, r = pore radius, H= transition enthalpy, ps = density of solid, o= interfacial energy between phases, and b = geometric factor (sphere = 2, long cylinder = 1). The sample absorbed in Porasil can be pictured as a string of spheres joined together [7]. We assume the long cylinder value b = I. The COSCY factor accounts for the change in sample-silica interface energy at the transition [6]. Angle

NAFHi HALENE DSC

2

330 Fig. 1. Naphthalcnc

1 December 1976

CIIEMICAL PHYSICS LITIXRS

Volume 44, number 2

tSt i

PORASIL

5./M

340

lK

350 I

360

in Porasif 100-200 A diameter pore size. Melting thermogram DSC 2,2 mC/s, 5O/min.

PAA

DSC

I

20

309

300 i 2

PORASIL

0*3VM

pc/s

lK

309

Fig. 2. PAA in Porasd 200-400 A diamctcr pore xx. Nematic to isotropic thermogram, DSC 2, 0.2 mC/s, 0.3f”/min. (Y is

the equilibrium contact angle for the liquid-solid and solid-silica interfaces. When interfacial strain energy is taken into account [6], the coscy * -1. We assume cost = -1. Hydrostatic pressure is accounted for by the term C. The capillary induces a negative pressure in the liquid state of upper limit 2 upv/f. Application of the Clapyron relation yields: C=2 opv(l/p, - I/p,), where pa =hquid density and liquid-vapor surface tension. For an organic solid, C< 5 erg/cm2 is expected. However, the pressure may be controlled by the larger pore sizes and material externa1 to the pores. Moreover, in a rapid melting situation the equilibrium may not be established. Both of these considerations reduce the parameter C. Contraction of the sample on freezing can increase Cvia the pressure coefficient. Table 1 shows values of u + C derived from AT, assuming r is the arithmetic mean of the pore distribution. The values are seen to be in reasonable agreement with those derived from nucleation studies [I ,I 0], implying that the correction Cis small. The correIation length in the isotropic phase prior to the nematic transition is of order 100 A. Therefore the interfacial energy is associated with a thickness of order 100 A. When the pore diameter is also of order 100 A, a surface energy between the two phases is not physically meaningful. The situation can be described in terms of an elastic distortion energy. It can be shown [ 11 ,I Z] that, using the elastic constants for PAA, AT= oQv

=

CHEMICAL PHYSICS

Volume 44, number 2

LETTERS

1 December

1976

Table 1 Size effect on transition temperature _---__--Transition a)

Sample

Pore diamctcr (A)

-_ O+C

~iluc

(erg/cm*)

(erg/cm2)

benzoic acid

C-I

395

100 150

;‘K’; ---16 7.9

naphthalene

C-I

353

1.50 300

7.2 2.8

30 23

cholcsteryl myristatc

c-s*

343

S-Ch Ch-I

352 358

150 300 300 300

2.4 2.2 0.6 0.3

4 7 0.04 0.02

C-N

391

N-t

409

150 300 300

4.4 2.8 0.27

9.9 12.6 0.03

C-SC

347

2.5 3.5 1.2

3 7 0.09

TKI

-

p-azoxyanisote

hcptyloxyazoxybenzene

--

__---_-----

LOO 1.50 S-N 369 150 --__-_--_-_-_ a) C = crystal, SA =smectic-A, SC = smectic_C, Ch = cholesteric, N = nematic, c) Ref. [ 161. b, Refs. [ 1,101. d, Ref. [ 191.

O.l”C for distortions significant over 100 A range. At 100 A pore diameter the transition enthalpy is still observable; hence the first order character of the transition is not suppressed. In the liquid crystal phases, the correction C could become dominant. The maximum predicted negative pressure causes AT = O.l°C. The temperature depression of the smectic phase is greater, in accord with the larger elastic constant, resulting in a higher apparent o. The pre-transition increase in heat capacity makes the observation barely possible in the cholesteric phase of CM and masks the effect completely in the nematic phase of HAB. The behavior of the solid phase at small pore size is anomalous. Porasil A has pores < 100 A but is not as well defined as Porasil B, range 100-200 A, or Porasil C, range 200-400 A. The smaller the pore size, the larger the effect; therefore the optimum precision should correspond to Porasil B. The samples BA and NAP show an increase of [Tfor smaller pore diameter, while HAB and CM show the opposite behavior. The PAA melt data is dubious because of two solid phases [13]. The inconsistency may be related to the approach’ of the pore diameter to the basic size dimension of the crystal. In CM the largest unit cell dimension [14] is 101 A. At small pore diameter the crystals may be

. 30 22

35 h) 30 b) 6 =)

0.05 j: 0.03 d)

--I = isotropic.

oriented relative to the pore, giving rise to a different surface energy average. When the dimensions of a crystal approach the interaction range of molecular forces, the transition enthalpy should fall. We observe a steady dechne of 25% in H with decreasing pore size. However, accuracy of measurement deteriorates with increasing transition width, and this accounts for some of the decrease. The sample layer in contact with the silica surface may not crystallize, and this could account for the observed magnitude of reduction in H. There is a similar fall in H for the liquid crystaf transitions. The precision further deteriorates for these weaker transitions. Earlier attempts [13,15] to observe surface effects on liquid crystal transitions by a similar technique gave results inconsistent with our own. We conchrde that the increased sensitivity of the DSC 2 over the DSC I B and the uniform pore size of Porasil has pemzitted an improved experiment. DSC observation of crystallization of samples in Porasil shows that the nucleation temperature is depressed several degrees relative to the bulk of the material. The main influence here is that the bulk material requires only one nucleus, whiIe the Porasil sampIe requires many. The temperature remains well above 307

Volume 44, number

2

CHEMICAL

PHYSICS LETTERS

that of homogeneous nucleation temperature [I]. The low temperature tail on thermograms such as fig. 1 shows that some melting is taking place as much as 20°C below the bulk transition. Using 100 A Porasil, the fi_miting detectable temperature depression in BA and NAP is about 4O*C. Homogeneous nucleation in naphthaIene [II is at 94°C undercooling, which indicates that the nucleus state is not attainable in any significant proportion in this experiment. In CM and HAB the melting thermogram begins at about 20°C depression. This is approaching the region of heterogeneous nucleation in CM, at 25°C undercooling [ 161, an indication that the lower end of the pore size distribution is comparable with the nucleus size in CM. We are applying this technique to a study of phase stability of cholesteryl ester particles of biological interest [ 17 J. We are investigating the properties of various coatings on Porasil. A surface layer which orients the liquid crystal [ 181 should have a significant effect on the stability of the liquid crystal phase.

Useful discussions with Professors D.M. Small and G.G. Shipley of Boston University Medical Center and Professor D. Turnbull of Harvard University are gratefully acknowledged.

1 December

1976

References [ 11 A.C. Zettiemoycr,

ed., Nucleation (Dekker, New York, 1969). 12) A.R. Ubbelohde, Meltmg and crystal slruc:ure (Clarendon Press, Oxford, 1965). [31 K.J. Hanszen, 2. Physik 157 (1960) 523. [41 C.R.M. Wronski, Brit. J. Appl. Phys. 18 (1967) 1731. [5 1 C. Hodgson and R. McIntosh, Can. J. Chem. 38 (1960) 958. [6] K.A. Jackson and B. Chalmers, J. Appl. Phys. 29 (1958) 1178. [7] R.J. CharIes, J. Am. Ceram. Sot. 47 (1964) 154. [aj J.H.P. Watson, Phys. Rev. 148 (1966) 223. 191 C.L. Guiilemin, M. LoPage, R. Beau and A.J. de Vries, Anal. Chem. 39 (1967) 935,940. [lo] D.G. Thomas and L.A.K. Staveley, J. Chem. Sot (1952) d569. [ 111 P.G. deGenncs, Physics of liquid crystals (Clarendon Press, Oxford, 1974). [12 j M.J. Stcphcn and J.P. Straley, Rev. Mod. Phys. 46 (1974) 617. 1131 C.C. Chow and D.E. Martire, J. Phys. Chem. 73 (1969) 1127. [ 14 J B.M. Craven and G.T. Detitta, J. Chem. Sot. Perkin Trans. II 7 (1976) 814. [15] D.E. Martire, P.A. Blasco, P.F. Carone and H. Vicini, J. Phys. Chem. 72 (1968) 3489. (161 F.P. Price and A.K. Fritzsche, J. Phys. Chem. 77 (1973) 396. 117) R.J. DeckcIbaum,C.G. Shipley, D.M. Small, R.S. Lees and P.K. George, Science 190 (1975) 392. [ 181 F.J. Kahn, Appl. Phys. Letters 22 (1973) 386. [19] W.R. Runyan and A.W. Nolle, J. Chem. Phys. 27 (1957) 1081.