1144
J. Phys. Chem. 1996, 100, 1144-1152
Crystalline and Amorphous Phases in the Ternary System Water-Sucrose-Sodium Chloride Evgenyi Yu Shalaev† and Felix Franks* BiopreserVation DiVision, Pafra Ltd., 150 Cambridge Science Park, Cambridge CB4 4GG, U.K.
Patrick Echlin Department of Plant Sciences, UniVersity of Cambridge, Cambridge CB2 3EA, U.K. ReceiVed: April 13, 1995; In Final Form: June 9, 1995X
The glass transitions, softening points, devitrification, and melting have been determined by differential scanning calorimetry for the ternary system water-sucrose-sodium chloride over the accessible composition range. X-ray diffraction was used to identify the devitrification in freeze-dried samples. Devitrification is due to NaCl crystallization from the wholly amorphous mixtures and of sucrose or the ternary compound sucrose. NaCl‚2H2O in the crystalline freeze-dried mixtures. The part of the solid/liquid state diagram with glass transitions and softening temperature surfaces and the line of the “maximally” freeze-concentrated solutions are represented as projections on the composition triangle.
Introduction The thermochemical and thermomechanical properties of and crystallization processes in amorphous carbohydrates have grown into topics of interest and considerable research activity. Following the pioneering studies of Slade and Levine,1-3 the significance of glass transitions of anhydrous carbohydrates and their mixtures with low amounts of water has been increasingly recognized, especially by the food processing industry. More recently, interest in such phenomena has also spread to the pharmaceutical and bioindustries.4-6 For example, it is now recognized that the glass transitions of sugars in frozen, supersaturated solutions are the single most important determinants for the development of effective pharmaceutical freezedrying processes.7,8 In the past, most physicochemical studies of solid/liquid phase relationships have been limited to equilibrium phase diagrams, but it is now becoming clear that metastable and thermodynamically unstable, supersaturated states are of great practical importance, especially for mixtures in which eutectic phase separation does not occur spontaneously in observable periods and which, therefore, commonly exist as amorphous solids. The combination of conventional phase coexistence curves with glass transition/composition profiles and, possibly, crystal nucleation information in single diagrams has given rise to the description “state diagram”.9 The state diagram thus aims to incorporate a time dimension into the pictorial representation, in the sense that both vitrification and nucleation phenomena are kinetic rate processes, functionally unrelated to phase transitions. The experimental establishment of solid/solid and solid/liquid state relationships has in the past relied to a large extent on differential scanning calorimetry (DSC), sometimes used in conjunction with X-ray diffraction. Thus, DSC has been widely used in studies of binary aqueous solutions of carbohydrates, but there are at present few reports of its application to more complex mixtures. Water-glycerol-sodium chloride,10 waterhydroxyethyl starch-sodium chloride,11 and water-sucroseglycine12,13 appear to be the only ternary systems for which detailed information is available. † Present address: School of Pharmacy, University of Wisconsin, Madison, WI 5306-1515. X Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-1144$12.00/0
As has been repeatedly demonstrated, the study of vitrification, nucleation, and crystallization phenomena by DSC introduces complexities, because the measurements are often affected by the thermal history of the sample under study, so that the experimental procedures may need to rely for their reliability on annealing protocols and the correction for artifacts due to scanning rate, change in sample configuration, etc. Where such corrections are not performed, DSC will only provide information about the crystallization and melting of one component, usually water, which is the least revealing aspect of the behavior of such complex mixtures. We have already reported the equilibrium phase behavior of the system water-sucrose-sodium chloride,14 and we now extend the previous results to include the amorphous region of the ternary state diagram. It is opportune to recall the complexity of the equilibrium phase diagram which, apart from the anhydrous crystalline phases, contains several crystal hydrates and a hydrated stoichiometric compound of sucrose and NaCl, with all of the above hydrates exhibiting peritectic behavior. It was therefore likely that a construction of the complete state diagram would require careful and comprehensive experimentation. The motivation for the study of this particular system derived in part from its importance in the manufacture and drying of therapeutic preparations designed for injection and infusion, such as blood coagulating factors and peptide hormones. Materials and Methods Pharmaceutical grade microcrystalline sucrose was a gift from Tate & Lyle Ltd. NaCl was of BDH Laboratory reagent grade (99.9%). The crystalline materials were used without further purification. Distilled water was used for all experimental work. The Perkin-Elmer DSC-2 instrument used in this work was fitted with autoscanning and subambient temperature accessories. The DARES data collection and handling system was used for recording and processing power-time curves. This system enables the normal sensitivity of the instrument to be increased by 3 orders of magnitude.15 The test solutions were cooled to 210-220 K, and the recording of DSC traces was started at 220-230 K. The melting points of ice (273.2 K) and indium (429.8 K) were used for temperature calibration. © 1996 American Chemical Society
Phases in the System Water-Sucrose-Sodium Chloride
Figure 1. Composition triangle for the ternary system water-sodium chloride-sucrose: (b) studied compositions; (-‚-) projection of the line of secondary crystallization of H2O + NaCl‚2H2O; (O) experimentally determined points on the projection of the line of freezeconcentrated solutions remaining after primary water crystallization. Their coordinates were determined from Tg curves for isoplethal sections for R ) 15, 5, 7, and 3.5 (Figure 10 and Tables 2 and 3) and were graphically extrapolated to the corresponding Tg′ ) f(R) values for freeze-concentrated solutions remaining after primary water crystallization. Broken portions of the e1Wg′′ and ab curves signify extrapolations. Wg′′: invariant point of the maximally freeze-concentrated solution after primary and secondary crystallization. The broken-dotted line shows the sucrose to sodium chloride ratio in the invariant mixture (see text and Figure 9 for explanation); dotted line show estimated errors in the R′′ value. The most probable location of Wg′′ lies within the rectangle.
Scanning rates for cooling and heating were 10 K/min for freezedried preparations and 5 K/min for solutions. A DSC-7 instrument was used to study the low temperature events ( 4, where only water had crystallized during freeze-drying. The addition of a small amount of NaCl produces a sharp decrease in the intensity of the devitrification exotherm D1, as compared to a similar scan for pure freeze-dried sucrose.16 The X-ray diffractogram of the dried preparation with R ) 6 shows no crystalline features (Figure 5.1). SEM micrographs for this sample (not shown) do not reveal any features which can be related to a crystalline phase. Thermal cycling at a temperature above the endothermic step led to changes similar to those observed for freeze-dried sucrose, namely, the disappearance of the second thermal event and an invariant low-temperature endothermic step (Figure 4, scans 2-4); the assignments are as before. DSC scans for the freeze-dried mixture which had undergone secondary crystallization during cooling are shown in Figure 6: only one endothermic step is observed; there is no indication of Ts. Probably in partially crystalline mixtures the general configu-
Figure 5. X-ray diffraction patterns of freeze-dried mixtures with R ) 6.0. Diffractograms 1 and 2: R ) 5.98 and 4.0% water content (devitrification temperature: 364.3 ( 1 K at a heating rate of 10 K/min) for 1 the untreated sample, and 2, the sample with the effects of thermal treatment (heating from room temperature to 358 K at the rate of 3-10 K/min, annealing at 353-358 K during 5 min). The main peaks correspond to NaCl (see also Table 1). Diffractogram 3: R ) 6.0 and 6.2% water content (Tg ) 284.7 ( 15 K at a heating rate of 10 K/min). The sample was annealed at 310 K during 21 days. The intense peaks correspond to NaCl lines (see Table 1). The SEM micrographs corresponding to diffraction pattern 3 are shown in the upper and lower panels of the right hand side of the figure. Scale bar ) 100 and 10 µm, respectively.
1148 J. Phys. Chem., Vol. 100, No. 4, 1996
Shalaev et al.
Figure 6. DSC heating scans for a partially crystalline freeze-dried mixture with R ) 0.568 and 1.4% water content: heating rate, 10 K/min. Scan 1: continuous heating. Scans 2 and 3: thermal cycling above Tg (heating up to 330 K (scan 2), followed by cooling and heating (scan 3)).
ration of the amorphous phase in the DSC pan only changes insignificantly at Ts, because the crystalline microstructure is unaffected up to its melting temperature and can provide mechanical support to the amorphous component. However, X-ray diffraction now reveals the crystalline peaks of NaCl, superimposed on a small contribution from the amorphous phase (Figure 7a). The SEM micrographs (Figure 5, the upper and lower panels on the right hand side) differ from those of the wholly amorphous sample and show the presence of needlelike patterns which can be assigned to NaCl crystals, in line with the X-ray diffraction data. Note that these crystals were obtained by the dehydration of the dihydrate during freeze-drying. The DSC scans of freeze-dried mixtures exhibit several interesting features (Figure 8). For wholly amorphous samples, with R ) 5, 6, and 10, heating to a temperature above that corresponding to the exotherm, followed by cooling and repeated heating, led to the following changes (Figure 8b-d): (1) a decrease in Tg, (2) a pronounced broadening of the strong exothermic peak, and (3) the appearance of a broad, strong endothermic peak. Thermal cycling of the mixtures with R ) 0.568 led to the disappearance of the exotherm (Figure 8a), with a slight increase in the intensity and width of the endotherm. X-ray patterns for the freeze-dried mixtures after thermal treatment are shown in Figures 5.2, 5.3, and 7b. The positions and relative intensities of the lines appearing after thermal cycling and annealing of the amorphous freeze-dried preparation (R ) 6) correspond to the main NaCl lines (Table 1). Thus, the exotherm D1, observed for the wholly amorphous samples, is due to NaCl crystallization. A typical SEM micrograph taken after annealing at 310 K for 21 days is shown in Figure 7. It shows the appearance of spherulites of dimensions 1-5 µm, consistent with earlier results in which a similar growth of NaCl crystals from freeze-dried amorphous sucrose had been detected by SEM.27 For mixtures which exhibited crystallization during freezedrying, subsequent thermal treatment led to the appearance of three additional, low intensity diffraction peaks (Figure 7b). They are attributed to sucrose and the ternary compound, already referred to.28 For this sample, therefore, the exotherm shown in Figure 6 is assigned to the crystallization of sucrose and, possibly, the compound. We conclude that, for wholly amorphous mixtures, the first heating process leads to the crystallization of NaCl at a devitrification temperature D1, while the annealing treatment produces crystalline sucrose and/or the ternary compound, at D2. It should be noted that D1 > D2!
Figure 7. Section of the X-ray diffractograms for the freeze-dried mixture as in Figure 6. (TD ) 381.2 ( 2 K): (a) untreated; (b) after thermal treatment (heating from room temperature to 358 K at 15-10 K/min; annealing at 353-358 K during 11 min). Weak additional peaks are visible; they correspond to diffraction peaks of sucrose and/or the ternary compound. A representative SEM micrograph is shown in the bottom panel. Scale bar ) 10 µm.
Three different melting temperatures (Mi) can now also be described (see Figure 8): (1) M1, corresponding to D1, (2) M2, corresponding to D2, and (3) M3, a melting process without corresponding glass and devitrification processes. Here M1 > M2 > M3. On the basis of the available evidence, we speculate that M1 is due to primary NaCl melting, M2 to the secondary melting of (ternary compound + sodium chloride) or (sucrose + sodium chloride), and M3 to the ternary melting of (sodium chloride + sucrose + compound). There are, however, insufficient data to establish these assignments unambiguously and to construct corresponding surfaces, e.g., the surface of NaCl solubility, in the ternary phase diagram. Construction of the Ternary Solid/Liquid State Diagram. It is now possible to employ previously published approaches to
Phases in the System Water-Sucrose-Sodium Chloride
J. Phys. Chem., Vol. 100, No. 4, 1996 1149
Figure 9. Glass transition and softening temperatures of freezeconcentrated solutions as a function of the sucrose/NaCl ratios: a′b′ and c′d′ are the softening and glass transition temperatures (Ts′ and Tg′) of freeze-concentrated solutions remaining after the primary crystallization of water. Lines ab and cd are the invariant softening and glass transition temperatures (Ts′′ and Tg′′) of the freezeconcentrated solutions after primary water and secondary (H2O + NaCl‚2H2O) crystallization. Broken lines indicate the confidence limits of Tg′′ and Ts′′: Tg′′ ) 203.2 ( 5 K; Ts′′ ) 227.7 ( 1.8 K. The intersection of c′d′ and cd gives the R value of the invariant freezeconcentrated solution after primary and secondary crystallization (see also Figure 1.). Explanation of symbols: 4, Tg′ (MacKenzie20); O, Tg′ (this work); b, Ts′ (this work); 2, Ts′ (MacKenzie20); 9, Ts′′ (this work); 0, Tg′′ (this work).
Figure 8. DSC heating scans for freeze-dried samples showing the effect of thermal cycling above the devitrification temperature: (a) R ) 0.568, 1.4% water; thermal history, heating above the glass transition temperature (scan is shown in Figure 6, scan 2)-cooling-heating above devitrification temperature (scan 1)-cooling-heating (curve 2). (b) R ) 4.97, 4.53% water; thermal history, heating above devitrification temperature (scan 1)-cooling-heating (scan 2). (c) R ) 6.0, 3.95% water; thermal history, heating above softening temperature (scan is not shown)-cooling-heating above devitrification temperature (scan 1)-cooling-heating (scan 2). (d) R ) 10.31, 2.8% water; thermal history, heating above softening temperature (scan 1)-cooling-heating above devitrification temperature (scan 2)-cooling-heating (scan 3). Apparently, devitrification D1 took place during the first heatingcooling scan because the glass transition temperature decreases after the first scan.
the construction of ternary state diagrams with crystallizable and vitrifying components12,13 to the water-sucrose-sodium chloride system. We use a geometric analogy between some elements of equilibrium phase diagrams and solid/liquid state
diagrams. Numerous experimental observations are on record for binary aqueous systems, indicating that the temperatures of two endothermic events (considered here as the glass transition and the softening point) after the crystallization of water, are independent of the initial solution concentration. Also, for water-rich ternary mixtures glass and softening temperatures after primary water crystallization are functions of the solute mass ratio and are independent of the initial water content. Tg and Ts values obtained after primary water and secondary (water + solute) crystallization are independent of the initial composition (e.g., ref. 13). Such behavior resembles the eutectic point in binary and ternary equilibrium phase diagrams and the surface of secondary crystallization in ternary systems. The Appendix provides a formal comparison between features of the equilibrium phase and solid/liquid state diagrams. The experimental data reported by MacKenzie26 and in this work can now be assigned to the following domains of the solid/liquid state diagram: (1) the glass transition surface for the low-moisture region, Tg ) f(R,W), where W is the water content; (2) the “softening transition” surface for the low-moisture region, Ts ) f(R,W); (3) the linear glass transition surface for the waterrich region, Tg′ ) f(R); (4) the linear softening transition surface for the water-rich region, Ts′ ) f(R). Note, however, that the Tg values for water-sucrose binary mixtures, reported by MacKenzie in ref 26, lie well below those published earlier by the same author.20 The available data also permit the construction of the projection of a curve of “maximally” freezeconcentrated solutions, i.e., after primary water crystallization, on the composition triangle, as well as the estimation of the coordinates of a “pseudoinvariant point” which corresponds to the maximally freeze-concentrated solution after primary water and secondary (H2O + NaCl‚2H2O) crystallization.
1150 J. Phys. Chem., Vol. 100, No. 4, 1996
Shalaev et al.
TABLE 1: X-ray Diffraction Results (I, Relative Intensity)a R ) 0.568, 1.45% water theoretical NaCl d, Å
I
3.258 2.821 1.994 1.701 1.628 1.410 1.294 1.261 1.1515 1.0855 0.9969 0.9533 0.9401 0.8917 0.8601 0.8503 0.841 a
nontreated (Figure 7a) d, Å
13 100 55 2 15 6 1 11 7 1 2 1 3 4 1 3 2
heated (Figure 7b) I
3.254 2.824 1.998 1.705 1.632 1.410 1.296 1.263 1.154 1.087 0.999 0.955 0.941 0.893 0.861 0.851
7.3 100 49 1.5 11.8 2.7 0.6 9.9 6.4 0.6 1.7 0.7 3.1 2.6 0.5 2.0
d, Å
I
4.715 3.595 3.254 2.820 1.996 1.704 1.631 1.413 1.295 1.263 1.153
0.8 0.8 10.1 100 49.5 1.7 12.5 4.8 0.5 10.8 6.5
0.998 0.955 0.942 0.893
1.6 0.6 3.3 2.8
0.850
1.2
R ) 5.98, 4% water heated (Figure 5.2)
R ) 6.0, 6.2% water annealed (Figure 5.3)
d, Å
I
d, Å
I
3.256 2.823 1.996
9.9 100 53.8
2.832 2.002
100 61
1.631
13.1
1.263 1.153
12.4 7.1
0.945
1.8
1.630 1.412
23 33.1
0.940
74.5
For treatment conditions, see Figures 5 and 7.
TABLE 2: Polynomial Coefficients for the Glass Transition Temperature, Tg′, as a Function of X ) Concentration of (Sucrose + Sodium Chloride) in % w/w; Tg ) a + bX + cX2; r2 is the Correlation Coefficient sucrose/ NaCl
a
b
c
r2
3.97 15 5 7
-249 1444 1033 1453
5.630 63 -32.004 76 -22.882 7 -32.000
0 0.209 9764 0.159 582 0.208 90
0.9961 0.955 0.9877 0.9955
a
Xa 88 82 82 80
96 100 98 100
Range of concentrations over which the equations are applicable.
TABLE 3: Polynomial Coefficients for Softening Temperatures, Ts, of Freeze-Dried Samples as a Function of X ) Concentration of (Sucrose + Sodium Chloride) in % w/w; Ts ) a + bX; r2 is the Correlation Coefficient sucrose/NaCl
a
b
r2
15 5
-439 -565
8.130 29 9.463 2
0.971 0.789
a
Xa 93 94
100 98
Range of concentrations over which the equations are applicable.
Figure 9 combines Tg and Ts data for water-rich compositions as functions of R. Lines ab and cd refer to the freezeconcentrated solution after both primary and secondary crystallization (Ts′′ and Tg′′), while a′b′ and c′d′ describe Ts′ and Tg′ after primary crystallization only. The points of intersection b and d indicate the solute concentration ratio for the freezeconcentrated solution after primary and secondary crystallization. To describe the glass transition and softening surfaces in the low-moisture region, the method of isotherms on the composition triangle was employed.13 The experimental points for isoplethal sections with R ) 4.0, 5.0, 7.0, and 15.0 were smoothed by second-order polynomials (Tables 2 and 3). The section for R ) 15.0 is shown in Figure 10, as an example. The compositions were determined graphically at six selected temperatures for the Tg surface and at three temperatures for the Ts surface; they are shown on the composition triangle in Figure 11. The composition of the maximally freeze-concentrated solution after primary water crystallization, Wg′, in a binary system is a pseudoinvariant point and can be determined as the intersection of the Tg line for solutions in which complete
Figure 10. Low-moisture portion of the isoplethal section of the solid/ liquid state diagram for R ) 15. Tg: glass transition temperatures. Ts: softening temperature. TD1, TM1: see text for explanation. Tg and Ts curves were fitted by polynomial equations (see Tables 2 and 3 for coefficients).
primary crystallization has taken place (Tg ) constant) and the curve for completely vitrified solution Tg ) f(W).19 For the ternary system water-X-Y, Wg′ ) f(R), where R ) X/Y. Coordinates of the points belonging to this curve were determined with the aid of isoplethal sections for R ) 5.0, 7.0, and 15.0 and Tg′ data for maximally freeze-concentrated solutions, shown as c′d′ in Figure 9. The line ab in Figure 1 presents the estimated coordinates of points belonging to the curve of the maximally freeze-concentrated solutions after primary water crystallization. Note that a graphical extrapolation was used to determine the composition coordinates of these points. The estimated uncertainties in the concentrations are 3-4%. The point which describes the maximally freeze-concentrated solution after complete phase separation of ice and NaCl‚2H2O is pseudoinvariant (see 2f in the Appendix) and is characterized in the ternary solid/liquid diagram by Tg′′ ) 203.2 ( 5 K and Ts′′ 227.7 ( 1.8 K (Figure 9). The intersection of the surface
Phases in the System Water-Sucrose-Sodium Chloride
J. Phys. Chem., Vol. 100, No. 4, 1996 1151 Ternary Systems.
surface of solute primary crystallization Tp ) f(R,W)
(1c)
linear surface of secondary crystallization Tsec ) f(R)
(1d)
The expression “linear surface” means that the intersection of the surface by a plane which is parallel to the composition triangle produces not a curve but a line that meets the water apex. A two-dimensional representation thus becomes possible, as shown in Figure 9.
projection of the curve of secondary crystallization on the composition triangle Xsec ) f(R)
Figure 11. Sucrose corner of the composition triangle, showing glass transition (solid lines) and softening (broken lines) isotherms. Glass transition isotherms: ., 330 K; 0, 315 K; 4, 300 K; 3, 285 K; ), 270 K; ", 255 K; O, 240 K. Softening isotherms: b, 340 K; 4, 320 K; 9, 300 K.
of Tg′ ) f(R) by the plane for Tg′′ which is parallel to the composition triangle gives the line connecting the water apex and this pseudoinvariant point (point d in Figure 9 and the broken-dotted line in Figure 1). The projection of this point on the composition triangle can be estimated as the intersection of the Wg′ curve (ab in Figure 1) and the broken-dotted line in Figure 1. The composition of this point lies within the rectangle in Figure 1. From the data in Figures 1 and 9-11, an optimal freezedrying pathway can be charted and corresponding processing conditions can be specified. These practical implications of the work here reported will be discussed elsewhere.
(1e)
This is the curve representing the intersection of the linear surface of secondary crystallization and the surface of primary crystallization of X1 in the equilibrium phase diagram, and the intersection of the linear surface Tg′ ) f(R) and the glass transition surface for low-moisture compositions, Tg ) f(R,W), in the solid/liquid state diagram.
eutectic point Te, Xe ) constant
(1f)
2. Solid/Liquid State Diagram. Binary System.
glass transition (softening point) curve Tg(Ts) ) f(X)
(2a)
point of MFCS after water crystallization Tg′′, Wg′′ ) constant
(2b)
Ternary System. Acknowledgment. We express our gratitude to Ross Hatley, Barry Aldous, and Tony Auffret for constructive discussions and to members of the Department of Materials Science for their assistance with the low-temperature DSC and the X-ray diffraction studies. E.Yu.S. also thanks the Royal Society for the award of a Fellowship, the Fellows of Clare Hall, Cambridge, U.K., for a Visiting Associateship and Pafra Biopreservation for hospitality during his stay in the U.K.
glass transition (softening point) surface for low-moisture compositions Tg(Ts) ) f(R,W)
linear glass transition and softening point surfaces of FCS after primary water crystallization Tg′ ) f(R), Ts′ ) f(R)
Appendix Comparison between geometric elements of an equilibrium phase diagram and a solid/liquid state diagram for water-X and water-X1-X2 systems: FCS ) freeze-concentrated solution; MFCS ) maximally freeze-concentrated solution. 1. Equilibrium Phase Diagram. Binary Systems.
(2c)
(2d)
projection of the FCS curve after primary water crystallization on the composition triangle Wg′ ) f(R)
(2e)
(See discussion above, immediately after eq 1e.)
curve of solute primary crystallization (solubility) Tp ) f(X)
point of MFCS after primary water and secondary (water + X1) crystallization (1a)
eutectic point
Tg′′, Wg′′, Ts′′ ) constant
(2f)
References and Notes
Te, Xe ) constant
(1b)
(1) Levine, H.; Slade, L. J. Chem. Soc., Faraday Trans. 1 1988, 84, 2619.
1152 J. Phys. Chem., Vol. 100, No. 4, 1996 (2) Levine, H., Slade, L. Water Relationships in Foods. AdV. Exp. Med. Biol. 1991, 302, 29. (3) Levine, H.; Slade, L. In The Glassy State in Foods; 1993, Blanshard, J. M. V., Lillford, P. J., Eds.; Nottingham University Press: Nottingham, U.K., p 35. (4) Franks, F.; Hatley, R. H. M.; Mathias, S. F. Biopharm 1991, 4, 38. (5) Finegold, L.; Franks, F.; Hatley, R. H. M. J. Chem. Soc., Faraday Trans. 1 1989, 85, 2945. (6) Ahlneck, C.; Zografi, G. Int. J. Pharm. 1990, 62, 87. (7) Franks, F. Cryo-Letters 1990, 11, 93. (8) Ablett, S.; Izzard, M. J.; Lillford, P. J. J. Chem. Soc., Faraday Trans. 1992, 88, 789. (9) Franks, F. In Water-A ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1982; Vol. 7, p 215. (10) Shepard, M. L.; Goldston, C. S., Cocks, F. H. Cryobiology 1976, 13, 9. (11) Jochem. M.; Ko¨rber, Ch. Cryobiology 1987, 24, 513. (12) Suzuki, T.; Franks, F. J. Chem. Soc., Faraday Trans. 1993, 89, 3283. (13) Shalaev, E. Yu.; Kanev, A. N. Cryobiology 1994, 31, 374. (14) Shalaev, E. Yu.; Franks, F. Thermochim. Acta 1995, 255, 49. (15) Hatley, R. H. M., Franks, F.; Green, M. Thermochim. Acta 1989, 156, 247.
Shalaev et al. (16) Shalaev, E. Yu.; Franks, F. J. Chem. Soc., Faraday Trans. 1995, 91, 1511. (17) Chang, B. S.; Randall, C. S. Cryobiology 1992, 29, 632. (18) Kanev, A. N.; Kosyakov, V. I.; Malakhov, D. V.; Shalaev, E. Yu. IzV. So AN SSSR, Ser. Khim., 1989, 2, 11. (19) Rasmussen, D.; Luyet, B. Biodynamica 1968, 10, 167, 319. (20) MacKenzie, A. P. Philos. Trans. R. Soc. 1977, B287, 167. (21) Franks, F. Biophysics and Biochemistry at Low Temperatures; Cambridge University Press: Cambridge, U.K., 1985. (22) Shalaev, E. Yu. Ph.D. thesis, VECTOR Inst. Koltsovo, Russia, 1991. (23) Williams, R. J.; Carnahan, D. L. Cryobiology 1990, 27, 479. (24) Orford, P. D.; Parker, R.; Ring, S. G. Carbohydr. Res. 1990, 196, 11. (25) Hatley, R. H. M.; Mant, A. Int. J. Biol. Macromol. 1993, 15, 227. (26) MacKenzie, A. P. Proceedings of the Meeting Comission C1, Tokyo; Institute International du Froid: Paris, 1985; p 21. (27) Franks, F.; Van den Berg, C. In Topics in Pharmaceutical Sciences; Crommelin, D. J. A., Midha, K. K., Eds.; Medpharm: Stuttgart, Germany, 1991; p 233. (28) Druzhinin, I. G.; Arbayev, S. A. IzV. Akad. Nauk Kirg. SSR 2 1960, 95.
JP951052R
