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Ice propagation in systems of biological interest
Ice Propagation in Systems of Biological Interest. I. Effect of Membranes and Solutes in a Model Cell System1 C. V. Lusena and W. H. Cook’ From the Division
of Applied
Biology,
National
Research Laboratories,
Ottawa, Canada Received March 4, 1953 INTRODUCTION
To fully understand winter hardiness and the problems involved in the preservation of biological materials by freezing and freeze-drying, a fuller knowledge of the mechanism of ice propagation in cells and tissues is necessary. At slow freezing rates the ice phase in biological materials is essentially continuous as the water moves through the tissues to support crystal growth. However, if at rapid freezing rates crystal growth exceeds the mean rate of moisture movement, either the existing ice crystals will penetrate to the water, or the ice phase will be discontinuous. Both living and dead tissues are reported to resist ice-crystal penetration (1, 3). Such resistance could be caused either by cell membranes acting as barriers to ice crystals or by the cell contents retarding icecrystal growth. Other than the work of Galos (5) with regenerated cellulose bags, there is little direct evidence that hydrophilic membranes act as barriers. On the other hand, the rate of crystal growth is greatly reduced in gelatin jellies (2) and various solutions (6). If, at fast cooling rates, the rate of crystal growth were so reduced that the heat released by crystallization were less than the heat removed, supercooling and nucleation might occur beyond the ice front, and the ice phase would be discontinuous. The present work was undertaken to determine the resistance of vari1 Contribution issued as National Research Council No. 3040. f With the technical assistance of J. M. Ross. 232
ICE PROPAGATION IN SYSTEMS. I
233
ous membranes and jellies to the penetration of ice crystals during freezing. As biological tissues are complex, a model cell system was used to simplify experimental procedures and facilitate interpretation of the results. METHOD The model consisted of a vertical cylinder of liquid separated transversely into cells by membranes. The cylinder was cooled from the lower end, and the progress of freezing was followed by the sequence of temperature changes associated with
: 14/
Y-CORK
i
/ I/
G;
INSULATION
THERMOCOUPLE--,
/
-T&T
YA’TERIAC
L&i FIQ. 1. Model cell system.
crystal formation, i.e., a gradual fall to below the freezing point (supercooling) followed by a sharp rise. The argument taken was that supercooling to induce nucleation would occur separately in each cell if the membranes acted as barriers to crystal penetration. If, on the other hand, there were no barriers, supercooling would occur in one cell only (4). The model (Fig. 1) was mounted on an aluminum cooling platform connected by an insulated brass rod to a solid aluminum cylinder immersed in either Dry Ice or liquid air. The freezing rate was determined by the choice of cooling medium and the length of the brass rod. The dimensions of each cell (inside diameter 6 cm., height 0.6 cm.) and wall thickness (0.5 cm.) were such that the vertical heat conduction through the wall was negligible compared with that through the contents. A Dewar flask was inverted over the model to reduce the heat gain from the surroundings. Cooling from the bottom minimized convection within the cells.
C. V. LUSENA AND W. H. COOK
234
The cell assembly proper, starting from the cooling platform, consisted of a test membrane, a 30-mesh copper screen to which a thermocouple was soldered, and a polymethyl methacrylate (Lucite) ring 6 mm. high. This sequence was repeated to provide a minimum of at least five unit cells separated by membranes and screens. The screens were used to support fragile membranes and to provide more uniform temperature readings. All temperature readings were made on fast electronic recorders. The experimental error in the recorders was &0.2”C. and in the thermocouples fO.l”C. When assembled, starting with the top cell, each unit was filled with about 24 ml. of solution through small holes drilled in the side and fitted with screw plugs. This sequence of filling distended the membranes downward and allowed for expansion on freezing. The total volume was always 120 ml. in the five-cell assembly, and the freezing rate is expressed as the time required to freeze this volume. When permeable membranes (e.g., nylon fabric) were used, supercooling occurred only in the lowest cell. When the membranes were impermeable (e.g., rubber sheet), supercooling occurred independently in each cell, in succession from the lowest upward, and the degree of supercooling in each cell was remarkably uniform (4). With partially permeable membranes, supercooling again occurred successively in all cells but was greatest in the lowest cell. Crystals from this cell must, therefore, have penetrated the membrane into the next cell before independent nucleation occurred. Partial supercooling and crystal penetration occurred subsequently at each of the remaining membranes. To condense the results and provide a relative estimate of permeability, the average degree of supercooling of the upper cells is expressed as a percentage of that observed in the lowest cell. The permeability of membranes to ice may be related to moisture content and porosity. Moisture content was determined, after soaking in water, by blotting off the excess liquid under standardized conditions, weighing, oven-drying, and reweighing. Porosity was estimated by measuring the diffusion of potassium chloride through the membranes. Eighty-five ml. of 0.1 M potassium chloride was separated from 10 ml. of water by a 30-sq. cm. membrane uniformly distended by 25 cm. hydrostatic pressure for 30 min. at 25°C. The potassium chloride found in the water, expressed as a percentage of the equilibrium concentration, is a relative measure of porosity. RESULTS
The Table terials liquids
results obtained with a number of selected membranes I. With the exception of the regenerated cellulose films, were completely permeable to ice crystals and too to permit measurement of the diffusion of potassium
The moisture
content
of the membranes
showed
no relation
appear in these maporous to chloride. to their
permeability to either ions or ice crystals. A special ultrafilter membrane, contained only 7 y0 moisture, was which after drying and rewetting, completely permeable to ice crystals. The behavior of regenerated cellulose films warranted further study.
ICE PROPAGATION
IN SYSTEMS.
235
I
Water and 0.1 M potassium chloride were frozen at two rates with various numbers and thicknesses of film. With increasing thickness, the film became less permeable to ions and more resistant to ice crystal penetration. This relation, shown in Fig. 2, indicates that with a given material the permeability to ice is a function of the porosity. The resistance of the membranes was also increased in the presence TABLE Moisture,
Permeability
I
-
to Chloride Ions and Resistance Wet Membrane Materials
to Ice Crystals
of Various
(120 ml. of 0.1 M KC1 frozen in each test ;I Membranematerial
Moisture
-
Supercoolingin upper cells as per cent of 1st cell
Pf9TlW abilitya
ZS-hr.rate 2.5-hr. rate ~___
% Regenerated cellulose film (0.76 mm. thick) b Regenerated cellulose film (0.38 mm. thick) Goldbeater skins, two Goldbeater skin, one Other membraneac
-
55
16
100
100
54
41
70
loo
41 58 -
0 0 0
0 0 0
‘67 67 7-78
1-
-
a Amount of potassium chloride passedthrough the membranesin 30 min., under standardized conditions expressed as per cent of the equilibrium concen-
tration. bTwo sheets of 0.38-mm. regeneratedcelluloseand binder. c Parchment paper mucous membrane of beef colon, parchment ultrafilter membrane, and ultrafilter membrane dried and rewetted: all too porous to assess permeability.
of 0.1 M potassium chloride (Fig. 2). When ice crystals formed in solutions at subeutectic concentrations, a solution of lower freezing point advanced ahead of the ice front and apparently enhanced the resistance of the membrane to crystal penetration. After freezing, high concentrations (l-3 M) of potassium chloride were found at the membrane. The effect of solutes was demonstrated by replacing the membrane with polystyrene sheets, each perforated with a single hole. At a freezing rate of 2.5 hr., ice crystals from distilled water readily penetrated a 0.05-mm. hole, but, at this fast rate of freezing, ice crystals from 0.1 M sucrose did not penetrate a 0.5~mm. hole and ice crystals from 0.1 M
236
C. V.
FILM NUMBER I 3 FILY,~H~&KWLSS 0.76 0.30
LUSENA
AND
0.:.
H.
0.A
PCRYEAIILITY
TO
COOK
0.L
40
30
20
W.
SO
POYA5SlUY
0.:5
so
CNLOAIDE
FIG. 2. Relation between ice crystals permeability and potassium chloride permeability in regenerated cellulose films : (120 ml. of solution frozen in each test; moisture content of all films about 55%; permeability to potassium chloride expressed as per cent of equilibrium concentration under standardized conditions,)
TABLE Resistance
II
of Gelatin Membranes
to Ice Penetration
(120 ml. of 5% gelatin at pH 4.7” in 0.1 M KC1 frozen in each test; gelatin membranes 3 mm. thick; at the 2.5-hr. rate) Gelatin membrane
Supercooling in upper cells as per cent of 1st cell
%
40 20 15 10
100 100 80 20
0 Similar results were obtained at various pH Ievels between pH 3.5 and 8.0.
237
ICE PROPAGATION IN SYSTEMS. I
potassium chloride did not penetrate a 3.0~mm. opening. Evidently solutes have a marked effect on the penetration of ice crystals through pores. 25 HOUR
2.5 HOUR
RATE
RATE
1
+5 0 -I
-5 -10 0
5
IO
I5
20
0 TIME,
0.5
I.0
1.5
2.0
HOURS
FIG. 3. Comparison of freezing patterns for gelatin jellies with and without impermeable membranes. The arrows indicate the approximate time at which ice passed the thermocouple of each unit cell. Impermeable membranes were placed at positions marked ‘l(C).” In addition to this general effect of solutes that depress the freezing point, certain solutes may exert a specific effect. Gelatin is known to reduce the rate of crystal growth (2), although the freezing-point depres-
238
C. V. LUSENA
AND W. H. COOK
sion is negligible. The addition of 5 !?JO gelatin to 0.1 M potassium chloride made a 0.38-mm. cellulose film impermeable at the 25-hr. freezing rate (cf. Table I for value without gelatin), but did not change the ice permeability of more porous membranes. The permeability of gelatin membranes to ice crystals was also investigated. Five per cent gelatin jellies were used to support more concentrated gelatin membranes about 3 mm. thick (Table II). Films containing 10 and 15 ‘% gelatin resisted crystal penetration, and those containing more than 20% gelatin were impermeable at the 2.5-hr. freezing rate. Results at slower rates were not reliable becauseof diffusion of water into the more concentrated jellies. To study the effect of gelatin in the freezing medium, the basic technique was modified by using a six-cell assembly with an impermeable membrane between alternate cells. The results in Fig. 3 show the temperature sequence within the three paired cells and at the impermeable membranes. With 15 and 20 % gelatin, independent supercooling was evident in the paired cells even in the absence of an impermeable membrane, but normal cooling curves were obtained at gelatin concentrations of up to 10 %. The method was less sensitive at the slower freezing rate but plateaus in the cooling curves were usually evident. Presumably these anomalies occurred throughout the length of the gelatin cylinders between the barrier membranes but could be detected only at the thermocouple position. This behavior of gelatin, particularly at fast freezing rates, may be due either to the depression of the rate of crystal growth (2) or may be characteristic of jellies. However, agar jellies which do not depress the rate of crystal growth (2) showed no evidence of an anomalous temperature sequence indicative of supercooling at gel strength greater than that of 15 % gelatin. A 2 M sucrose solution, which retards the rate of crystal growth (6), gave anomalous freezing patterns similar to those of the higher concentration of gelatin. DISCUSSION
No evidence was found to support Bergh’s suggestion (1) that a membranes’s permeability to ice crystals might depend on its moisture content. Membranes containing as little as 7 % moisture were permeable while other materials (e.g., gelatin) containing over ten times as much water were impermeable. For the present results, the permeability of membranes to ice crystals
ICE
PROPAGATION
IN
SYSTEMS.
I
239
appears to vary with membrane porosity and compositon. With the methods and materials employed, a direct relation between porosity (estimated by permeability to potassium chloride) and ice-crystal permeability was established only for regenerated cellulose film. Since other membranes with similar porosity had markedly different permeability to ice crystals, the composition of the membrane must affect permeability. Solutes in the freezing medium may enhance the resistance of the membrane to ice crystals by depressing the freezing point or by retarding the rate of crystal growth. During freezing, solutes are concentrated and the concentrated solution is driven ahead of the ice front to the membrane. If the concentrated solute retained at the membrane sufficiently lowers the freezing point or retards crystal growth, the supercooling necessary to produce spontaneous nucleation can occur in the dilute solution in the adjacent cell, and the membrane therefore behaves as a barrier to ice crystals. On the other hand, the data obtained with gelatin indicate that the ice phase is discontinuous even in the absence of membranes when, at rapid freezing rates, the heat of crystallization is less than the heat removed. This discontinuity is caused by retardation of the rate of crystal growth by the solute, and it is not a property of jellies since sucrose solutions behaved similarly, but agar jellies did not. A further study of the effect of solutes on the crystal growth is being prepared for publication. If membranes of comparable porosity to those tested exist in tissues, the more porous type could be permeable to crystals at any rate of freezing, but less porous ones would be more resistant to crystal penetration at rapid rates of freezing. The latter condition would be an additional reason for the more normal structural behavior and viability of rapidly frozen tissues or organisms. The behavior of certain solutes in retarding crystal growth and membrane penetration suggests that the composition of the cell contents or of the freezing medium may be more important than membrane structure in determining the pattern of freezing in tissues. This interpretation would also, in part, explain the protective action of certain added solutes in the freezng of viable materials. SUMMARY
Membranes freely permeable to liquids may be either permeable, partly permeable, or impermeable to growing ice crystals. These differ-
240
C. V. LUSENA AND W. H. COOK
ences are not related to the moisture content of the membranes. In a given material (e.g., regenerated cellulose films) permeability to ice crystals increases with porosity, but is also affected by the rate of cooling by membrane composition, and by the properties and concentration of the solute in the aqueous phase. When solutes greatly retard the rate of ice-crystal growth, the ice phase may be discontinuous at fast cooling rates even in the absence of membranes. REFERENCES 1. BEROH, F., Formation of Ice in Tissues in Freezing Foods. Pub. No. 9, Danish Refrigeration Research Laboratory, Copenhagen, Denmark, 1948. 2. CALLOWS, E. E., Proc. Roy. Sot. (London) A108, 307 (1925). 3. CHAMBERS, R., AND HALE, H. P., Proc. Roy. Sot. (London) BllO, 612 (1932). 4. COOK, W. H., AND LUSENA, C. V., Proc. Intern,. Congr. Refrig. 8th Congr. London 357 (1951). 5. GALOS, G., Biodynumica 3, 209 (1941). 6. TAMMANN, G., AND B~~CHNER, A., 2. anorg. u. allgem. Chem. 222, 371 (1935).
of Applied
Biology,
National
Research Laboratories,
Ottawa, Canada Received March 4, 1953 INTRODUCTION
To fully understand winter hardiness and the problems involved in the preservation of biological materials by freezing and freeze-drying, a fuller knowledge of the mechanism of ice propagation in cells and tissues is necessary. At slow freezing rates the ice phase in biological materials is essentially continuous as the water moves through the tissues to support crystal growth. However, if at rapid freezing rates crystal growth exceeds the mean rate of moisture movement, either the existing ice crystals will penetrate to the water, or the ice phase will be discontinuous. Both living and dead tissues are reported to resist ice-crystal penetration (1, 3). Such resistance could be caused either by cell membranes acting as barriers to ice crystals or by the cell contents retarding icecrystal growth. Other than the work of Galos (5) with regenerated cellulose bags, there is little direct evidence that hydrophilic membranes act as barriers. On the other hand, the rate of crystal growth is greatly reduced in gelatin jellies (2) and various solutions (6). If, at fast cooling rates, the rate of crystal growth were so reduced that the heat released by crystallization were less than the heat removed, supercooling and nucleation might occur beyond the ice front, and the ice phase would be discontinuous. The present work was undertaken to determine the resistance of vari1 Contribution issued as National Research Council No. 3040. f With the technical assistance of J. M. Ross. 232
ICE PROPAGATION IN SYSTEMS. I
233
ous membranes and jellies to the penetration of ice crystals during freezing. As biological tissues are complex, a model cell system was used to simplify experimental procedures and facilitate interpretation of the results. METHOD The model consisted of a vertical cylinder of liquid separated transversely into cells by membranes. The cylinder was cooled from the lower end, and the progress of freezing was followed by the sequence of temperature changes associated with
: 14/
Y-CORK
i
/ I/
G;
INSULATION
THERMOCOUPLE--,
/
-T&T
YA’TERIAC
L&i FIQ. 1. Model cell system.
crystal formation, i.e., a gradual fall to below the freezing point (supercooling) followed by a sharp rise. The argument taken was that supercooling to induce nucleation would occur separately in each cell if the membranes acted as barriers to crystal penetration. If, on the other hand, there were no barriers, supercooling would occur in one cell only (4). The model (Fig. 1) was mounted on an aluminum cooling platform connected by an insulated brass rod to a solid aluminum cylinder immersed in either Dry Ice or liquid air. The freezing rate was determined by the choice of cooling medium and the length of the brass rod. The dimensions of each cell (inside diameter 6 cm., height 0.6 cm.) and wall thickness (0.5 cm.) were such that the vertical heat conduction through the wall was negligible compared with that through the contents. A Dewar flask was inverted over the model to reduce the heat gain from the surroundings. Cooling from the bottom minimized convection within the cells.
C. V. LUSENA AND W. H. COOK
234
The cell assembly proper, starting from the cooling platform, consisted of a test membrane, a 30-mesh copper screen to which a thermocouple was soldered, and a polymethyl methacrylate (Lucite) ring 6 mm. high. This sequence was repeated to provide a minimum of at least five unit cells separated by membranes and screens. The screens were used to support fragile membranes and to provide more uniform temperature readings. All temperature readings were made on fast electronic recorders. The experimental error in the recorders was &0.2”C. and in the thermocouples fO.l”C. When assembled, starting with the top cell, each unit was filled with about 24 ml. of solution through small holes drilled in the side and fitted with screw plugs. This sequence of filling distended the membranes downward and allowed for expansion on freezing. The total volume was always 120 ml. in the five-cell assembly, and the freezing rate is expressed as the time required to freeze this volume. When permeable membranes (e.g., nylon fabric) were used, supercooling occurred only in the lowest cell. When the membranes were impermeable (e.g., rubber sheet), supercooling occurred independently in each cell, in succession from the lowest upward, and the degree of supercooling in each cell was remarkably uniform (4). With partially permeable membranes, supercooling again occurred successively in all cells but was greatest in the lowest cell. Crystals from this cell must, therefore, have penetrated the membrane into the next cell before independent nucleation occurred. Partial supercooling and crystal penetration occurred subsequently at each of the remaining membranes. To condense the results and provide a relative estimate of permeability, the average degree of supercooling of the upper cells is expressed as a percentage of that observed in the lowest cell. The permeability of membranes to ice may be related to moisture content and porosity. Moisture content was determined, after soaking in water, by blotting off the excess liquid under standardized conditions, weighing, oven-drying, and reweighing. Porosity was estimated by measuring the diffusion of potassium chloride through the membranes. Eighty-five ml. of 0.1 M potassium chloride was separated from 10 ml. of water by a 30-sq. cm. membrane uniformly distended by 25 cm. hydrostatic pressure for 30 min. at 25°C. The potassium chloride found in the water, expressed as a percentage of the equilibrium concentration, is a relative measure of porosity. RESULTS
The Table terials liquids
results obtained with a number of selected membranes I. With the exception of the regenerated cellulose films, were completely permeable to ice crystals and too to permit measurement of the diffusion of potassium
The moisture
content
of the membranes
showed
no relation
appear in these maporous to chloride. to their
permeability to either ions or ice crystals. A special ultrafilter membrane, contained only 7 y0 moisture, was which after drying and rewetting, completely permeable to ice crystals. The behavior of regenerated cellulose films warranted further study.
ICE PROPAGATION
IN SYSTEMS.
235
I
Water and 0.1 M potassium chloride were frozen at two rates with various numbers and thicknesses of film. With increasing thickness, the film became less permeable to ions and more resistant to ice crystal penetration. This relation, shown in Fig. 2, indicates that with a given material the permeability to ice is a function of the porosity. The resistance of the membranes was also increased in the presence TABLE Moisture,
Permeability
I
-
to Chloride Ions and Resistance Wet Membrane Materials
to Ice Crystals
of Various
(120 ml. of 0.1 M KC1 frozen in each test ;I Membranematerial
Moisture
-
Supercoolingin upper cells as per cent of 1st cell
Pf9TlW abilitya
ZS-hr.rate 2.5-hr. rate ~___
% Regenerated cellulose film (0.76 mm. thick) b Regenerated cellulose film (0.38 mm. thick) Goldbeater skins, two Goldbeater skin, one Other membraneac
-
55
16
100
100
54
41
70
loo
41 58 -
0 0 0
0 0 0
‘67 67 7-78
1-
-
a Amount of potassium chloride passedthrough the membranesin 30 min., under standardized conditions expressed as per cent of the equilibrium concen-
tration. bTwo sheets of 0.38-mm. regeneratedcelluloseand binder. c Parchment paper mucous membrane of beef colon, parchment ultrafilter membrane, and ultrafilter membrane dried and rewetted: all too porous to assess permeability.
of 0.1 M potassium chloride (Fig. 2). When ice crystals formed in solutions at subeutectic concentrations, a solution of lower freezing point advanced ahead of the ice front and apparently enhanced the resistance of the membrane to crystal penetration. After freezing, high concentrations (l-3 M) of potassium chloride were found at the membrane. The effect of solutes was demonstrated by replacing the membrane with polystyrene sheets, each perforated with a single hole. At a freezing rate of 2.5 hr., ice crystals from distilled water readily penetrated a 0.05-mm. hole, but, at this fast rate of freezing, ice crystals from 0.1 M sucrose did not penetrate a 0.5~mm. hole and ice crystals from 0.1 M
236
C. V.
FILM NUMBER I 3 FILY,~H~&KWLSS 0.76 0.30
LUSENA
AND
0.:.
H.
0.A
PCRYEAIILITY
TO
COOK
0.L
40
30
20
W.
SO
POYA5SlUY
0.:5
so
CNLOAIDE
FIG. 2. Relation between ice crystals permeability and potassium chloride permeability in regenerated cellulose films : (120 ml. of solution frozen in each test; moisture content of all films about 55%; permeability to potassium chloride expressed as per cent of equilibrium concentration under standardized conditions,)
TABLE Resistance
II
of Gelatin Membranes
to Ice Penetration
(120 ml. of 5% gelatin at pH 4.7” in 0.1 M KC1 frozen in each test; gelatin membranes 3 mm. thick; at the 2.5-hr. rate) Gelatin membrane
Supercooling in upper cells as per cent of 1st cell
%
40 20 15 10
100 100 80 20
0 Similar results were obtained at various pH Ievels between pH 3.5 and 8.0.
237
ICE PROPAGATION IN SYSTEMS. I
potassium chloride did not penetrate a 3.0~mm. opening. Evidently solutes have a marked effect on the penetration of ice crystals through pores. 25 HOUR
2.5 HOUR
RATE
RATE
1
+5 0 -I
-5 -10 0
5
IO
I5
20
0 TIME,
0.5
I.0
1.5
2.0
HOURS
FIG. 3. Comparison of freezing patterns for gelatin jellies with and without impermeable membranes. The arrows indicate the approximate time at which ice passed the thermocouple of each unit cell. Impermeable membranes were placed at positions marked ‘l(C).” In addition to this general effect of solutes that depress the freezing point, certain solutes may exert a specific effect. Gelatin is known to reduce the rate of crystal growth (2), although the freezing-point depres-
238
C. V. LUSENA
AND W. H. COOK
sion is negligible. The addition of 5 !?JO gelatin to 0.1 M potassium chloride made a 0.38-mm. cellulose film impermeable at the 25-hr. freezing rate (cf. Table I for value without gelatin), but did not change the ice permeability of more porous membranes. The permeability of gelatin membranes to ice crystals was also investigated. Five per cent gelatin jellies were used to support more concentrated gelatin membranes about 3 mm. thick (Table II). Films containing 10 and 15 ‘% gelatin resisted crystal penetration, and those containing more than 20% gelatin were impermeable at the 2.5-hr. freezing rate. Results at slower rates were not reliable becauseof diffusion of water into the more concentrated jellies. To study the effect of gelatin in the freezing medium, the basic technique was modified by using a six-cell assembly with an impermeable membrane between alternate cells. The results in Fig. 3 show the temperature sequence within the three paired cells and at the impermeable membranes. With 15 and 20 % gelatin, independent supercooling was evident in the paired cells even in the absence of an impermeable membrane, but normal cooling curves were obtained at gelatin concentrations of up to 10 %. The method was less sensitive at the slower freezing rate but plateaus in the cooling curves were usually evident. Presumably these anomalies occurred throughout the length of the gelatin cylinders between the barrier membranes but could be detected only at the thermocouple position. This behavior of gelatin, particularly at fast freezing rates, may be due either to the depression of the rate of crystal growth (2) or may be characteristic of jellies. However, agar jellies which do not depress the rate of crystal growth (2) showed no evidence of an anomalous temperature sequence indicative of supercooling at gel strength greater than that of 15 % gelatin. A 2 M sucrose solution, which retards the rate of crystal growth (6), gave anomalous freezing patterns similar to those of the higher concentration of gelatin. DISCUSSION
No evidence was found to support Bergh’s suggestion (1) that a membranes’s permeability to ice crystals might depend on its moisture content. Membranes containing as little as 7 % moisture were permeable while other materials (e.g., gelatin) containing over ten times as much water were impermeable. For the present results, the permeability of membranes to ice crystals
ICE
PROPAGATION
IN
SYSTEMS.
I
239
appears to vary with membrane porosity and compositon. With the methods and materials employed, a direct relation between porosity (estimated by permeability to potassium chloride) and ice-crystal permeability was established only for regenerated cellulose film. Since other membranes with similar porosity had markedly different permeability to ice crystals, the composition of the membrane must affect permeability. Solutes in the freezing medium may enhance the resistance of the membrane to ice crystals by depressing the freezing point or by retarding the rate of crystal growth. During freezing, solutes are concentrated and the concentrated solution is driven ahead of the ice front to the membrane. If the concentrated solute retained at the membrane sufficiently lowers the freezing point or retards crystal growth, the supercooling necessary to produce spontaneous nucleation can occur in the dilute solution in the adjacent cell, and the membrane therefore behaves as a barrier to ice crystals. On the other hand, the data obtained with gelatin indicate that the ice phase is discontinuous even in the absence of membranes when, at rapid freezing rates, the heat of crystallization is less than the heat removed. This discontinuity is caused by retardation of the rate of crystal growth by the solute, and it is not a property of jellies since sucrose solutions behaved similarly, but agar jellies did not. A further study of the effect of solutes on the crystal growth is being prepared for publication. If membranes of comparable porosity to those tested exist in tissues, the more porous type could be permeable to crystals at any rate of freezing, but less porous ones would be more resistant to crystal penetration at rapid rates of freezing. The latter condition would be an additional reason for the more normal structural behavior and viability of rapidly frozen tissues or organisms. The behavior of certain solutes in retarding crystal growth and membrane penetration suggests that the composition of the cell contents or of the freezing medium may be more important than membrane structure in determining the pattern of freezing in tissues. This interpretation would also, in part, explain the protective action of certain added solutes in the freezng of viable materials. SUMMARY
Membranes freely permeable to liquids may be either permeable, partly permeable, or impermeable to growing ice crystals. These differ-
240
C. V. LUSENA AND W. H. COOK
ences are not related to the moisture content of the membranes. In a given material (e.g., regenerated cellulose films) permeability to ice crystals increases with porosity, but is also affected by the rate of cooling by membrane composition, and by the properties and concentration of the solute in the aqueous phase. When solutes greatly retard the rate of ice-crystal growth, the ice phase may be discontinuous at fast cooling rates even in the absence of membranes. REFERENCES 1. BEROH, F., Formation of Ice in Tissues in Freezing Foods. Pub. No. 9, Danish Refrigeration Research Laboratory, Copenhagen, Denmark, 1948. 2. CALLOWS, E. E., Proc. Roy. Sot. (London) A108, 307 (1925). 3. CHAMBERS, R., AND HALE, H. P., Proc. Roy. Sot. (London) BllO, 612 (1932). 4. COOK, W. H., AND LUSENA, C. V., Proc. Intern,. Congr. Refrig. 8th Congr. London 357 (1951). 5. GALOS, G., Biodynumica 3, 209 (1941). 6. TAMMANN, G., AND B~~CHNER, A., 2. anorg. u. allgem. Chem. 222, 371 (1935).