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Flexural strength of ice grown from chemically impure melts
Cold Regions Science and Technology, 4(1981)81-92 Elsevier ScientificPublishing Company, Amsterdam - Printed in The Netherlands
FLEXURAL
S T R E N G T H OF ICE G R O W N F R O M C H E M I C A L L Y
81
IMPURE MELTS
Garry W. Timco Division of Mechanical Engineering, National Research Council of Canada, Ottawa, Ontario K IA OR6 (Canada)
(Received June 10, 1980; acceptedin revisedform September23, 1980)
ABSTRACT
A series of experiments have been performed to measure the ultimate (flexural) strength of ice grown from impure melts containing one of a number of chemical dopants (chloride and sulfate salts, salts of the carboxylic acids, alcohols, amides and sugars). The results of these experiments indicate: (1) within a homologous series, the greatest strength reduction in the ice usually occurs for the lowest member of the series; (2) the overall reduction in strength of the ice to a limiting value is greater for the lower molecular weight dopants; and (3) of the chemical families tested, the most effective ice-strength reducing ones were the R - O H alcohols, the salts of the carboxylic acids and the amides. These results are discussed in terms of the structural features of the ice. An empirical relationship is presented for electrolytic dopants which predicts the optimum concentration of dopant necessary for reducing the strength of ice.
INTRODUCTION
When ice grows from an impure melt, its crystal structure and its mechanical, electrical and thermal properties depend greatly on the type and amount of impurity in the melt. This results in spite of the fact that ice is a very selective lattice which incorporates very few substitutional defects directly into the host lattice (Pounder 1965). Accordingly, as the ice sheet forms, the impurity particles are rejected into the melt such that the amount of impurity which is trapped in the ice is very much less than that in the
melt. If both the initial concentration of dopant particles in the melt is low enough, and the growth rate is slow enough, this rejection process effectively produces an ice sheet which is very similar in both appearance and mechanical properties to that grown from an undoped melt (i.e. fresh water ice). In this case, although the rejected particles build up and raise the impurity level in the liquid adjacent to the interface, the diffusion of these particles away from the interface into the body of the melt is sufficiently fast to prevent any large-scale entrapment of dopant particles in the solid. If, on the other hand, the concentration of solute particles in the melt is higher, and/or the growth rate is more rapid, this diffusion process is not fast enough, and this results in a large build-up of impurities at the growth interface. If, owing to the phase relationship of the components involved, the impurities depress the local liquidus temperature, then at some critical value the actual temperature of the liquid ahead of the interface will be below the liquidus temperature. As a result, the liquid has a region of lower freezing-point solution at the ice-liquid interface, with solution some finite distance from the interface with a greater tendency to freeze. As such, the liquid is "constitutionally supercooled" (i.e. supercooling as a result of composition (Rutter and Chalmers 1953))with the result that the initial planar solid-liquid interface becomes unstable. When this occurs, the planar front solidification ceases and long ice dendrites begin to grow into the melt. These dendrites reach for that liquid which is most ready to freeze and thereby mechanically entrap liquid which is high in solute. As such, this ice consists of a mechanically hard upper layer and a lower columnar layer which consists of long crystal
0165-232X/81/0000-0000/$02.50 © 1981 ElsevierScientific PublishingCompany
82 platelets, some of which extend to the bottom of the ice sheet. These structural features have a pronounced influence on the overall physical properties of this ice (see Weeks and Lofgren 1967, Timco 1978 for more details). This process of constitutionally supercooled growth (Rutter and Chalmers 1953, Tiller et al. 1953), results in an ice sheet whose structure and physical properties are quite different from that of fresh water ice. The specific details of the growth mechanism will depend upon several parameters, including the initial impurity content in the melt, the growth rate (i.e. freezing temperature), the molecular weight of the solute, the adsorption properties of the solute in water, the size, shape and flexibility of the dopant particle, the particle-particle interactions, and the particle-solvent interactions. As might be expected, different dopants can produce vastly different results. To date, however, there have been only a handful of studies on the strength of ice grown from chemically doped aqueous solutions (Moesveld 1937, Pounder 1958, Coble and Kingery 1963). This is in spite of the obvious practical nature and significance of this problem for chemical methods of ice control. Clearly, studies of this type can give good insight into the nature of various chemical-ice interactions and in so doing increase our understanding of the growth mechanism in multi-doped systems such as sea ice. The present experiments were designed to investigate systematically the ice strength-reducing properties of a large number of chemicals by measuring the flexural strength of ice grown from melts containing various concentrations of different dopants. This was done in support of a related engineering activity in this field (Timco 1979a). The purpose of the experiments was to test each chemical dopant (1) to determine its relative effectiveness in reducing the strength of ice; (2) to find the minimum concentration required to reduce effectively the strength of the ice; and (3) to determine general trends in the strengthreducing properties both within and between homologous series. The chemicals chosen for this study were based on the criteria of water solubility, nontoxicity, non-flammability and non-volatility. Based on these criteria, the homologous series of chlorides and sulfates, salts of carboxylic (fatty) acids, alcohols, amides and sugars were chosen for study (see Timco 1979b for a detailed discussion on the method for
choosing these dopants). In this paper, the detailed results of this study are presented, along with the resuiting guidelines for the chemical strength reduction of ice. EXPERIMENTAL These experiments were performed by measuring the flexural strength using the cantilever beam method on ice grown from doped solutions in 225-1 insulated plastic trays which were in a large walk-in cold chamber. The general procedure was to pre-cool the solution overnight at an ambient air temperature of +2 °C, and then freeze to form ice sheets at T = - 2 0 °C for approximately 22 h. For these experiments, the ice was self-nucleated and no artificial seeding was introduced. After the freeze, the ice was allowed to warm up for 3 h to an isothermal equilibrium of approximately -0.5 °C before testing. This was done to eliminate the temperature gradient in the ice and to provide the same test conditions for each test. In testing, 12 cantilever beams were cut in the ice using a standard pruning saw. The thickness of the ice varied somewhat from day to day since the growth rate appeared to be a function of both the amount and kind of impurity in the solution. In general, however, the ice thickness (h) ranged from 3.0 to 4.5 cm for these tests. The cantilever beams were cut to be 6 cm wide so that the beam width (w) was 1 - 2 times the ice thickness. The beam lengths (L) were cut to be 2 0 - 2 5 cm long to maintain a beam length to ice thickness ratio of 5 - 7 for these tests. In loading the beams, one of three Chatillon instrument push-pull gauges ( 0 - 1 kg, 0--2.2 kg, 0-4.5 kg) was used to determine the breaking load (P) for each beam. Each of the rod plungers of these gauges was outfitted with a small inverted-T shaped nylon foot to distribute the load evenly along the end of the beam. All cantilever tests were of the push down type and loading times to failure were typically 1 - 2 s. The flexural strength was calculated from the elastic beam equation of = 6PL/wh 2
(1)
and used as a strength index for this test. Because the apparent flexural strength of the ice can depend upon both the length of the warm-up period (Schwarz 1977, Timco 1979a) and the dimensional ratio of the
83
cantilever beams (S~tec and Frederking 1981), care was taken to ensure that each ice sheet was grown and tested under the same experimental conditions. Nevertheless, the flexural strength of the ice calculated using Eqn.(1) should be regarded only as a strength index for the ice. Before melting the ice foUowing a test, samples of both the ice and the solution were taken in order to estimate the relative dopant concentrations in each. This estimate was done by simply measuring the specific gravity of each with a standard hydrometer. From this, the bulk equilibrium partition coefficient (ke = average concentration of dopant in the ice sample/average dopant concentration in the solution) was calculated. After testing, the ice was melted using immersion heaters, and additional dopant was added while the solution was being agitated with an air bubbler system to ensure thorough mixing. This general testing arrangement allowed three testing days per week. Over 30 dopants were tested for solution concentrations up to 2% (by weight).
RESULTS Preliminary comments
In this section, the results for each dopant will be presented. For comparison purposes, each graph will show the results for an individual homologous series. In every case, each point on the graph represents an average of at least six cantilever beam test results. The order of presentation will be that of the chloride salts, sulfate salts, salts of the carboxylic acids, alcohols, amides and sugars. Chloride salts
Figure 1 shows a graph of the flexural strength (of) versus solution concentrations (Cs) for the monovalent cation-monovalent anion series of chloride salts [lithium chloride (LiCI), sodium chloride (NaC1), potassium chloride (KC1)]. From this graph it is evident that for each dopant, with increasing concentration, the strength of the ice decreases rapidly to a limiting value. Qualitatively, all of the dopants tested produced behaviour of this type, although as shown in Fig. 1, the concentration required for the initial
sharp decrease in strength, as well as the limiting strength of the ice, varied for each individual dopant. The sharp drop in the strength of the ice can be directly correlated to the structural properties of the ice, and in particular, to the onset of the dendritic growth phase for the ice (Timco 1979a). For this ice which is grown from low-concentration melts, the strength is primarily controlled by the thickness of the upper, non-dendritic ice layer - the "incubation length". This is so since almost all of the strength of the ice is in this upper ice layer. As would be expected from consideration of growth from constitutionally supercooled (CS) melts, the time to the onset of the CS instability (i.e. the thickness of the upper layer) decreased for increasing initial impurity content in the melt. As such, as shown in Fig. 1, the overall strength of the ice decreases rapidly with increasing concentration. To produce mechanically weak ice from an impure melt, the impurity concentration must be greater than or equal to that which results in rapid dendritic growth. As shown in Fig. 1, this amount is different for different dopants. In Fig. 1, there are two important features which should be noted: (1) less of the lower molecular weight solute is required to bring about the reduction in strength of the ice; and (2) the saturation or limiting strength value is higher for the higher molecular weight solute. The most effective strength 800 CHLORIDES - C I
o '=: I -r I-(.9 Z I-U')
hx i .J LL
600
400
200
0
0
0,4
0.8 DOPANT
I .2 CONCENTRATION
1.6
2.0
-%
Fig. 1. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of monovalent cation chlorides.
84 reduction occurs tor the lowest member of the series. This observed dependence of strength reduction within a homologous series seems reasonable since, for a given weight of dopant added to the water, there would be more dissociated particles from the lower molecular weight solute. This would increase the number of particles at the ice-solution growth interface. Since the depression of the freezing point is directly related to the number of particles in the melt (Raoult's law), this should produce a more rapid attainment of the constitutionally supercooled instability and the resultant decrease in the mechanical strength of the ice for the lower molecular weight solutes. Qualitatively, therefore, this approach explains the experimentally observed result. However, this situation is not that straightforward. If, for example, a plot is made of the strength of the ice as a function of the number of dopant particles in the melt (or the molality)* for each chemical, based on the above simple picture, the initial drop portion of the curve would be expected to coincide regardless of the type of cation. This, however, is not found to be the case; A plot of this type has the same general features as that shown in Fig. 1. This indicates that: (1) physically less of the lower molecular weight particles are required to bring about the strength reduction; (2) the strength of the ice is not solely determined by the brine volume in the ice; and (3) the lower molecular weight dopants produce a lower limiting strength of the ice. The reason for this is not known, although undoubtedly the solid-liquid interfacial energy as well as the diffusion and adsorption properties of the dopant play an important role. Figure 2 shows a graph of the flexural strength versus solution concentration for the divalent c a t i o n monovalent anion series of chloride salts [magnesium chloride (MgClz), calcium chloride (CaC12), copper chloride (CuCI2)]. In general, this series shows identical behaviour to that of the monovalent cation chlorides (Fig. 1).
•
800
•
x 600 I I
2
•
M• Cl 2
@
Co Cl z
•
Cu Cl 2
X 400
%,
)
X
200
J
• 0
I
1
I O.4
0
I 0.8
DOPANT
I
I 1.2
I
I 1.6
CONCENTRATION
I
I 2.0
-%
Fig. 2. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of divalent cation chlorides. Sulfate salts
Figures 3 and 4 show graphs of the flexural strength versus solution concentration for the monovalent cation-divalent anion series of sulfate salts [sodium sulfate (Na2S04), potassium sulfate (K2S04)] and the divalent cation-divalent anion series of sulfate salts [magnesium sulfate (MgS04),
800
\ i
n°"~ 6 0 0
\
I bo Z w ~ 400
1
SULFATES - SO 4
\
I
,o
NozS04
.\
< x uJ _J LL
200 &__
0
I 0
*It should be pointed out that since all of the ice was tested at the same isothermal temperature, this graph would be the same as plotting the strength of the ice as a function of the brine volume in the ice for each series.
CHLORIDES--Ct
o
I 0.4
I
DOPANT
I 0.8
I
I 1.2
CONCENTRATION
I
I 1.6
I
I 2.0
-%
Fig. 3. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of monovalent cation sulfates.
85
8OO
~ttV I
8OOI[ I1~'i/
SULFATES- SO4
600
",r" (.9 Zhi ~. 4 0 G CO .J
SO4
•
Mg
•
N i SO 4
•
Cu
-
SODIUMSALTSOFCARBOXYLtCACIDS
sool-|I
•
ooF
SO 4
soD,uM FO,M TE
• SODIUMPROPIONATE
rr
::2)
x iJJ 200
2oor
•..... I
I
I
I
I
I
I
I
0.4 0.8 1.2 1.6 DOPANT CONCENTRATION-%
I
I
•
2.0
\\\ "
o
0
0.4
0.8 1.2 1,6 DOPANT CONCENTRATION-%
2.0
Fig. 4. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of divalent cation sulfates.
Fig. 5. Graph of the flexural strength versus the dopant concentration (by weight) for the sodium salts of the carboxylic (fatty) acids.
nickel sulfate (NiSO4), copper sulfate (CuSO4)], respectively. Both these series show the trends previously discussed for the chloride series. Note, however, that the saturation or limiting strength of
reduction in the strength of the ice occurs at a lower concentration for the heavier molecular weight dopant (sodium propionate). However, in agreement with the chloride and sulfate salts, Che saturation or limiting strength of the ice is less for the lower molecular weight dopant (sodium formate). To explain this apparent difference with the chloride and sulfate salts, it should be noted that for organic
this ice is considerably higher than that of the lower molecular weight chloride series. In this case it would seem that although these heavy sulfate particles can bring about the CS instability with a relatively low solution concentration (presumably because of the low rate of diffusion of these heavy particles away from the interface), the high eutectic temperature of this series with water (approximately -1.5 °C) limits the size of the impurity pockets in the ice. This, correspondingly, does not allow for the production of low strength ice from the sulfate series.
800
n°
1
600 1"I ZW('gl--
\ ~ / ~
Salts of the carboxylic (fatty) acids
~.~ 400 CO
Figure 5 shows a graph of the flexural strength versus solution concentration for the sodium salts of the three lowest members of the carboxylic acids [sodium formate, Na(CHO2), sodium acetate, Na(C2H302) and sodium propionate, Na(C3HsO2)]. For this series, the strength-reducing properties on ice are quite good. Although the strength-reducing properties of the first three constant cation salts in this series are similar, it would appear that, in contrast to the chloride and sulfate salts, the sharp
<
ACETATES-C2H302 • Li C2H302 • NO C2H302 • K C2H302
xi~J 200 .J
0 0
I 0.4
0.8
1.2
1.6
I
I 2.0
DOPANT CONCENTRATION-% Fig. 6. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of monovalent cation acetates.
86 compounds such as these, the adsorption of the molecule at the surface markedly increases with increasing molecular chain length (Becher 1977). As such, the relative number of sodium propionate particles at the growth interface would be more than that of sodium formate for equal numbers of dopant particles in the melt. This mechanism, therefore, could bring about the CS instability more rapidly for the heavier sodium propionate dopant. In any event, it is clear that this series is very effective in bringing about a strength reduction in the ice. Figure 6 shows a graph of the flexural strength versus solution concentration for three salts in the acetate series [lithium acetate, Li(C2H302), sodium acetate, Na(C2H302), potassium acetate, K(C2H302)]. In this case, the general strength reduction trends are identical with those observed for the series of chloride and sulfate salts. Figure 7 shows a graph of the flexural strength versus solution concentration for divalent cation formate and acetate series [calcium formate, Ca(CH02)2, magnesium acetate, Mg(C2H302)2, calcium acetate, Ca(C2H302)2]. This graph emphasizes the findings discussed for the other salts of the carboxylic acids (Figs. 5 and 6); viz. (1) for different anion weights for a given cation, the strength reduction is more rapidly attained for the heavier molecular weight anion, and (2) for different cation
weights for a given anion, the strength reduction is greater for the lowest molecular weight cation. Alcohols
Figure 8 shows a graph of the flexural strength versus solution concentration for the R-OH series of alcohols [methyl alcohol (CH3OH), ethyl alcohol (C2HsOH), propyl alcohol (C3HTOH)]. For this series, very low strength ice is achieved at low impurity levels in the solution. In this case, contrary to the chlorides and sulfates, there is virtually no difference between the strength reduction properties of these three members of this series. This ice consisted of a relatively hard upper layer and a lower layer which consisted of many unconnected dendritic platelets suspended vertically into the melt. Presumably these alcohols, which are all less dense than water, congregate at the growth interface to bring about the observed incoherent dendritic growth (see Shulhan et al. 1978 for more details on methyl alcohol as a dopant in ice). Figure 9 shows a graph of the flexural strength versus solution concentration for the series of polyhydric alcohols [ethylene glycol (HOCH2CH2OH), propylene glycol (CH3CH(OH)CH2OH), glycerol (HOCH2CH(OH)CH2OH), and carbowax (HOCH2(CH2OCH~)nCH2OH)]. For these alcohols
800
800
x
I I t-(O Z LU
,
600
\ ~ \
¢r" 400
~"~/
~t'0H ALCOHOLS
"~ 600 f / / I
• CALCIUM FORMATE • MAGNESIUM ACETATE • CALCIUM ACETATE
\
m .J ,<
@ METHYL • ETHYL a PROPYL
L~J
~ ' ~ 1 ~
n,-
xLU
~L
FORMATES - CHOz ACETATES- C2H30z
.
•0
200
200
J_ - •
0
I
I
I
o.a
I~ o.e
,.2
,.s
I
I 2.o
DOPANT C O N C E N T R A T I O N - %
Fig. 7. Graph of the flexural strength versus solution concentration (by weighO for the series of divalent cation formates and acetates.
OO
l 0.4
O. 8
Ill-- I t.2
I
L t.6
I
I 2.0
DOPANT CONCENTRATION - %
Fig. 8. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of ROH alcohols (R = alkyl radicaD.
87
800
-~ 6 0 0 I
1" I(.9 Z b,.I rr
400
x w
200
I-(/3
!
800 AMIDES
POLYHYDRIC ALCOHOLS
II I\ I\
\ \ ~
I\
, ETHYLENEGLYCOL • PROPYLENEGLYCOL .i~ GLYCEROL
\
&\
600
1
•
FORM~.M IDE
•
ACETAMIDE
& CARBAMtDE
.+++DO
4.00
.\.. 200
&-0I 0
I
I
0.4
I
0.8
I
I
1.2
I
I
1.6
I
I
O
2.0
I
I
I
0.4
DOPANT CONCENTRATION-%
.I 0
I
8
12
I
I.
I
I
1.6
I
2.0
DOPANT CONCENTRATION-%
Fig. 9. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of polyhydric alcohols.
Fig. 10. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of amides.
there is no clear trend in their relative strength reduction as a homologous series. In this case, although ethylene glycol is more effective in strength reduction than glycerol, it is less effective than the higher molecular weight propylene glycol. These dopants were only of average effectiveness in reducing the strength of the ice (compare to the R - O H alcohols). The carbowax results are interesting since, considering the relatively high molecular weight of the molecules (approximately 600), they were quite effective in strength reduction. This ice, however, did not show the usual dendritic growth at the lower strengths. Instead, the carbowax appeared to congregate along large crystal grain boundaries and produce macroscopic defects in the ice. As such, the cantilever ice beams with this dopant seldom broke at the root. Although the ice strength for this dopant was low, the mechanism for strength reduction was quite different from that of the lower molecular weight dopant.
of the ice. With respect to the observed variation with molecular weight within the series, it showed the same general trends as the chlorides, sulfates and acetates. Sugars
Figure 11 shows a graph of the flexural strength versus solution concentration for sucrose sugar 800
•
I
Figure 10 shows a graph of the flexural strength versus solution concentration for the series of amides [formamide (HCONH2), acetamide (CH3CONH2) , carbamide (urea) (NH2CONH2)]. This series of chemicals was also quite effective in reducing the strength
600
"1" I-'..9 Z
l.- 400 (h
x
Amides
SUGAR
., J ta
200
0
I 0
I 0.4
I
| 0.8
I
I 1.2
I
I 1.6
I
I 2. O
DOPANT CONCENTRATION-%
Fig. 11. Graph of the flexural strength versus solution concentration (by weight) for the sucrose sugars.
88
(C12H22011).
For this heavy molecular weight dopant, no appreciable strength reduction occurred for concentrations less than approximately 2%.
ANALYSIS OF RESULTS In analysing the results, it would seem that it is necessary to characterize the a f ~ 7 s curves (Figs. 1 - 1 1 ) by two parameters: (1) a parameter which quantitatively defines the concentration of dopant required to reduce the strength of the ice; and (2) a TABLE1 Test results for each dopant: WT - total molecular weight of the dopant; ni - effective number of particles in solution after dissociation; Ct - concentration of dopant required to give "zero" strength ice; a s - saturation strength of the ice; ke - effective bulk partition coefficient. Chemical name
WT
ni
Ct (%)
us (kPa)
ke
Lithium chloride Sodium chloride Potassium chloride Magnesium chloride Calcium chloride Copper chloride Sodium sulfate Potassium ~ulfate Magnesium sulfate Nickel sulfate Copper sulfate Sodium formate Sodium acetate Sodium propionate Lithium acetate Potassium acetate Calcium formate Magnesium acetate Calcium acetate Methyl alcohol Ethyl alcohol Propyl alcohol Ethylene glycol Propylene glycol Glycerol Carbowax 600 Formamide Acetamide Carbamide Sucrose
43 59 75 95 111 135 142 174 120 155 160 68 82 96 66 98 130 142 158 32 46 60 62 76 92 600 45 59 60 342
1.9 1.9 1.8 2.8 2.6 2.6 2.4 2.4 1.2 1.2 1.2 1.9 1.9 1.9 1.9 1.8 2.8 2.8 2.8 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.4 0.8 1.3 0.75 1.1 1.35 0.75 1.05 0.75 0.9 1.1 0.55 0.5 0.45 0.25 0.75 0.8 0.5 0.7 0.35 0.35 0.25 0.65 0.6 0.8 1.3 0.5 0.6 0.75 1.9
30 30 80 40 50 50 80 100 120 120 180 30 40 30 30 50 50 40 60 40 40 50 100 90 100 60 50 80 160
0.30 0.32 0.38 0.313 0.28 0.33 0.28 0.27 0.17 0.28 0.35 0.37 0.41 0.45 0.29 0.36 0.42 0.35 0.66 0.87 0.92 0.59 0.45 0.23 0.50 0.44 0.39 0.17
parameter which defines the saturation or limiting strength of the ice tor higher concentrations. To determine a value for the latter parameter (Os) is quite straightforward. In this case a smooth curve was drawn through the higher concentration strength values. This was then linearly extrapolated backwards parallel to the C s axis to obtain the saturation (i.e. high dopant concentration) flexural strength of the ice for that dopant. To obtain a value for the first parameter, several methods were attempted to quantify the relative strength reduction properties of the different chemicals. However, because of differences in the shape of the individual curves, no strict quantitative technique could be found to do this. A semi-quantitative technique which proved quite suitable and usable for all of the dopants was to draw a smooth curve through the experimental points of each o f - C s plot. The sharp "initial drop" region was then smoothly extrapolated to the Cs axis (i.e. of = 0) and this value was defined as the concentration of dopant required for "zero" strength ice (Ct). Such a technique is, of course, not rigorous, but it does provide a semi-quantitative measure of the chemicals' effectiveness in reducing the strength of the ice. To avoid experimenter bias as much as possible, all Ct and as values were determined before any comparisons between chemical dopants were attempted. It is estimated that using this technique, the Ct values could be determined to -+0.1%. Using the procedures described above, the Ct and a s values for each chemical tested were determined and the results are listed in Table 1. In addition, this table includes the total molecular weight for each chemical, and the effective number of particles from each formula weight after dissociation (ni)*. The latter was calculated from n i = AT/Kfm,
(2)
where AT is the depression of the freezing point per percent dopant in solution, Kf is the molal depression constant (= 1.86 °C/mol for aqueous solutions) and m is the molality of the solution. In addition, in Table 1, the effective bulk partition coefficient (ke) *Note that n i is actually the van't Hoff i of solution chemistry. This is a correction factor which quantitatively takes into account the fact that electrolytes dissociate in aqueous solutions (see e.g. Cragg and Graham (1954) for details).
89 for each chemical is listed. Based on the criteria that an effective strength reducing chemical for ice is one in which both Ct and Os are low, from Table 1, it would seem that the most effective chemicals are lithium acetate and lithium chloride, the R - O H alcohols, the sodium salts of the carboxylic acids and the amides.
DISCUSSION
From the results presented in Table 1 and the discussion of results for each family of chemicals given above, it is clear that within an individual homologous series, the results are quite consistent. Qualitatively, the results can be explained on the basis of the structural features of the ice as described from the theory of constitutionally supercooled melts. Within a homologous series, both Ct and Os depend upon the molecular weight of the dopant such that C t increases with increasing average molecular weight (usually) and a s increases with increasing average molecular weight (almost always). In general, within a homologous series, the most effective strength reduction of ice is obtained with the lowest member of the series.
125
•
//
•
WT leT = - - C t
/ / ,.z I "1" I-Z L61 r~
•
/
/
•
•
Ill
/ /
75 / / • 50
/
tl411 /
IV •
II/~HII•
nr t,-
• ,4(o 25
•
/ /
O3
/ / 0 0
I 25
I 50
I 75
+ --
ni
na+nc
naWA,
(3)
where n a and nc are the number of anion and cation groups in each formula weight respectively and NA is the anion weight. A nonlinear relationship between Ct and WT of this type derives from the observation that within a homologous series, the total number of dopant particles at Ct increases with increasing average molecular weight of the particles. Rearrangement of equation (3) yields
/
U') Z 0 I--
ni
/
I00
Between homologous series, the situation is somewhat more complex. Ideally, it would be desirable to be able to predict both the Ct and Os values for a specific dopant without having to do the laborious testing of the present experiments. In this regard, a first guess might be to plot these parameters as a function of the average molecular weight (WT/ni) of each dopant. Such a plot, however, reveals that there is no direct relationship between the Ct value and the average molecular weight of the dopant in solution. On the other hand, as shown in Fig. 12, there is a very definite, but quite general relationship between as and WT[ni for the dopants tested in the present experiments. The saturation strength of the ice is lower for lower average molecular weight dopants. A general rule of thumb is that the limiting strength (in kPa) is simply equal to the average molecular weight of the dopant in solution. This relationship is not valid within any individual homologous series; nevertheless, it provides a means of semi-quantitative comparison of the limiting flexural strength of ice frozen from chemically impure melts. To relate the C t value to the physical properties of the dopant is not as straightforward. To date, no relationship has been found which would correlate the results for all dopants. However, for the strong electrolytes, the Ct value can be related to the total molecular weight (leT) by
I tO0
I 125
[
150
AVERAGE MOLECULAR WEIGHT OF DOPANT
Fig. 12. Graph of the saturation strength (as) value versus the average molecular weight of the dopant in solution (WT/ni). The dashed line indicates the general rule-of-thumb that the limiting strength (in kPa) is equal to the average molecular weight of the dopant in solution.
Ct = ni 1
ninaleA ] . na +nc WT
(4)
This expression is plotted as a function of the experimentally observed Ct values for the single cation electrolytes in Fig. 13. There is a definite relationship between the calculated C t values (from equation (4)) and the experimentally observed Ct values. This
9O 1.4 CL 2 KCI • 1.2 • CoCl z
CuSO4 •
I d < IZ uJ
J .0
N
SO,•
NoC l~If
0.8-
M so4 •
/
/
rr w 13.. 0 . 6 x LLI
• Ca F o r m z
0 0 MgCl z
~ • C ° Ace'z K Acet
• No F o r m 0•
• 0.4-
LiCl
Mg Ace I' 2
~ No Acet No Pro p
Li A c e t 0.2
I
0 0
0.2
0.4
I 0.6
I 0.8
Ct (EQUATION
I 1.0
1 1.2
1 I .4
1.6
4 ) -- %
Fig. 13. Graph of the experimentally determined dopant concentration required for 'zero' strength ice (Ct experimental) versus that calculated using only the physical proper-
ties of the dopants with equation (4). The solid line indicates the least squares fit through the points.
empirical relationship, therefore, apparently provides a method of estimating the optimum concentration of an electrolytic dopant to reduce effectively the strength of ice grown from an impure melt. Equation (4) has several interesting consequences. For strong electrolytes, ni/(na+nc)= 1, so that for Ct to approach zero, naWA/WT-+I. This says that as the total anion weight approaches the total molecular weight, the amount o f dopant required in solution for the strength reduction of ice decreases. This explains the observed trend in the strength reducing properties of the sodium salts of the carboxylic acids (Fig. 5).
Recall that for this series (and in contrast to the chlorides and sulfates), the relative strength reduction was greatest for the highest molecular weight dopant - sodium propionate; that is, for the highest anion weight to total weight ratio in the series*. If the trend predicted by equation (4) continued to very high
*Note that in the chloride, sulfate and acetate series, the anion weight is constant for each series and the cation weight v'aries. Thus with increasing total weight within a series, the ratio of the anion weight to total weight decreases, and, as predicted by equation (4), Ct increases.
91
molecular weight dopants, this would suggest that a dopant such as sodium stearate (CH3(CH2)I6COONa - soap) would reduce the strength of the ice with only a small quantity in solution. This has in fact been confirmed in the present experiments. Unfortunately, however, the strength reduction in this case is minimal. For fresh water ice (with no dopant), the flexural strength was measured to be 1200-1400 kPa, whereas with sodium stearate in concentration of 0.05-0.4%, the strength was reduced to approximately 800 kPa. This high limiting strength value is what would have been expected on the basis of Fig. 12; that is, the limiting strength of the ice is higher for the higher average molecular weight of the particles in solution. As such, in this case there is a definite trade-off between a low Ct value and a high as value. It would seem, therefore, that there are only a small number of chemicals (such as lithium chloride and lithium acetate) which can give low values for both.
pockets in the ice. These pockets, which become increasingly larger liquid inclusions for increasing temperatures above the dopant-water eutectic temperature, aid in the strength reduction for temperatures close to the melting point. On the other hand, the large molecular weight particles assist in strength reduction by inhibiting the growth of large ice crystals (i.e. a chemical poison). Since the fracturing process is frequently along grain boundaries, a large number of small crystals would result in structurally weaker ice. As such, although some chemical series are very effective as strength reducers for ice, it would seem that a low molecular weight-high molecular weight combination of chemicals would be required for the optimum chemical strength reduction of ice.
ACKNOWLEDGMENTS The author would like to thank Mr. R.A. Martin for technical assistance in this program.
CONCLUDING REMARKS Although the experimental procedures used in the present experiments were quite simple, the results and analysis of these experiments have provided useful information on the effects of a large number of chemicals on the strength reduction of ice. It has been found that: (1) within a homologous series, the greatest strength reduction generally occurs for the lowest member of the series; (2) several chemical series ( R - O H alcohols, salts of the carboxylic acids and amides) are especially effective in strength reduction, and (3) for electrolytic dopants, Ct increases with increasing cation weight for a constant anion, but decreases with increasing anion weight for a constant cation. From the results of these experiments, as well as the results of a previous study by the author on the structural characteristics of impure ice (Timco 1978), it would seem that in chemical methods of strength reduction of ice, there are two different, independent processes. On the one hand, the low molecular weight particles decrease the local interface liquidus temperature and thereby bring about the dendritic growth which is necesssary for strength-reduced ice. In addition, these particles become trapped as impurity
REFERENCES Becher, P. (1977), Emulsions: Theory and Practice, R.E. Krieger Publ. Co., Hungington, New York. Coble, R.L. and W.D. Kingery (1963), Ice reinforcement. In: W.D. Kingery (Ed.), Ice and Snow, M.I.T. Press, Cambridge. Cragg, L.H. and R.P. Graham (1954), An Introduction to the Principles of Chemistry, Clarke, Irwin and Co. Ltd., Toronto. Moesveld, A.L.T. (1937), Ice crust preventing process, Can. Patent No. 367,852.
Pounder, E.R. (1958), Mechanical strength of ice frozen from an impure melt, Can. J. Phys., 36: 363-370. Pounder E.R. (1965), The Physics of Ice, Pergamon Press, New York. Rutter, J.W. and B. Chalmers (1953), A prismatic substructure formed during the solidification of metals, Can. J. Phys., 31: 15-39. Schwarz, J. (1977), On the flexural strength and elasticity of saline ice, Proc. 3rd Int. Symp. on Ice Problems, IAHR, Hanover, U.S.A., pp. 373-386. Shulhan, G.M., J.F. Lane and G.W. Timco (1978), The mechanical properties of methanol-doped ice, Nat. Res. Council of Canada, Div. of Mech. Eng. Rep. LTR-LT-83. Svec, O.J. and Frederking, R. (1981), Cantilever beam tests in an ice cover: Influence of plate effects at the root, Cold. Reg. Sci. Tech. 4: 93-101.
92
Tiller, W.A., K.A. Jackson, J.W. Rutter and B. Chalmers (1953), The distribution of solute atoms during the solidification of metals, Acta Metall. 1: 4 2 8 - 4 3 7 . Timco, G.W. (1978), Morphological characteristics of ice grown from an impure melt, Nat. Res. Council of Canada, Div. of Mech. Eng.,Rep. LTR-LT-91. Timco, G.W. (1979a), The mechanical and morphological properties of doped ice: A search for a better structurally simulated ice for model test basins, 5th Int. Conf. on Ports and Ocean Engineering under Arctic Conditions,
Proc. POAC '79, Vol. I, Trondheim, Norway, pp. 719 739. Timco, G.W. (1979b), A chemical survey to determine potential dopants for a model ice test basin, Nat. Res. Council of Canada, Div. of Mech. Eng. Rep. LTR-LT-95. Weeks, W.F. and G. Lofgren (1967), The effective solute distribution coefficient during the freezing of NaC1 solutions. In: H. Dura (Ed.), Physics of Ice and Snow, Vol. 1, Hokkaido University, Sapporo, Japan, pp. 579-597.
FLEXURAL
S T R E N G T H OF ICE G R O W N F R O M C H E M I C A L L Y
81
IMPURE MELTS
Garry W. Timco Division of Mechanical Engineering, National Research Council of Canada, Ottawa, Ontario K IA OR6 (Canada)
(Received June 10, 1980; acceptedin revisedform September23, 1980)
ABSTRACT
A series of experiments have been performed to measure the ultimate (flexural) strength of ice grown from impure melts containing one of a number of chemical dopants (chloride and sulfate salts, salts of the carboxylic acids, alcohols, amides and sugars). The results of these experiments indicate: (1) within a homologous series, the greatest strength reduction in the ice usually occurs for the lowest member of the series; (2) the overall reduction in strength of the ice to a limiting value is greater for the lower molecular weight dopants; and (3) of the chemical families tested, the most effective ice-strength reducing ones were the R - O H alcohols, the salts of the carboxylic acids and the amides. These results are discussed in terms of the structural features of the ice. An empirical relationship is presented for electrolytic dopants which predicts the optimum concentration of dopant necessary for reducing the strength of ice.
INTRODUCTION
When ice grows from an impure melt, its crystal structure and its mechanical, electrical and thermal properties depend greatly on the type and amount of impurity in the melt. This results in spite of the fact that ice is a very selective lattice which incorporates very few substitutional defects directly into the host lattice (Pounder 1965). Accordingly, as the ice sheet forms, the impurity particles are rejected into the melt such that the amount of impurity which is trapped in the ice is very much less than that in the
melt. If both the initial concentration of dopant particles in the melt is low enough, and the growth rate is slow enough, this rejection process effectively produces an ice sheet which is very similar in both appearance and mechanical properties to that grown from an undoped melt (i.e. fresh water ice). In this case, although the rejected particles build up and raise the impurity level in the liquid adjacent to the interface, the diffusion of these particles away from the interface into the body of the melt is sufficiently fast to prevent any large-scale entrapment of dopant particles in the solid. If, on the other hand, the concentration of solute particles in the melt is higher, and/or the growth rate is more rapid, this diffusion process is not fast enough, and this results in a large build-up of impurities at the growth interface. If, owing to the phase relationship of the components involved, the impurities depress the local liquidus temperature, then at some critical value the actual temperature of the liquid ahead of the interface will be below the liquidus temperature. As a result, the liquid has a region of lower freezing-point solution at the ice-liquid interface, with solution some finite distance from the interface with a greater tendency to freeze. As such, the liquid is "constitutionally supercooled" (i.e. supercooling as a result of composition (Rutter and Chalmers 1953))with the result that the initial planar solid-liquid interface becomes unstable. When this occurs, the planar front solidification ceases and long ice dendrites begin to grow into the melt. These dendrites reach for that liquid which is most ready to freeze and thereby mechanically entrap liquid which is high in solute. As such, this ice consists of a mechanically hard upper layer and a lower columnar layer which consists of long crystal
0165-232X/81/0000-0000/$02.50 © 1981 ElsevierScientific PublishingCompany
82 platelets, some of which extend to the bottom of the ice sheet. These structural features have a pronounced influence on the overall physical properties of this ice (see Weeks and Lofgren 1967, Timco 1978 for more details). This process of constitutionally supercooled growth (Rutter and Chalmers 1953, Tiller et al. 1953), results in an ice sheet whose structure and physical properties are quite different from that of fresh water ice. The specific details of the growth mechanism will depend upon several parameters, including the initial impurity content in the melt, the growth rate (i.e. freezing temperature), the molecular weight of the solute, the adsorption properties of the solute in water, the size, shape and flexibility of the dopant particle, the particle-particle interactions, and the particle-solvent interactions. As might be expected, different dopants can produce vastly different results. To date, however, there have been only a handful of studies on the strength of ice grown from chemically doped aqueous solutions (Moesveld 1937, Pounder 1958, Coble and Kingery 1963). This is in spite of the obvious practical nature and significance of this problem for chemical methods of ice control. Clearly, studies of this type can give good insight into the nature of various chemical-ice interactions and in so doing increase our understanding of the growth mechanism in multi-doped systems such as sea ice. The present experiments were designed to investigate systematically the ice strength-reducing properties of a large number of chemicals by measuring the flexural strength of ice grown from melts containing various concentrations of different dopants. This was done in support of a related engineering activity in this field (Timco 1979a). The purpose of the experiments was to test each chemical dopant (1) to determine its relative effectiveness in reducing the strength of ice; (2) to find the minimum concentration required to reduce effectively the strength of the ice; and (3) to determine general trends in the strengthreducing properties both within and between homologous series. The chemicals chosen for this study were based on the criteria of water solubility, nontoxicity, non-flammability and non-volatility. Based on these criteria, the homologous series of chlorides and sulfates, salts of carboxylic (fatty) acids, alcohols, amides and sugars were chosen for study (see Timco 1979b for a detailed discussion on the method for
choosing these dopants). In this paper, the detailed results of this study are presented, along with the resuiting guidelines for the chemical strength reduction of ice. EXPERIMENTAL These experiments were performed by measuring the flexural strength using the cantilever beam method on ice grown from doped solutions in 225-1 insulated plastic trays which were in a large walk-in cold chamber. The general procedure was to pre-cool the solution overnight at an ambient air temperature of +2 °C, and then freeze to form ice sheets at T = - 2 0 °C for approximately 22 h. For these experiments, the ice was self-nucleated and no artificial seeding was introduced. After the freeze, the ice was allowed to warm up for 3 h to an isothermal equilibrium of approximately -0.5 °C before testing. This was done to eliminate the temperature gradient in the ice and to provide the same test conditions for each test. In testing, 12 cantilever beams were cut in the ice using a standard pruning saw. The thickness of the ice varied somewhat from day to day since the growth rate appeared to be a function of both the amount and kind of impurity in the solution. In general, however, the ice thickness (h) ranged from 3.0 to 4.5 cm for these tests. The cantilever beams were cut to be 6 cm wide so that the beam width (w) was 1 - 2 times the ice thickness. The beam lengths (L) were cut to be 2 0 - 2 5 cm long to maintain a beam length to ice thickness ratio of 5 - 7 for these tests. In loading the beams, one of three Chatillon instrument push-pull gauges ( 0 - 1 kg, 0--2.2 kg, 0-4.5 kg) was used to determine the breaking load (P) for each beam. Each of the rod plungers of these gauges was outfitted with a small inverted-T shaped nylon foot to distribute the load evenly along the end of the beam. All cantilever tests were of the push down type and loading times to failure were typically 1 - 2 s. The flexural strength was calculated from the elastic beam equation of = 6PL/wh 2
(1)
and used as a strength index for this test. Because the apparent flexural strength of the ice can depend upon both the length of the warm-up period (Schwarz 1977, Timco 1979a) and the dimensional ratio of the
83
cantilever beams (S~tec and Frederking 1981), care was taken to ensure that each ice sheet was grown and tested under the same experimental conditions. Nevertheless, the flexural strength of the ice calculated using Eqn.(1) should be regarded only as a strength index for the ice. Before melting the ice foUowing a test, samples of both the ice and the solution were taken in order to estimate the relative dopant concentrations in each. This estimate was done by simply measuring the specific gravity of each with a standard hydrometer. From this, the bulk equilibrium partition coefficient (ke = average concentration of dopant in the ice sample/average dopant concentration in the solution) was calculated. After testing, the ice was melted using immersion heaters, and additional dopant was added while the solution was being agitated with an air bubbler system to ensure thorough mixing. This general testing arrangement allowed three testing days per week. Over 30 dopants were tested for solution concentrations up to 2% (by weight).
RESULTS Preliminary comments
In this section, the results for each dopant will be presented. For comparison purposes, each graph will show the results for an individual homologous series. In every case, each point on the graph represents an average of at least six cantilever beam test results. The order of presentation will be that of the chloride salts, sulfate salts, salts of the carboxylic acids, alcohols, amides and sugars. Chloride salts
Figure 1 shows a graph of the flexural strength (of) versus solution concentrations (Cs) for the monovalent cation-monovalent anion series of chloride salts [lithium chloride (LiCI), sodium chloride (NaC1), potassium chloride (KC1)]. From this graph it is evident that for each dopant, with increasing concentration, the strength of the ice decreases rapidly to a limiting value. Qualitatively, all of the dopants tested produced behaviour of this type, although as shown in Fig. 1, the concentration required for the initial
sharp decrease in strength, as well as the limiting strength of the ice, varied for each individual dopant. The sharp drop in the strength of the ice can be directly correlated to the structural properties of the ice, and in particular, to the onset of the dendritic growth phase for the ice (Timco 1979a). For this ice which is grown from low-concentration melts, the strength is primarily controlled by the thickness of the upper, non-dendritic ice layer - the "incubation length". This is so since almost all of the strength of the ice is in this upper ice layer. As would be expected from consideration of growth from constitutionally supercooled (CS) melts, the time to the onset of the CS instability (i.e. the thickness of the upper layer) decreased for increasing initial impurity content in the melt. As such, as shown in Fig. 1, the overall strength of the ice decreases rapidly with increasing concentration. To produce mechanically weak ice from an impure melt, the impurity concentration must be greater than or equal to that which results in rapid dendritic growth. As shown in Fig. 1, this amount is different for different dopants. In Fig. 1, there are two important features which should be noted: (1) less of the lower molecular weight solute is required to bring about the reduction in strength of the ice; and (2) the saturation or limiting strength value is higher for the higher molecular weight solute. The most effective strength 800 CHLORIDES - C I
o '=: I -r I-(.9 Z I-U')
hx i .J LL
600
400
200
0
0
0,4
0.8 DOPANT
I .2 CONCENTRATION
1.6
2.0
-%
Fig. 1. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of monovalent cation chlorides.
84 reduction occurs tor the lowest member of the series. This observed dependence of strength reduction within a homologous series seems reasonable since, for a given weight of dopant added to the water, there would be more dissociated particles from the lower molecular weight solute. This would increase the number of particles at the ice-solution growth interface. Since the depression of the freezing point is directly related to the number of particles in the melt (Raoult's law), this should produce a more rapid attainment of the constitutionally supercooled instability and the resultant decrease in the mechanical strength of the ice for the lower molecular weight solutes. Qualitatively, therefore, this approach explains the experimentally observed result. However, this situation is not that straightforward. If, for example, a plot is made of the strength of the ice as a function of the number of dopant particles in the melt (or the molality)* for each chemical, based on the above simple picture, the initial drop portion of the curve would be expected to coincide regardless of the type of cation. This, however, is not found to be the case; A plot of this type has the same general features as that shown in Fig. 1. This indicates that: (1) physically less of the lower molecular weight particles are required to bring about the strength reduction; (2) the strength of the ice is not solely determined by the brine volume in the ice; and (3) the lower molecular weight dopants produce a lower limiting strength of the ice. The reason for this is not known, although undoubtedly the solid-liquid interfacial energy as well as the diffusion and adsorption properties of the dopant play an important role. Figure 2 shows a graph of the flexural strength versus solution concentration for the divalent c a t i o n monovalent anion series of chloride salts [magnesium chloride (MgClz), calcium chloride (CaC12), copper chloride (CuCI2)]. In general, this series shows identical behaviour to that of the monovalent cation chlorides (Fig. 1).
•
800
•
x 600 I I
2
•
M• Cl 2
@
Co Cl z
•
Cu Cl 2
X 400
%,
)
X
200
J
• 0
I
1
I O.4
0
I 0.8
DOPANT
I
I 1.2
I
I 1.6
CONCENTRATION
I
I 2.0
-%
Fig. 2. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of divalent cation chlorides. Sulfate salts
Figures 3 and 4 show graphs of the flexural strength versus solution concentration for the monovalent cation-divalent anion series of sulfate salts [sodium sulfate (Na2S04), potassium sulfate (K2S04)] and the divalent cation-divalent anion series of sulfate salts [magnesium sulfate (MgS04),
800
\ i
n°"~ 6 0 0
\
I bo Z w ~ 400
1
SULFATES - SO 4
\
I
,o
NozS04
.\
< x uJ _J LL
200 &__
0
I 0
*It should be pointed out that since all of the ice was tested at the same isothermal temperature, this graph would be the same as plotting the strength of the ice as a function of the brine volume in the ice for each series.
CHLORIDES--Ct
o
I 0.4
I
DOPANT
I 0.8
I
I 1.2
CONCENTRATION
I
I 1.6
I
I 2.0
-%
Fig. 3. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of monovalent cation sulfates.
85
8OO
~ttV I
8OOI[ I1~'i/
SULFATES- SO4
600
",r" (.9 Zhi ~. 4 0 G CO .J
SO4
•
Mg
•
N i SO 4
•
Cu
-
SODIUMSALTSOFCARBOXYLtCACIDS
sool-|I
•
ooF
SO 4
soD,uM FO,M TE
• SODIUMPROPIONATE
rr
::2)
x iJJ 200
2oor
•..... I
I
I
I
I
I
I
I
0.4 0.8 1.2 1.6 DOPANT CONCENTRATION-%
I
I
•
2.0
\\\ "
o
0
0.4
0.8 1.2 1,6 DOPANT CONCENTRATION-%
2.0
Fig. 4. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of divalent cation sulfates.
Fig. 5. Graph of the flexural strength versus the dopant concentration (by weight) for the sodium salts of the carboxylic (fatty) acids.
nickel sulfate (NiSO4), copper sulfate (CuSO4)], respectively. Both these series show the trends previously discussed for the chloride series. Note, however, that the saturation or limiting strength of
reduction in the strength of the ice occurs at a lower concentration for the heavier molecular weight dopant (sodium propionate). However, in agreement with the chloride and sulfate salts, Che saturation or limiting strength of the ice is less for the lower molecular weight dopant (sodium formate). To explain this apparent difference with the chloride and sulfate salts, it should be noted that for organic
this ice is considerably higher than that of the lower molecular weight chloride series. In this case it would seem that although these heavy sulfate particles can bring about the CS instability with a relatively low solution concentration (presumably because of the low rate of diffusion of these heavy particles away from the interface), the high eutectic temperature of this series with water (approximately -1.5 °C) limits the size of the impurity pockets in the ice. This, correspondingly, does not allow for the production of low strength ice from the sulfate series.
800
n°
1
600 1"I ZW('gl--
\ ~ / ~
Salts of the carboxylic (fatty) acids
~.~ 400 CO
Figure 5 shows a graph of the flexural strength versus solution concentration for the sodium salts of the three lowest members of the carboxylic acids [sodium formate, Na(CHO2), sodium acetate, Na(C2H302) and sodium propionate, Na(C3HsO2)]. For this series, the strength-reducing properties on ice are quite good. Although the strength-reducing properties of the first three constant cation salts in this series are similar, it would appear that, in contrast to the chloride and sulfate salts, the sharp
<
ACETATES-C2H302 • Li C2H302 • NO C2H302 • K C2H302
xi~J 200 .J
0 0
I 0.4
0.8
1.2
1.6
I
I 2.0
DOPANT CONCENTRATION-% Fig. 6. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of monovalent cation acetates.
86 compounds such as these, the adsorption of the molecule at the surface markedly increases with increasing molecular chain length (Becher 1977). As such, the relative number of sodium propionate particles at the growth interface would be more than that of sodium formate for equal numbers of dopant particles in the melt. This mechanism, therefore, could bring about the CS instability more rapidly for the heavier sodium propionate dopant. In any event, it is clear that this series is very effective in bringing about a strength reduction in the ice. Figure 6 shows a graph of the flexural strength versus solution concentration for three salts in the acetate series [lithium acetate, Li(C2H302), sodium acetate, Na(C2H302), potassium acetate, K(C2H302)]. In this case, the general strength reduction trends are identical with those observed for the series of chloride and sulfate salts. Figure 7 shows a graph of the flexural strength versus solution concentration for divalent cation formate and acetate series [calcium formate, Ca(CH02)2, magnesium acetate, Mg(C2H302)2, calcium acetate, Ca(C2H302)2]. This graph emphasizes the findings discussed for the other salts of the carboxylic acids (Figs. 5 and 6); viz. (1) for different anion weights for a given cation, the strength reduction is more rapidly attained for the heavier molecular weight anion, and (2) for different cation
weights for a given anion, the strength reduction is greater for the lowest molecular weight cation. Alcohols
Figure 8 shows a graph of the flexural strength versus solution concentration for the R-OH series of alcohols [methyl alcohol (CH3OH), ethyl alcohol (C2HsOH), propyl alcohol (C3HTOH)]. For this series, very low strength ice is achieved at low impurity levels in the solution. In this case, contrary to the chlorides and sulfates, there is virtually no difference between the strength reduction properties of these three members of this series. This ice consisted of a relatively hard upper layer and a lower layer which consisted of many unconnected dendritic platelets suspended vertically into the melt. Presumably these alcohols, which are all less dense than water, congregate at the growth interface to bring about the observed incoherent dendritic growth (see Shulhan et al. 1978 for more details on methyl alcohol as a dopant in ice). Figure 9 shows a graph of the flexural strength versus solution concentration for the series of polyhydric alcohols [ethylene glycol (HOCH2CH2OH), propylene glycol (CH3CH(OH)CH2OH), glycerol (HOCH2CH(OH)CH2OH), and carbowax (HOCH2(CH2OCH~)nCH2OH)]. For these alcohols
800
800
x
I I t-(O Z LU
,
600
\ ~ \
¢r" 400
~"~/
~t'0H ALCOHOLS
"~ 600 f / / I
• CALCIUM FORMATE • MAGNESIUM ACETATE • CALCIUM ACETATE
\
m .J ,<
@ METHYL • ETHYL a PROPYL
L~J
~ ' ~ 1 ~
n,-
xLU
~L
FORMATES - CHOz ACETATES- C2H30z
.
•0
200
200
J_ - •
0
I
I
I
o.a
I~ o.e
,.2
,.s
I
I 2.o
DOPANT C O N C E N T R A T I O N - %
Fig. 7. Graph of the flexural strength versus solution concentration (by weighO for the series of divalent cation formates and acetates.
OO
l 0.4
O. 8
Ill-- I t.2
I
L t.6
I
I 2.0
DOPANT CONCENTRATION - %
Fig. 8. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of ROH alcohols (R = alkyl radicaD.
87
800
-~ 6 0 0 I
1" I(.9 Z b,.I rr
400
x w
200
I-(/3
!
800 AMIDES
POLYHYDRIC ALCOHOLS
II I\ I\
\ \ ~
I\
, ETHYLENEGLYCOL • PROPYLENEGLYCOL .i~ GLYCEROL
\
&\
600
1
•
FORM~.M IDE
•
ACETAMIDE
& CARBAMtDE
.+++DO
4.00
.\.. 200
&-0I 0
I
I
0.4
I
0.8
I
I
1.2
I
I
1.6
I
I
O
2.0
I
I
I
0.4
DOPANT CONCENTRATION-%
.I 0
I
8
12
I
I.
I
I
1.6
I
2.0
DOPANT CONCENTRATION-%
Fig. 9. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of polyhydric alcohols.
Fig. 10. Graph of the flexural strength versus the dopant concentration (by weight) for the homologous series of amides.
there is no clear trend in their relative strength reduction as a homologous series. In this case, although ethylene glycol is more effective in strength reduction than glycerol, it is less effective than the higher molecular weight propylene glycol. These dopants were only of average effectiveness in reducing the strength of the ice (compare to the R - O H alcohols). The carbowax results are interesting since, considering the relatively high molecular weight of the molecules (approximately 600), they were quite effective in strength reduction. This ice, however, did not show the usual dendritic growth at the lower strengths. Instead, the carbowax appeared to congregate along large crystal grain boundaries and produce macroscopic defects in the ice. As such, the cantilever ice beams with this dopant seldom broke at the root. Although the ice strength for this dopant was low, the mechanism for strength reduction was quite different from that of the lower molecular weight dopant.
of the ice. With respect to the observed variation with molecular weight within the series, it showed the same general trends as the chlorides, sulfates and acetates. Sugars
Figure 11 shows a graph of the flexural strength versus solution concentration for sucrose sugar 800
•
I
Figure 10 shows a graph of the flexural strength versus solution concentration for the series of amides [formamide (HCONH2), acetamide (CH3CONH2) , carbamide (urea) (NH2CONH2)]. This series of chemicals was also quite effective in reducing the strength
600
"1" I-'..9 Z
l.- 400 (h
x
Amides
SUGAR
., J ta
200
0
I 0
I 0.4
I
| 0.8
I
I 1.2
I
I 1.6
I
I 2. O
DOPANT CONCENTRATION-%
Fig. 11. Graph of the flexural strength versus solution concentration (by weight) for the sucrose sugars.
88
(C12H22011).
For this heavy molecular weight dopant, no appreciable strength reduction occurred for concentrations less than approximately 2%.
ANALYSIS OF RESULTS In analysing the results, it would seem that it is necessary to characterize the a f ~ 7 s curves (Figs. 1 - 1 1 ) by two parameters: (1) a parameter which quantitatively defines the concentration of dopant required to reduce the strength of the ice; and (2) a TABLE1 Test results for each dopant: WT - total molecular weight of the dopant; ni - effective number of particles in solution after dissociation; Ct - concentration of dopant required to give "zero" strength ice; a s - saturation strength of the ice; ke - effective bulk partition coefficient. Chemical name
WT
ni
Ct (%)
us (kPa)
ke
Lithium chloride Sodium chloride Potassium chloride Magnesium chloride Calcium chloride Copper chloride Sodium sulfate Potassium ~ulfate Magnesium sulfate Nickel sulfate Copper sulfate Sodium formate Sodium acetate Sodium propionate Lithium acetate Potassium acetate Calcium formate Magnesium acetate Calcium acetate Methyl alcohol Ethyl alcohol Propyl alcohol Ethylene glycol Propylene glycol Glycerol Carbowax 600 Formamide Acetamide Carbamide Sucrose
43 59 75 95 111 135 142 174 120 155 160 68 82 96 66 98 130 142 158 32 46 60 62 76 92 600 45 59 60 342
1.9 1.9 1.8 2.8 2.6 2.6 2.4 2.4 1.2 1.2 1.2 1.9 1.9 1.9 1.9 1.8 2.8 2.8 2.8 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.4 0.8 1.3 0.75 1.1 1.35 0.75 1.05 0.75 0.9 1.1 0.55 0.5 0.45 0.25 0.75 0.8 0.5 0.7 0.35 0.35 0.25 0.65 0.6 0.8 1.3 0.5 0.6 0.75 1.9
30 30 80 40 50 50 80 100 120 120 180 30 40 30 30 50 50 40 60 40 40 50 100 90 100 60 50 80 160
0.30 0.32 0.38 0.313 0.28 0.33 0.28 0.27 0.17 0.28 0.35 0.37 0.41 0.45 0.29 0.36 0.42 0.35 0.66 0.87 0.92 0.59 0.45 0.23 0.50 0.44 0.39 0.17
parameter which defines the saturation or limiting strength of the ice tor higher concentrations. To determine a value for the latter parameter (Os) is quite straightforward. In this case a smooth curve was drawn through the higher concentration strength values. This was then linearly extrapolated backwards parallel to the C s axis to obtain the saturation (i.e. high dopant concentration) flexural strength of the ice for that dopant. To obtain a value for the first parameter, several methods were attempted to quantify the relative strength reduction properties of the different chemicals. However, because of differences in the shape of the individual curves, no strict quantitative technique could be found to do this. A semi-quantitative technique which proved quite suitable and usable for all of the dopants was to draw a smooth curve through the experimental points of each o f - C s plot. The sharp "initial drop" region was then smoothly extrapolated to the Cs axis (i.e. of = 0) and this value was defined as the concentration of dopant required for "zero" strength ice (Ct). Such a technique is, of course, not rigorous, but it does provide a semi-quantitative measure of the chemicals' effectiveness in reducing the strength of the ice. To avoid experimenter bias as much as possible, all Ct and as values were determined before any comparisons between chemical dopants were attempted. It is estimated that using this technique, the Ct values could be determined to -+0.1%. Using the procedures described above, the Ct and a s values for each chemical tested were determined and the results are listed in Table 1. In addition, this table includes the total molecular weight for each chemical, and the effective number of particles from each formula weight after dissociation (ni)*. The latter was calculated from n i = AT/Kfm,
(2)
where AT is the depression of the freezing point per percent dopant in solution, Kf is the molal depression constant (= 1.86 °C/mol for aqueous solutions) and m is the molality of the solution. In addition, in Table 1, the effective bulk partition coefficient (ke) *Note that n i is actually the van't Hoff i of solution chemistry. This is a correction factor which quantitatively takes into account the fact that electrolytes dissociate in aqueous solutions (see e.g. Cragg and Graham (1954) for details).
89 for each chemical is listed. Based on the criteria that an effective strength reducing chemical for ice is one in which both Ct and Os are low, from Table 1, it would seem that the most effective chemicals are lithium acetate and lithium chloride, the R - O H alcohols, the sodium salts of the carboxylic acids and the amides.
DISCUSSION
From the results presented in Table 1 and the discussion of results for each family of chemicals given above, it is clear that within an individual homologous series, the results are quite consistent. Qualitatively, the results can be explained on the basis of the structural features of the ice as described from the theory of constitutionally supercooled melts. Within a homologous series, both Ct and Os depend upon the molecular weight of the dopant such that C t increases with increasing average molecular weight (usually) and a s increases with increasing average molecular weight (almost always). In general, within a homologous series, the most effective strength reduction of ice is obtained with the lowest member of the series.
125
•
//
•
WT leT = - - C t
/ / ,.z I "1" I-Z L61 r~
•
/
/
•
•
Ill
/ /
75 / / • 50
/
tl411 /
IV •
II/~HII•
nr t,-
• ,4(o 25
•
/ /
O3
/ / 0 0
I 25
I 50
I 75
+ --
ni
na+nc
naWA,
(3)
where n a and nc are the number of anion and cation groups in each formula weight respectively and NA is the anion weight. A nonlinear relationship between Ct and WT of this type derives from the observation that within a homologous series, the total number of dopant particles at Ct increases with increasing average molecular weight of the particles. Rearrangement of equation (3) yields
/
U') Z 0 I--
ni
/
I00
Between homologous series, the situation is somewhat more complex. Ideally, it would be desirable to be able to predict both the Ct and Os values for a specific dopant without having to do the laborious testing of the present experiments. In this regard, a first guess might be to plot these parameters as a function of the average molecular weight (WT/ni) of each dopant. Such a plot, however, reveals that there is no direct relationship between the Ct value and the average molecular weight of the dopant in solution. On the other hand, as shown in Fig. 12, there is a very definite, but quite general relationship between as and WT[ni for the dopants tested in the present experiments. The saturation strength of the ice is lower for lower average molecular weight dopants. A general rule of thumb is that the limiting strength (in kPa) is simply equal to the average molecular weight of the dopant in solution. This relationship is not valid within any individual homologous series; nevertheless, it provides a means of semi-quantitative comparison of the limiting flexural strength of ice frozen from chemically impure melts. To relate the C t value to the physical properties of the dopant is not as straightforward. To date, no relationship has been found which would correlate the results for all dopants. However, for the strong electrolytes, the Ct value can be related to the total molecular weight (leT) by
I tO0
I 125
[
150
AVERAGE MOLECULAR WEIGHT OF DOPANT
Fig. 12. Graph of the saturation strength (as) value versus the average molecular weight of the dopant in solution (WT/ni). The dashed line indicates the general rule-of-thumb that the limiting strength (in kPa) is equal to the average molecular weight of the dopant in solution.
Ct = ni 1
ninaleA ] . na +nc WT
(4)
This expression is plotted as a function of the experimentally observed Ct values for the single cation electrolytes in Fig. 13. There is a definite relationship between the calculated C t values (from equation (4)) and the experimentally observed Ct values. This
9O 1.4 CL 2 KCI • 1.2 • CoCl z
CuSO4 •
I d < IZ uJ
J .0
N
SO,•
NoC l~If
0.8-
M so4 •
/
/
rr w 13.. 0 . 6 x LLI
• Ca F o r m z
0 0 MgCl z
~ • C ° Ace'z K Acet
• No F o r m 0•
• 0.4-
LiCl
Mg Ace I' 2
~ No Acet No Pro p
Li A c e t 0.2
I
0 0
0.2
0.4
I 0.6
I 0.8
Ct (EQUATION
I 1.0
1 1.2
1 I .4
1.6
4 ) -- %
Fig. 13. Graph of the experimentally determined dopant concentration required for 'zero' strength ice (Ct experimental) versus that calculated using only the physical proper-
ties of the dopants with equation (4). The solid line indicates the least squares fit through the points.
empirical relationship, therefore, apparently provides a method of estimating the optimum concentration of an electrolytic dopant to reduce effectively the strength of ice grown from an impure melt. Equation (4) has several interesting consequences. For strong electrolytes, ni/(na+nc)= 1, so that for Ct to approach zero, naWA/WT-+I. This says that as the total anion weight approaches the total molecular weight, the amount o f dopant required in solution for the strength reduction of ice decreases. This explains the observed trend in the strength reducing properties of the sodium salts of the carboxylic acids (Fig. 5).
Recall that for this series (and in contrast to the chlorides and sulfates), the relative strength reduction was greatest for the highest molecular weight dopant - sodium propionate; that is, for the highest anion weight to total weight ratio in the series*. If the trend predicted by equation (4) continued to very high
*Note that in the chloride, sulfate and acetate series, the anion weight is constant for each series and the cation weight v'aries. Thus with increasing total weight within a series, the ratio of the anion weight to total weight decreases, and, as predicted by equation (4), Ct increases.
91
molecular weight dopants, this would suggest that a dopant such as sodium stearate (CH3(CH2)I6COONa - soap) would reduce the strength of the ice with only a small quantity in solution. This has in fact been confirmed in the present experiments. Unfortunately, however, the strength reduction in this case is minimal. For fresh water ice (with no dopant), the flexural strength was measured to be 1200-1400 kPa, whereas with sodium stearate in concentration of 0.05-0.4%, the strength was reduced to approximately 800 kPa. This high limiting strength value is what would have been expected on the basis of Fig. 12; that is, the limiting strength of the ice is higher for the higher average molecular weight of the particles in solution. As such, in this case there is a definite trade-off between a low Ct value and a high as value. It would seem, therefore, that there are only a small number of chemicals (such as lithium chloride and lithium acetate) which can give low values for both.
pockets in the ice. These pockets, which become increasingly larger liquid inclusions for increasing temperatures above the dopant-water eutectic temperature, aid in the strength reduction for temperatures close to the melting point. On the other hand, the large molecular weight particles assist in strength reduction by inhibiting the growth of large ice crystals (i.e. a chemical poison). Since the fracturing process is frequently along grain boundaries, a large number of small crystals would result in structurally weaker ice. As such, although some chemical series are very effective as strength reducers for ice, it would seem that a low molecular weight-high molecular weight combination of chemicals would be required for the optimum chemical strength reduction of ice.
ACKNOWLEDGMENTS The author would like to thank Mr. R.A. Martin for technical assistance in this program.
CONCLUDING REMARKS Although the experimental procedures used in the present experiments were quite simple, the results and analysis of these experiments have provided useful information on the effects of a large number of chemicals on the strength reduction of ice. It has been found that: (1) within a homologous series, the greatest strength reduction generally occurs for the lowest member of the series; (2) several chemical series ( R - O H alcohols, salts of the carboxylic acids and amides) are especially effective in strength reduction, and (3) for electrolytic dopants, Ct increases with increasing cation weight for a constant anion, but decreases with increasing anion weight for a constant cation. From the results of these experiments, as well as the results of a previous study by the author on the structural characteristics of impure ice (Timco 1978), it would seem that in chemical methods of strength reduction of ice, there are two different, independent processes. On the one hand, the low molecular weight particles decrease the local interface liquidus temperature and thereby bring about the dendritic growth which is necesssary for strength-reduced ice. In addition, these particles become trapped as impurity
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Pounder, E.R. (1958), Mechanical strength of ice frozen from an impure melt, Can. J. Phys., 36: 363-370. Pounder E.R. (1965), The Physics of Ice, Pergamon Press, New York. Rutter, J.W. and B. Chalmers (1953), A prismatic substructure formed during the solidification of metals, Can. J. Phys., 31: 15-39. Schwarz, J. (1977), On the flexural strength and elasticity of saline ice, Proc. 3rd Int. Symp. on Ice Problems, IAHR, Hanover, U.S.A., pp. 373-386. Shulhan, G.M., J.F. Lane and G.W. Timco (1978), The mechanical properties of methanol-doped ice, Nat. Res. Council of Canada, Div. of Mech. Eng. Rep. LTR-LT-83. Svec, O.J. and Frederking, R. (1981), Cantilever beam tests in an ice cover: Influence of plate effects at the root, Cold. Reg. Sci. Tech. 4: 93-101.
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Tiller, W.A., K.A. Jackson, J.W. Rutter and B. Chalmers (1953), The distribution of solute atoms during the solidification of metals, Acta Metall. 1: 4 2 8 - 4 3 7 . Timco, G.W. (1978), Morphological characteristics of ice grown from an impure melt, Nat. Res. Council of Canada, Div. of Mech. Eng.,Rep. LTR-LT-91. Timco, G.W. (1979a), The mechanical and morphological properties of doped ice: A search for a better structurally simulated ice for model test basins, 5th Int. Conf. on Ports and Ocean Engineering under Arctic Conditions,
Proc. POAC '79, Vol. I, Trondheim, Norway, pp. 719 739. Timco, G.W. (1979b), A chemical survey to determine potential dopants for a model ice test basin, Nat. Res. Council of Canada, Div. of Mech. Eng. Rep. LTR-LT-95. Weeks, W.F. and G. Lofgren (1967), The effective solute distribution coefficient during the freezing of NaC1 solutions. In: H. Dura (Ed.), Physics of Ice and Snow, Vol. 1, Hokkaido University, Sapporo, Japan, pp. 579-597.