LiBr Crystallization Inhibition in the Presence of Soluble Additives

Terry A. Ring‡, James A. Dirksen, Kristin N. Duvall and Nathalie Jongen

Department of Chemical Engineering, University of Utah, 50 S Central Campus Drive, Salt Lake City, Utah 84112

‡To whom correspondence should be directed.

Abstract

Experiments have been performed to measure the effect of additives on the crystallization temperature of concentrated LiBr solutions. The measured crystallization temperatures do not correspond to the temperatures of equilibrium solubility but to the critical temperature for heterogeneous nucleation of the hydrated LiBr salt on the glass wall of the test tube containing the sample solution. Various additives at a concentration around 500 ppm have been measured. Some soluble additives further decreased the experimental crystallization temperature by up to 13 ° C, corresponding to 22 ° C below the equilibrium solubility. Large decreases in the crystallization temperature can be correlated with large complexation constants between the additive and the Li+ ion in solution. Solution complexation, however, is not sufficient to explain the magnitude of the decrease in the crystallization temperature. The only phenomenon capable of quantitatively explain the magnitude of the decrease in the crystallization temperature is the change in the crystal/solution interfacial energy due to adsorption of the additive on the surface of the pre-nucleation embryos. This different crystal/solution interfacial energy due to adsorption plays a critical role in the free energy of cluster formation and the rate of nucleation.

Introduction

Concentrated LiBr solutions are used in absorption heat pumps for heating and cooling whole buildings. Water is evaporated and condensed from LiBr solution that is the refrigerant analogous to freon in compressive heat pumps (1) while the LiBr solution acts as the compressor at different temperature and concentration. Like any heat engine cycle, the Carnot efficiency is given by difference in the high and low temperatures divided by the high temperature (2), h=(TH-TL/TH). The LiBr solution and its water vapor can reach temperatures as high as 98 ° C, 177 ° C and 232 ° C depending on the machine type. The low temperatures the LiBr solution and its water vapor can reach for cold air conditioning are typically 4-7 ° C and outdoor ambient air temperatures in winter for heat pump cycles. At this coldest temperature, the LiBr solution is close to the crystallization point as the solubility of LiBr in solution decreases with decreasing temperature. By adding the appropriate additive to the LiBr solution, the Carnot efficiency of the heat pump may be increased by decreasing the temperature at which crystallization takes place.

The freezing point of concentrated LiBr solutions depends upon their concentration since different solids (e.g. ice, tri-, di- and mono- hydrates of LiBr) are produced depending on the concentration of the LiBr solution. When cooled a concentrated LiBr solution, like all particulate free salt solutions, does not freeze at the equilibrium freezing point but at a temperature below the equilibrium freezing point, due to the need to supersaturate the solution before nucleation can take place. This difference in temperature is called the Ostwald-Meyers meta-stable zone: its size depends on the type of solution. A previous paper (3) showed that the onset LiBr salts nucleation could be detected by a 0.4 ° C deviation from the theoretical cooling curve. Nucleation occurs as surface nucleation on the Pyrex glass surface of the test tube containing the solution. The observed freezing points for various LiBr solution concentrations were predicted using the classical nucleation theory whose most useful equations are reviewed here.

The driving force for nucleation is the saturation ratio defined as the ratio of the actual solution concentration when crystallization takes place to the equilibrium concentration, S = C/Ceq. When the saturation ratio is greater than 1.0, the solution is supersaturated with respect to the solid. Supersaturation in this case is due to supercooling, T-Teq, in the solution given as:

[1]

where D Hf is the heat of crystallization of the crystallizing solid, T is the actual temperature of crystallization, Teq is the equilibrium crystallization temperature and Rg is the gas constant.

Using the concept of the critical supersaturation, Sc, which is defined as the value of S necessary to give a nucleation rate which is humanly observable -1 nuclei per cm2 per minute for surface nucleation. The classical surface nucleation equation

[2]

was used to determine a critical supersaturation that is responsible for this humanly observable nucleation rate. In the above equations D is the solution diffusion coefficient, No is the number concentration of LiBr in solution, g is the surface energy for the crystal/solution interface, ge [» gd] is the edge energy per unit length and d is the center to center distance of two LiBr× nH2O molecules and is related to the molar volume,  of the crystal. bL is the edge length conversion factor and bA is the surface area conversion factor for surface nucleation (for a cylindrical embryo of height, d/2, above the surface, bA= p and bL=2p , for cubic embryo with an effective radius = L/2, bA=1 and bL=4), kB is Boltzmann's constant.

Using the surface nucleation theory, the experimental crystallization temperatures could be predicted in agreement with experimental observations when a crystal/solution interfacial surface energy, g, of 40.0±1.2 erg/cm2 was used (3).

The objective of the present study is to explain the effect of additives on the crystallization of hydrated LiBr salts. Active additives, forming very stable complexes with the species involved in the crystallization reaction, decrease the nucleation rate by diminishing the activity of these species: The more stable the complex, the larger the inhibition. Another inhibitor effect can come from a structural matching between the additive and the solid. Sarig (4) highlighted this phenomenon by showing the inhibitory effect of polyglutamic acid, with distances between carboxylate groups around 8 Å, on the precipitation of CaSO4.2H2O, with intercationic distances of about 8.1 Å.

A 1995 book by Nyvlt and Ulrich (5) entitled "Admixtures in Crystallization" qualitatively discusses the effect additives have in various aspects of crystallization and gives 195 pages of tables identifying the effects of various additives on the crystallization of 287 different salts. Unfortunately, hydrated LiBr salts are not part of this compilation. However the authors point out that a consistent theory of the effect of admixtures on individual aspects of the process of crystallization is still missing. In addition, the 1996 book entitled "Crystal Growth of Organic Materials" by Myerson, Green and Meenan (6) contains several articles from a 1995 symposium. Articles of interest are one by Niehorster, et al. (7) on the modeling of the effect of an additive on crystal habit modification and another by Sun and Myerson (8) on the effect of an additive on nucleation. Molecular modeling of the attachment energy for additives at various crystal surfaces has been performed and the effect of this change in attachment energy for the various crystal surfaces used to predict the new crystal habit.

In the present work, the adsorption of soluble additives and their effect on the energy of the heterogeneous surface was quantitatively used to predict the width of the Ostwald-Meyer metastable region that is responsible for actual freezing point of a LiBr solution. In addition, molecular modeling was carried out to predict the critical parameters of the additive adsorption from solution.

Experimental Method

Concentrated stock LiBr solutions were prepared by mixing Analytical Reagent grade LiBr (PFaltz & Bauer Inc., Waterbury, CT 06708) with doubly distilled deionized water and filtering the solution through a 0.2 ”m millipore filter. The concentrations were established by measuring the specific density of the solution and the index of refraction, and comparing the data with standard tables (9-10)..

Test tubes were filled with 25 mL of a concentrated LiBr solution (60.54 or 60.82 wt %). Small quantities of additives were added to some of them (typically 500 mole ppm based upon LiBr): Methylene Diphosphoric Acid (MDPA), Pyrophosphoric Acid (PPA), Aminotri(methylenephosphonic acid) (ATMP), Diethylenetriaminepenta(methylene phosphonic acid) (DTPMP), 1-Hydroxyethylidene-1,1-diphosphonic acid) (HEDP), Potassium Iodate (KIO3) and 5-Amino-2,4,6-trioxo-1,3-perhydrodizine-N,N-diacetic acid (Uramil-N,N-diacetic acid). MDPA and PPA were supplied by Aldrich Chemical Co., Milwaukee, WI 53233, ATMP, DTPMP and HEDP were supplied by Monsanto Chemical Co. (Now Solutia Inc.) in St Louis, MO 63167; KIO3 by J. T. Baker Chemical Co., Phillipsburg, NJ 08865 and Uramil by Pfaltz & Bauer Inc., Waterbury, CT 06708. The tubes were then placed in a temperature programmable cooling bath. The bath could hold 16 test tubes, the LiBr solutions were individually monitored for the solution temperature allowing freezing point statistics to be obtained. These test tubes were then sealed and heated for 24 hours at 50 șC to assure solubilization of the LiBr solutions. After solubilization was ensured, the test tube was cooled at a ramp of 20 șC/hr. Inside the test tube a thermal well with a thermocouple of precision 0.01 șC recorded the temperature of the solution as a function of time using computerized data logging equipment. The bath temperature was undergoing a ramped decrease in the set point: Excellent fits with errors less than 0.1 șC were obtained (3). When the solution froze, the heat of crystallization was released and the temperature of the solution increased slightly.

Results and discussion

An example of the cooling curve for various samples is given in Figure 1. The freezing points for the tested additives are easily identified by the deviation of the temperature from the cooling curve of a blank solution. This blank solution has a cooling curve that is easily predicted by a continuation of the nearly linear cooling curve of the solution above the freezing point to temperatures below the freezing point. The mathematical derivation of the cooling curve of the sample has been shown previously (3). Experimental results of the freezing temperature for the tested soluble additives are given in Table 1. It should be noted that the crystallization from pure LiBr solution starts on the curved bottom of the test tube and continues until the test tube is approximately 3/4 filled with large plate like crystals (Figure 2a). The crystals are lithium bromide dihydrate, LiBr·2H2O, according to the literature (11) and verified using X-ray diffraction. When some additives are present (e.g. Uramil-N,N-diacetic acid), the crystal habit is drastically modified to needles which are up to 5 mm long and 1 mm in diameter (Figure 2b).

 

Table 1 Crystallization temperatures measured in the presence of soluble additives. The most efficient additives are displayed first.

Additive

LiBr conc. (wt %)

Additive conc.

(mole ppm#)

Crystallization temperature

Tmin± Std. Deviation (șC)

MDPA

60.54

250

-10.16 ± 3.17

PPA

60.82

500

-8.52 ± 4.17

ATMP

60.82

500

-8.24 ± 2.25

DTPMP

60.82

500

-6.67 ± 6.79

HEDP

60.82

500

-6.15 ± 7.49

Uramil-N,N-diacetic acid

60.54

500

-5.69 ± 2.92

KIO3

60.54

250

-4.31 ± 0.70

None

60.54

60.82

-

3.30 ± 0.44

4.38 ± 0.59

# moles of additive per mole of LiBr solution on a ppm basis

 

Our concern is the identification of the additives inhibiting LiBr crystallization and the determination of their mechanism of action. Crystallization inhibition can take place following mechanisms including: 1) decrease of the crystallization driving force, i.e. supersaturation, 2) increase of the critical supersaturation necessary for nucleation, and 3) decrease of the crystal growth rate. This paper concentrates on the first two effects.

Effect of the complexation constant

A soluble additive is able to influence the LiBr solubility by being a complexant for Li+ ions in solution.

Knowing the solubility of LiBr·2H2O (3) in the form of the solubility product (Ksp = 0.020±0.002 = [Li+][Br-][H2O]2, activity based upon mole fraction), the effect of a soluble complexing additive can be determined. If an additive complexes the Li+ ions, these ions are effectively removed from the solubility equilibrium according to the following equation:

[3]

where B-b is the complexant with a charge -b. This complexation reaction results in a lower effective Li+ concentration in solution requiring a higher supersaturation level and thus decreases the crystallization temperature. The larger the complexation constant, the more the crystallization temperature decreases. However the freezing temperature of LiBr solutions in the presence of additives cannot be explained with the complexation caused by these K values.

One possible explanation is that the surface energy of the crystal and/or embryo in the saturated solution is also altered by the presence of additive molecules adsorbing on the crystal surfaces. Drastic changes in crystal habit have been observed from large platelets to small crystallite needles with the addition of 500 ppm Uramil-N,N-diacetic acid. This observation suggests that the surface energy of the crystal faces is strongly altered by this additive. In the calculation of the crystallization temperature due to surface nucleation, the surface energy plays an important role, as will be discussed later. An increase in the surface energy of 10 erg/cm2 is sufficient to decrease the freezing point temperature by several degrees centigrade. We need now to be able to predict the new surface energy that an additive at a given concentration would induce in order to be able to calculate the freezing temperature of the LiBr solution.

Effect of additives on the crystal/solution interfacial energy

The additives alter the interfacial energy between the LiBr·2H2O and the solution as they are able to complex the surface of LiBr·2H2O crystals. The effect of the surface energy on the crystallization temperature due to surface nucleation is plotted in Figure 3. The crystallization temperatures were calculated by inverting equation [2] for several surface energy values and assuming that Is, the nucleation rate, equals 1 nucleus per cm2 per minute and the LiBr concentration is 60.54 wt %.

In Figure 3 we see that an increase in the crystal/solution interfacial energy from zero to 90 erg/cm2 gives a 50 șC decrease in the crystallization temperature. In this range of interfacial energies several values are well established:

a) 0 erg/cm2 with seed crystals of the same material present in sufficient amount to generate nucleation sites; b)29 erg/cm2, the surface energy of the ice/water interface (12); c) 40 erg/cm2, the value of the best fit of the experimental crystallization temperature of LiBr·2H2O without additive; d) 61 erg/cm2, the value of the best fit of the experimental crystallization temperature of LiBr·2H2O with 500 ppm Uramil-N,N-diacetic acid; e) 90 erg/cm2, the value of the solution/air interface at this LiBr concentration (13)

This is in good agreement with our experimental observations, i.e. compare Figure 3 to data in Table 1. Directly measuring this energy experimentally is very difficult and has not been done under crystal growth conditions in any systems that we are aware of. Nonetheless computational means are possible if the adsorption isotherm can be established and the analogy to the Gibbs adsorption equation can be used.

The crystal/solution interfacial energy is altered by additive adsorption according to the Gibbs Adsorption equation (14):

[4]

where Ga(1) is the adsorbed amount, gs is the crystal/solution interfacial energy and aa is the solution activity of the surface complexant or additive in our case. As derived, the above equation relates the surface energy of the liquid/air interface to the adsorbed amount given by the adsorption isotherm and could be used to relate the effect of the crystal/solution interfacial energy if the adsorbed amount, Ga(1), is either measured or predicted by the Langmuir adsorption isotherm:

[5]

where Gm is the adsorbed amount at monolayer coverage and KLangmuir is the adsorption equilibrium constant.

In order to obtain g =f(Gm,KLangmuir, T), equation [4] is transformed into

[6]

Ga(1) is then substituted from [5] into [6] and integrated to give :

[7]

resulting in:

[8]

To test this concept freezing point experiments were performed at various concentrations aa for several additives. The corresponding crystallization temperatures are shown in Table 2. Using this theoretical concept, the freezing point due to surface nucleation as a function of the concentration of Uramil-N,N-diacetic acid is presented in Figure 4. As it can be seen from the good fit of the experimental data, we have a quantitative explanation of the freezing point data confirming the theoretical approach. The adsorbed area at monolayer coverage Gm-1 and KLangmuir resulting from this fit for the tested additives are also shown in Table 2.

We can now focus on what makes a molecule adsorb at the surface. The monolayer adsorption density, Gm, and the adsorption equilibrium constant, KLangmuir are two parameters of the Langmuir adsorption isotherm. Gm corresponds to the surface area covered by one molecule and relates to the size of the molecule and the density of sites at the surface where the molecule can be attached. Using molecular modeling (15) the 0 0 surface of LiBr·2H2O crystal and the energy relaxed conformation of various additives at the surface of this crystal were modeled. This crystal surface has bound H2O molecules exposed to the solution and in between and below them Li+ and Br- ions as seen in Figure 5. Figure 5 also presents the sizes of MDPA and Uramil-N,N-diacetic acid in their preferential binding sites, i.e. a pocket in the crystal surface over a Li atom in the second layer of atoms in the crystal: MDPA sits at essentially the same location as Uramil-N,N-diacetic acid on the crystal surface due to the geometric similarity of the amine diphosphoric acid and the amine diacetic acid groups. However, the area occupied by Uramil-N,N-diacetic acid (0.92 nm2) covers slightly more than two of these sites while MDPA (0.34 nm2) covers one. This difference in surface monolayer coverage will have profound effects on the surface energy and the freezing point of the LiBr solution with additive. Thus twice the amount of molecules of MDPA on the surface as that of Uramil-N,N-diacetic acid in a monolayer if they have equal effects on the surface energy. The interaction energy of the additive molecule either MDPA or Uramil-N,N-diacetic acid with the surface at various locations (frames) at the surface is also plotted in Figure 5. The lowest energy of all the locations sampled, -11.5 kcal/mole for MDPA and -15.0 kcal/mole for Uramil-N,N-diacetic acid are the energies of relaxed structures in the absence of solvent molecules. But since Uramil-N,N-diacetic acid sits on two sites the per site energy of MDPA is larger than that of Uramil-N,N-diacetic acid suggesting that KLangmuir for MDPA is larger than that of Uramil-N,N-diacetic acid. Both the adsorbed conformation and interaction energy observations agree with the experimental observations that a LiBr solution containing 500 ppm of MDPA has a freezing point of -10.16±3.17 șC while that of Uramil-N,N-diacetic acid is -5.69±2.92 șC compared to a freezing point of the same 60.54 wt % LiBr solution without additive of +3.30±0.44 șC. Comparing the molecular area of Uramil-N,N-diacetic acid obtained from molecular modeling, i.e. 0.92 nm2, with that obtained by the best fit of the freezing point data as a function of Uramil-N,N-diacetic acid concentration, i.e. 1 nm2, we find very good agreement. The algorithm that will allow prediction of the adsorption equilibrium constant, KLangmuir, from molecular modeling calculation has not been found yet but it is related to the energy calculations shown in Figure 5.

Table 2 Effect of additive concentration on the freezing point of 60.82 wt % LiBr solutions and fit results for Gm-1, the adsorbed area at monolayer coverage, and KLangmuir, the adsorption equilibrium constant.

Additive

Additive Conc.

(mole ppm)

Crystallization Temp.

Tmin± Std. Deviation (șC)

Gm-1 (nm2)

KLangmuir

None

0

4.65 ± 0.56

   

MDPA

50

-4.80 ± 3.67

0.65

10

 

150

-2.63 ± 5.11

   
 

250

-8.88 ± 3.17

   

ATMP

200

-5.93 ± 3.62

1.0

0.5

 

500

-8.24 ± 2.25

   
 

1500

-14.22 ± 0.74

   

DTPMP

200

-12.72 ± 3.56

0.7

20

 

500

-6.67 ± 6.79

   
 

1500

-13.47 ± 2.20

   

PPA

200

-9.55 ± 3.83

0.65

10

 

500

-8.52 ± 4.17

   
 

750

-8.89 ± 7.96

   

HEDP

200

-10.97 ± 6.61

0.7

20

 

500

-6.15 ± 7.49

   
 

1500

-13.01 ± 1.71

   

Uramil-N,N-diacetic acid

200

-2.36 ± 2.69

1.0

0.09

 

500

-4.69 ± 3.73

   
 

1000

-6.10 ± 3.30

   
 

1500

-7.50 ± 2.38

   

 

Conclusions

The effect of additives at a concentration of 200 ppm and higher on the crystallization temperature of LiBr aqueous solution has been studied. One of these additives decreased the crystallization temperature 13 șC below the experimental freezing point and 22 șC below the equilibrium freezing point of the same solution without additive. Large decreases in the crystallization temperature can be correlated with large values of complexation constants between the additive and the Li+ ion in solution. However, solution complexation is not sufficient to explain the magnitude of the decrease in the crystallization temperature. This freezing point diminution has been quantitatively justified by the additive adsorption at the crystal/solution interface, altering the surface energy.

Ackowledgements

This project was sponsored by the Gas Research Institute under contract No 5094-260-2895. N. J. would like to thank the "Stiftung Entwicklungsfond Seltene Metalle" (Switzerland) for a scholarship, the Commission for Educational Exchange between the USA, Belgium and Luxembourg for a Fulbright Award and the North Atlantic Treaty Organization for a scholarship.

References

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2. Smith, J.M. and Van Ness, H.C., "Introduction to Chemical Engineering Thermodynamics", 2nd Edition, McGraw-Hill, New York, 1959.

3. Duvall, K., Dirksen, James A. and Terry A. Ring, Terry A., paper submitted to J. Colloid Interface Sci.

4. Sarig S., Kahana F., J. Cryst. Growth, 35 145-152 (1976).

5. Nyvlt, J. and Ulrich, J., "Admixtures in Crystallization," VCH Weinheim, Germany ,1995.

6. Myerson, A.S. , Green, D.A. and Meenan, P., eds. "Crystal Growth of Organic Materials," ACS Conference Prodeedings Series, American Chemical Society, Washington, DC, 1996.

7. Niehorster, S. Henning S. and Ulrich, J., in "Crystal Growth of Organic Materials" (A.S. Meyerson, D.A. Green and P. Meenan , eds.), ACS Conference Prodeedings Series, p 58, American Chemical Society, Washington, DC, 1996.

8. Sun, W-M and Myerson, A. S., in "Crystal Growth of Organic Materials", (A.S. Meyerson, D.A. Green and P. Meenan , eds.), ACS Conference Prodeedings Series, p. 249, American Chemical Society, Washington, DC, 1996.

9. Zaltash, A., Ally, M.R., J. Chem. Eng. Data 37 110-113 (1992)

10. National Research Council, "International Critical Tables", (E.W. Washburn Ed.), Volume III, p.727, Mc Graw Hill, New York, 1928.

11. Broul, M., Nyvlt, J and Sohnel, O., "Solubility in inorganic two-component systems", Physical sciences data6, Elsevier Scientific Publishing Co. Amsterdam, 1981.

12. Adamson, A.W., "Physical Chemistry of Surfaces" 4th ed., p.322, John Wiley & Sons, New York, 1982.

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Figures

Figure 1 Cooling curves of 60.54% wt LiBr solutions with various additives. The deflection in the curve is caused by the release of the heat of fusion when the solution starts to freeze. The minimum in the curve to the left of the peak is the crystallization temperature measured experimentally. Additive concentrations are : A = 500 ppm KIO3, B = 500 ppm Uramil-N,N-diacetic acid, C = 500 ppm HEDP, D = DTPMP, E = 500 ppm MDPA.

(a) (b)

Figure 2 Picture of a) large crystals formed from 60.82 % LiBr solution without additive, b) slushy solid containing needle-like crystals obtained with Uramil-N,N-diacetic acid.

Figure 3 Crystallization temperature due to the surface nucleation versus crystal/solution interfacial energy. The points correspond to the experimental crystallization temperatures observed without additive and with 500 ppm Uramil-N,N-diacetic acid.

Figure 4 Freezing point (șC) as a function of Uramil-N,N-diacetic acid concentration. Data points (à ) are experimental freezing points with ± standard deviation indicated with + symbols. The central curve is predicted using the Gibbs adsorption equation to calculate the interfacial energy and the Langmuir adsorption isotherm with the following values for the Langmuir adsorption isotherm, Gm = 1 nm2 per adsorbed molecule, KLangmuir = 0.09/ppm. The upper and lower curves use the same proceedure by over and under predicting the energy by 3 % since that was of the accuracy in the energy measured by best fit without additive. This suggests that there is another effect influencing the distribution of surface energy when the additive is present at the interface as the experimental standard deviation is larger than the standard deviation of 3% depicted by the upper and lower curves.

Figure 5 Molecular modeling of MDPA and Uramil-N,N-diacetic acid additives at the 0 0 surface of LiBr•2H2O crystal surface. The two graphs show the interaction energy of the additive with the crystal's surface as a function of location (frame). The lowest energy configuration of the adsorbed molecule is depicted at the surface.