Sodium and Rubidium Dodecyl Sulfates - American Chemical Society

Modeling the Crystal Morphology of Alkali-Metal Alkyl Surfactants: Sodium and Rubidium Dodecyl Sulfates Lorna A. Smith Edinburgh Parallel Computing Centre, University of Edinburgh, Edinburgh EH9 3JZ, U.K.

CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 6 2164-2172

Gillian B. Thomson Centre for Molecular and Interface Engineering, School of Engineering and Physical Science, Heriot-Watt University, Edinburgh EH14 4AS, U.K.

Kevin J. Roberts* Institute of Particle Science and Engineering, School of Process, Environmental and Materials Engineering, University of Leeds, Leeds LS2 9JT, U.K.

David Machin and Gordon McLeod Unilever Research Port Sunlight, Quarry Road East, Bebington, Wirral CH63 3JW, U.K. Received February 22, 2005

ABSTRACT: Refined interatomic potential parameters are determined for sodium dodecyl sulfate (SDS) and rubidium dodecyl sulfate (RDS) and used to calculate the lattice energies of these systems. Comparisons of these values with the experimental “sublimation enthalpies” show good agreement between the calculated and experimental (-173.13, 145.50 kcal/mol; -176.40, 155.76 kcal/mol) values, respectively. These parameters are utilized to predict the morphology of sodium and rubidium dodecyl sulfates using the attachment energy method, with the simulations revealing a platelike morphology for both materials, in good agreement with the experimental morphologies. Analysis of the intermolecular bonding within the crystal structures of both SDS and RDS reveal weak van der Waals interactions between the hydrocarbon tails, resulting in a predicted slow growth perpendicular to the principal faces of these crystals. 1. Introduction Being able to successfully predict the shape of surfactant crystals from their root molecular and crystal structure can help in the control and manipulation of quantity, size distribution, and shape of crystallites.1-3 This can have concomitant impact downstream on product performance, providing an important resource for the design of improved surfactant-based products, for example yielding superior physicochemical and/or materials properties for home and personal care products. While a range of growth environmental factors, such as solvent and additives, may affect the morphology of a crystal, the basic morphological forms can be predicted from the materials bulk crystallographic structure. In the above context, the aim of this specific study is to predict the morphology of the important alkali-metal alkyl surfactants sodium and rubidium dodecyl sulfates (SDS and RDS, respectively) and through this to gain a greater understanding of the interrelationship between the intermolecular bonding involved within the crystal structure and the external growth morphology. These compounds are important components for a wide range of products, and hence, an improved understanding and potential control of particle shape offers promise for the development of improved formulations for these * To whom correspondence [email protected].

should

be

addressed.

E-mail:

and other surfactant-based materials. In this study the crystal morphologies are predicted and compared and contrasted with experimentally observed crystal morphologies. To achieve this, existing molecular force field parameters have been optimized and refined for these materials, with the results validated against the known bond lengths, unit cell parameters, and lattice energies.

2. Morphology Prediction 2.1. Attachment Energy Method. The morphology of a crystal can be related to the arrangement of the molecules within the crystal and their molecular bonding. Theory developed by Gibbs4 and later extended by Wulff5 can be utilized to determine the equilibrium morphology of a crystal. Models were developed by Bravais,6 by Friedel,7 and by Donnay and Harker8 to predict crystal morphology from the crystal lattice geometry (the so-called BFDH method). Hartman and Perdock9 related the external crystal morphology to the intermolecular forces between crystallizing entities through calculation of the attachment and slice energies for the habit planes (hkl) of the crystal. The attachment energy (Eatt) is the energy released on the addition of a growth layer (slice) of thickness dhkl to the surface (hkl) of a growing crystal, with the energy released on the formation of this slice being the slice energy (Esl). The

10.1021/cg058003g CCC: $30.25 © 2005 American Chemical Society Published on Web 09/30/2005

Alkali-Metal Alkyl Surfactants

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total lattice energy (Ecr) is thus1 a summation of these two values:

Ecr ) Esl + Eatt

(1)

Hartman and Bennema10 proposed that the attachment energy is a useful measure of the relative growth rate of a crystal habit force being proportional to growth rate. This implies that the faces with the lowest attachment energy should be taken as the slowest growing and hence be morphologically the most important: i.e., the largest surface area within the external crystal shape. Calculation of Eatt and Esl can be carried out via the partition of the intermolecular bonds, calculated through lattice summation, between the components without (Eatt) and within (Esl) the slice of thickness dhkl.11 In this, the slice position is usually optimized via translation along the growth normal to maximize the slice energy (i.e. to locate the most stable surface layer). In addition, this method assumes that the oncoming slice has a structure identical with a similar layer in the bulk and that the surface is a perfect termination of the bulk and no surface relaxation takes place. This methodology has been applied successfully in a number of studies to predict the morphology of molecular crystals (see ref 12, for example). The strength of the intermolecular bonds may be calculated using the atom-atom approximation: i.e., assuming the intermolecular force involved in the binding between two adjacent molecules can be modeled as a sum of its constituent atom-atom interactions. In this, an appropriate force field involving van der Waals interactions for the specific atom-atom interactions coupled to a Coulombic interaction representing the interatomic interactions between the partial electronic charges on the interacting atoms is typically used. 2.2. Atom-Atom Force Fields and Their Optimization. Numerous force fields have been developed for both molecular crystals and ionic crystals. One of the most utilized for organic materials is the force field of Williams,13 who derived intermolecular potential parameters for C-C, C-H, and H-H interactions. Other examples include force fields developed by Momany et al.14 and separately by Lifson et al.15 for hydrocarbons, carboxylic acids, amines, and amides. More recently Allen et al.16 and Meenan et al.17 have developed a force field for metal sulfates. Specific force fields parameterized for the atomic species of interest are clearly preferred, as they enable the often subtle molecular features of complex structures to be distinguished, leading to a more accurate predictive capability for modeling physical properties. Thus, more general force fields cannot be expected to be so effective in this respect. However, there is still demand for general force fields to model a wide variety of systems for which there are little or no experimental data to enable force field determination and optimization. Force fields of this latter type include the DREIDING,18 Universal,19 CVFF,20 and CFF9120,21 force fields. Force field parameters usually comprise two-body intermolecular (van der Waals and Coulombic) interactions together with two-, three-, and four-body terms representing the intramolecular interactions. To date, no force field data have apparently been published for the alkylmetal sulfates, and in this work

existing generic force field parameters have been reparametrized and optimized against available crystal structure data for SDS and RDS to allow a more accurate prediction of the physical properties for these systems. Interatomic potential parameters can be obtained using one of two methods: empirical fitting and energy surface fitting.22 The accuracy of the refined force field parameters can be assessed by optimizing the crystal structures used in the determination and the bond lengths of the molecules and the unit cell parameters and comparing these to their starting values, using the so-called relaxed fitting method. This is superior to conventional minimization of the forces at the experimental structure, since it also ensures that the local curvature is reasonable. The overall potential fitting function involves a combination of intra- and intermolecular functions. The former uses multibody interaction parameters to account for the strong interatomic interaction. These intermolecular parameters are important in morphology prediction and, hence, are of particular interest to this study. The applicability of these potential parameters can be tested by calculating the lattice energy and comparing this to the experimental sublimation enthalpy. The lattice energy of a three-dimensional crystal structure can be considered to consist of the summation of all atom-atom interactions between a central molecule and all the surrounding molecules in a crystal. For a central molecule (with n atoms) surrounded by N molecules (each containing n′ atoms) the lattice energy (Ecr) can be given by N n

n′

∑ ∑ ∑ Vk i)1 j)1k)1

Ecr ) 1/2

ij

(2)

where Vkij is the interaction energy between atom i of the central molecule and j of the kth surrounding molecule. The factor 1/2 is present so as to avoid doublecounting pairs of interactions. This equation relies on the atom-atom approximation,23 which assumes that the interaction between two molecules is equal to the sum of all constituent atom-atom interactions. Warshel and Lifson24 showed that lattice energy and sublimation enthalpy (∆Hsub) can be related by

∆Hsub ) -Ecr - 2RT

(3)

Thus, if the value of ∆Hsub can be obtained experimentally, it can be compared with the lattice energy calculated using an atom-atom potential set. This comparison can be used to assess the accuracy of the potential set. 3. Materials and Methods 3.1. Force Field Derivation. The partial charges on the atoms in SDS and RDS were determined using the approximation MNDO25 within MOPAC.26 The program GULP27 was used to carry out potential fitting and energy minimization. The published crystal structures of RDS28 and SDS29 were used to refine the force field parameters. Initial parameters were obtained from the sulfate potential developed by Allen,16 the hydrocarbon potential developed by Williams,13 and the general force field developed by Mayo18 (often referred to as the DREIDING force field). The

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accuracies of the refined force field parameters were assessed by optimizing the crystal structures used in the determination and the bond lengths of the molecules and the unit cell parameters and comparing these to their starting values. It is important to note that as existing force field parameter sets were optimized to model the physical properties for the two structures of interest, further study would clearly be needed to assess the general applicability of this potential to other surfactant systems. The intermolecular interactions were represented using a Buckingham potential of the form given in eq 4:

Vij ) A exp(-Br) -

q1 q 2 C + 6 4π0r r

(4)

where A, B, and C are the parameters being optimized. The two-body intramolecular interactions were represented by either the Morse function given by

Vij ) Dij[(1 - exp(-aij(r - r0)))2 - 1]

(5)

where Dij, aij, and r0 are the refineable parameters, or by the harmonic function given by

Vij ) 1/2k2(r - r0)2 + 1/6k3(r - r0)3 + 1/24k4(r - r0)4 (6) where k2, k3, k4, and r0 are the refineable parameters. The three-body intramolecular interactions were represented by

EB ) 1/2kb(θ - θ0)2

(7)

where kb and θ are the refineable parameters. The expression in parentheses describes the deviation from the equilibrium coordinate angle θ0. The four-body interactions were represented by the torsion function given by

Vij ) k(1 + cos(nφ))

(8)

where φ is the torsion angle and k and n are the refineable parameters. 3.2. Morphology Prediction. The morphology predictions carried out utilized the program HABIT95, whose basic operation is described and discussed in some detail elsewhere (see ref 30, for example). The faces most likely to dominate the crystal morphology were obtained using the BFDH model, as implemented in the Cerius2 software.31 The crystal morphology was plotted from the attachment energies calculated within HABIT95 using the program SHAPE,32 with the respective surface areas of the habit forces being calculated using the Cerius2 morphology module. In addition, surface energies for the predicted crystal habit forces were also calculated from the attachment energies for completeness using the relationship

Esurf )

ZEattdhkl 2V

(9)

where Esurf is the surface energy, Z is the number of molecules per unit cell, V is the unit cell volume, and dhkl is the interplanar spacing of a surface with Miller indices {hkl}. 3.3. Measurement of Enthalpy of Sublimation. Enthalpies of sublimation have been successfully measured for numerous systems using a variety of techniques. For example, experimental sublimation data are reported in the chemical literature,33-36 and a range of sublimation enthalpies have been determined by measuring vapor pressures as a function of temperature.37-39 Numerous other methods exist;40 however, in this particular case determining the enthalpy of sublimation from direct methods proved impossible for SDS and RDS due to sample decomposition.40 Approximate sublimation enthalpies have therefore been obtained using a more indirect route. The enthalpy of dissolution was measured and a Born-Haber cycle used to obtain a “sublimation enthalpy”. The enthalpies

Figure 1. Atom numbering of the dodecyl sulfate ion. of dissolution (below the critical micellar concentration (CMC)) were measured at Unilever Research41 using a Perkin-Elmer DSC-7 with liquid-nitrogen-controlled cooling. The enthalpies of solvation for the Na+ and Rb+ ions were taken from the literature42 and the enthalpy of solvation of the dodecyl sulfate ion calculated using the program DelPhi.43 The resulting enthalpy values were less accurate than a directly measured sublimation enthalpy, though they still provide a useful tool for the estimation of the accuracy of the intermolecular parameters of the force fields. 3.4. Crystal Growth. Small crystals of SDS and RDS were prepared by slow solvent evaporation of their saturated solutions within crystallization dishes partially covered with cling film at ambient temperatures. Representative samples were examined using an inverse optics Olympus microscope equipped with a video image capture system and associated image analysis software. Anhydrous SDS was purchased from BDH (purity >99%) and recrystallized from aqueous solution in the presence of 1% sodium citrate (to ensure crystallization of the anhydrous form). RDS was prepared through the sulfonation of I-dodecanol with chlorosulfonic acid, followed by neutralization with rubidium hydroxide and successive recrystallization from ethanol and then water. Final crystals for analysis were prepared as per SDS described above; see also refs 44 and 45.

4. Results and Discussion In this section results are presented for the enthalpies of sublimation and for the refined force field parameters. This is followed by a short description of the crystal chemistry of the systems. The intermolecular bonding within the systems is described, and finally the predicted morphologies are presented. These are compared to the experimental morphologies. 4.1. Enthalpy Measurement and Calculations. The enthalpy of dissolution of RDS was measured as 59.5 J/g (∼5.0 kcal/mol). The enthalpy of dissolution of SDS has been reported in the literature by Hutchinson et al.:46 7.63 ( 0.11 kcal/mol. A value of 67.00 kcal/mol was calculated for the enthalpy of solvation of the dodecyl sulfate ion. However it is important to note that this value only includes the electrostatic contribution to the solvation enthalpy. Values of 98.50 and 73.40 kcal/mol were obtained from the literature for Na+ and Rb+, respectively. Summing the determined enthalpies of solvation with the enthalpies of dissolution for each system resulted in sublimation enthalpies of 173.13 kcal/mol for SDS and 145.50 kcal/mol for RDS. 4.2. Molecular Force Field Parameters for Alkyl Metal Sulfates. The atom numbering used for the nonhydrogen atoms in the alkyl ion for SDS and RDS is given in Figure 1. 4.2.1. Calculation of the Partial Electronic Charges. Partial electronic charges were calculated from the optimized molecular structures of SDS and RDS using the MNDO,25 AM1,47 and PM348,49 formulations, as set up within MOPAC and implemented in the Cerius2 software. Examination of resultant fits of the optimized structures to the known crystallographic data40 revealed the best fit was with the MNDO forma-



Table 1. Calculated Partial Electronic Charges for SDS and the Two Crystallographically Independent Molecules in RDS

Table 2. Modeled Force Field Parameters for SDS and RDS Intermolecular Force Field Parameters

RDS atom type

SDS

molecule 1

molecule 2

atom 1

atom 2

potential form

A (eV)

B (Å)

C (eV Å6)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17 H18 H19 H20 H21 H22 H23 H24 H25 S1 O1 O2 O3 O4 Na1/Rb1

0.190 -0.022 -0.015 -0.012 0.000 -0.009 -0.019 -0.013 -0.012 -0.012 -0.019 0.025 0.032 0.012 0.014 0.028 0.011 0.004 0.004 0.009 0.007 0.007 -0.004 0.010 0.006 0.003 0.005 0.006 0.007 0.007 0.007 0.007 0.006 0.005 0.009 -0.015 -0.015 1.971 -0.781 -0.967 -0.888 -0.589 1.0000

1.9900 -0.5980 -0.8698 -0.8379 -0.8624 0.1986 -0.0131 -0.0176 -0.0129 -0.0089 -0.0110 -0.0122 -0.0108 -0.0136 -0.0128 -0.0236 0.0295 0.0068 0.0011 0.0138 0.0105 0.0024 0.0013 0.0057 -0.0001 0.0034 0.0028 0.0050 0.0032 0.0047 0.0049 0.0065 0.0045 0.0053 0.0038 0.0051 0.0057 0.0059 -0.0073 -0.0064 -0.0100 0.0079 1.0000

1.971 -0.589 -0.781 -0.888 -0.967 0.190 -0.022 -0.015 -0.012 0.000 -0.009 -0.019 -0.013 -0.012 -0.012 -0.019 0.025 0.032 0.012 0.014 0.028 0.011 0.004 0.004 0.009 0.007 0.007 -0.004 0.010 0.006 0.003 0.005 0.006 0.007 0.007 0.007 0.007 0.006 0.009 -0.015 -0.015 0.005 1.000

O O H H C O

Rb Na H C C O

Buckingham Buckingham Buckingham Buckingham Buckingham Buckingham

2723.99 709.14 151.96 878.77 5081.52 278971.62

0.2913 0.2955 0.2674 0.2725 0.2778 0.2000

0.00 0.00 1.59 6.65 27.93 25.98

Intramolecular Parameters (Two-Body) atom 1

atom 2

potential form

Dij or k2

aij

r0

O1 O2 C H C

S S O C C

Morse Morse harmonic harmonic harmonic

5.0 5.0 11.85 14.77 13.99

1.20 1.20

1.44 1.62 1.48 1.11 1.52

Intramolecular Parameters (Three-Body) atom 1

atom 2

atom 3

potential form

force constant k2(eV rad-2)

θ (deg)

S S C C C C O

O2 O1 H H C H C

O1 O1 H C C O S

harmonic harmonic harmonic harmonic harmonic harmonic harmonic

15.00 15.00 1.71 1.93 2.02 2.47 2.60

129.40 145.96 106.40 110.00 110.50 109.50 106.54

Intramolecular Parameters (Four-Body) atom 1

atom 2

atom 3

atom 4

potential form

k (eV)

n

H H C H C O

C C C C C S

C C C O O O

H C C S S C

torsion torsion torsion torsion torsion torsion

0.062 0.062 0.062 0.017 0.017 0.003

3 3 3 3 3 3

Table 3. Bond Lengths (Å) of the Dodecyl Sulfate Ions of SDS and RDS after Optimization Compared to the Literature Values28,29 SDS

tion, which was used for calculation of the partial electronic charges. Table 1 lists the resultant partial charges for both SDS and RDS. In the subsequent potential fitting, these calculated charges were not further refined. 4.2.2. Calculation of the Atom-Atom Non-Coulombic Force Field Parameters. The refined empirical force field parameters determined are summarized in Table 2. The bond lengths of the molecular anions of the optimized crystal structures of SDS and RDS are given in Table 3. The original bond lengths are given for comparison. The unit cell parameters of the optimized structures of SDS and RDS are given in Table 4, with the original values also being given for comparison. The bond lengths of the optimized molecular anions are in reasonable agreement with the original lengths for all the crystal structures. The same applies for the unit cell parameters, and hence reasonable reliance can be placed on the refined parameters. Lattice energy convergence was taken to have occurred at a cutoff distance of 80 Å (Figure 2). The lattice energy of SDS

bond C1-C2 C2-C3 C3-C4 C4-C5 C5-C6 C6-C7 C7-C8 C8-C9 C9-C10 C10-C11 C11-C12 C12-O1 O1-S1 S1-O2 S1-O3 S1-O4

RDS (molecule 2)

RDS (molecule 1)

opti- structural lit. lit. mized value optimized value optimized value 1.517 1.508 1.508 1.503 1.503 1.512 1.512 1.524 1.524 1.514 1.530 1.475 1.572 1.463 1.434 1.441

1.531 1.541 1.542 1.542 1.542 1.542 1.542 1.543 1.543 1.542 1.555 1.393 1.657 1.532 1.522 1.531

1.525 1.516 1.516 1.517 1.517 1.515 1.515 1.515 1.517 1.517 1.519 1.480 1.596 1.425 1.427 1.437

1.515 1.516 1.521 1.517 1.524 1.510 1.533 1.535 1.537 1.546 1.510 1.465 1.592 1.441 1.443 1.446

1.523 1.513 1.513 1.516 1.516 1.517 1.517 1.510 1.510 1.516 1.516 1.481 1.600 1.429 1.433 1.434

1.523 1.543 1.514 1.539 1.515 1.537 1.534 1.504 1.527 1.527 1.483 1.466 1.596 1.422 1.428 1.453

(corrected for 2RT) is -176.40 kcal/mol and for RDS is -155.76 kcal/mol. These compare with sublimation enthalpies of 173.13 and 145.50 kcal/mol. Considering the limitations in the methodology utilized to determine the sublimation enthalpy, comparison of the lattice energies with the sublimation enthalpies shows good

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Figure 2. Plot of the crystal lattice energy (ECR) (kcal/mol) as a function of intermolecular interaction distance, showing good convergence of the lattice summation with a higher ECR for SDS compared to RDS (angstroms). Table 4. Unit Cell Parameters of SDS and RDS after Optimization Compared to the Literature Values SDS

RDS

param

optimized

lit.29

a/Å b/Å c/Å R/deg β/deg γ/deg

39.05 4.84 8.56 90.00 92.92 90.00

38.92 4.71 8.20 90.00 93.29 90.00

optimized

lit.28

7.18 7.50 30.67 96.49 90.71 84.78

7.14 7.49 30.69 96.26 90.57 84.91

Table 5. Crystal Chemistry of SDS and RDS cell type space group a (Å) b (Å) c (Å) R (deg) β (deg) γ (deg) cell vol (Å3) cell density (g cm-3) no. of asym units no. of molecules in asym unit ref

SDS

RDS

monoclinic P21/c 38.915 4.709 8.198 90.00 93.29 90.00 1499.8 1.28 4 1 40

triclinic P1 h 7.14 7.49 30.69 96.26 90.57 84.91 1624.5 1.43 2 2 28

correlation. Hence, reasonable reliance can be placed on the refined intermolecular potentials to be used for morphology prediction. The calculated lattice energies of SDS for both force fields are higher than the corresponding RDS values. This is possibly a result of the larger rubidium ion size, which has caused a greater separation distance between the metal ion and the sulfate headgroups and hence lower atom-atom interaction strengths between the two ions. 4.3. Crystal Chemistry of SDS and RDS. The crystal chemistry of both of these systems is discussed elsewhere.28,29 However, this has a significant affect on the overall morphology, and hence their crystal chemistry is summarized here in Table 5. Figure 3 shows the unit cells of SDS and RDS. For SDS, in projection down the unique axis, molecules appear in layers with the main axis of the hydrocarbon tail oriented at angles of 14.8, 89.2, and 78.5° with respect to the crystallographic directions [100], [010], and [001], respectively. These angles were calculated with reference to the longest principal axis of the SDS anion that is roughly coincident with the hydrocarbon backbone. The structure of anhydrous SDS

Figure 3. Molecular packing diagram of crystallographic unit cells showing comparison between (a) SDS and (b) RDS solidstate structures, adopted from refs 28 and 29.

consists of double layers of molecules. Molecules in adjacent layers are related by 21 axes. Within layers the adjacent molecules are related by c glide planes. There are alternate polar and apolar regions lying perpendicular to the [100] direction, reminiscent of a typical bilayer structure. Electrostatic interactions dominate the intermolecular bonding and affect the tilt of the hydrocarbon chains. RDS has a structure similar to that of SDS in that, in projection down the unique axis, molecules appear in layers. The main axis of the hydrocarbon tail is oriented at angles of 1, 43, and 46° with respect to the crystallographic projection planes [ac], [bc], and [ab], respectively. It is clear that the larger rubidium ion size has caused a greater separation distance between the metal ion and the sulfate headgroups and has increased the tilt of the hydrocarbon tail. Like SDS, the structure of RDS consists of alternate polar and apolar regions, forming a bilayer-like structure. Electrostatic interactions dominate the intermolecular bonding and affect the tilt of the hydrocarbon chains. 4.4. Morphology Prediction of SDS and RDS. Table 6 gives a list of the calculated attachment energies, slice energies, surface energies, and slice shifts of the most morphologically important faces, their associated interplanar spacings (dhkl), their areas, and their percentage contribution to the total area for both systems. The aspect ratios (the maximum center to corner distance divided by the minimum center to face distance) are 103.3 for SDS and 5.8 for RDS. This demonstrates that the morphology of SDS is considerably thinner than that of RDS. Figure 4 shows the simulated crystal morphology of SDS and RDS. The predicted morphology of SDS (Figure 4a) reveals a long, thin morphology, dominated by the {100} form. The predictions in this work consider no effect of solvent



Table 6. Calculated Attachment (Eatt), Slice (Esl), and Surface (Esurf) Energies of the Most Morphologically Important Faces of SDS and RDS and Their Slice Shifts (for Maximum Slice), Corresponding Interplanar Spacings (dhkl), Areas, and Percentages of the Total Area

form

Eatt (kcal/ mol)

Esl (kcal/ mol)

{100} {110} {11-1} {011}

-0.12 -1.95 -5.99 -6.00 -4.01 -7.27 -20.65 -17.66

{001} {010} {101} {111}

Esurf slice (kcal/ shift mol) (Å)

dhkl (Å)

area (Å2)

total surface area (%)

-81.40 -79.56 -75.53 -75.52

SDS 0.01 0.01 0.03 0.03

0.00 0.00 0.00 0.00

38.6 4.7 4.1 4.1

80.8 2.0 0.2 0.7

46.6 1.2 0.1 0.4

-73.28 -70.02 -56.64 -59.63

RDS 0.08 0.03 0.09 0.06

0.00 0.00 1.15 0.00

30.5 604.8 7.4 310.2 6.9 85.1 5.2 47.6

28.9 14.8 4.1 2.3

and in an ideal situation would be compared to a vaporgrown crystal. However, attempts to obtain a vaporgrown crystal failed (due to sample decomposition40). The experimental morphology was thus obtained from an aqueous solution containing sodium citrate. The latter ensures the crystallization of the anhydrous form of SDS (see also ref 44) rather than one of its hydrated forms. The predicted morphologies reveal a pleasing similarity to the experimental morphology, although an extra face seems to be present in the experimental morphology, which is not present in the predicted morphology. We presume this to be the {001} face, but this could not be confirmed with any confidence, due to the thin nature of the crystal platelet. This could be due to the growth rate of that particular face being reduced by water molecule incorporation. Alternatively, mindful that this face is relatively small in terms of surface area,

this effect could reflect minor deficiency in the force field, which thus fails to predict this small crystal force. Overall, however, the morphology shows a good similarity to the experimental morphology with the angles between faces being in good agreement. The calculated angle between the {11-1} and {110} forms is 150.17°, and that between the {011} and {110} forms is 149.76°. These compare with experimental values of 144/142° and 147/148°, respectively, revealing acceptable agreement. The calculated crystal morphology of RDS (Figure 4b) revealed a long, platelike morphology, dominated by the {001} form. This morphology is thicker than SDS, a fact reflected in the aspect ratios given earlier. Growth perpendicular to the {010} form was also relatively slow and has a fairly large morphological importance. Both the {101} and {111} forms have relatively large attachment energies, causing fast growth perpendicular to these forms, and hence these forms have small morphological importance. The predicted morphology shows good similarity to the experimental morphology given in Figure 5. Once again, attempts to obtain a vaporgrown crystal failed due to sample decomposition, and the morphology was obtained from solution instead: i.e., recrystallized from ethanol and water. The angles between the faces of the predicted and experimental systems reveal a good correlation: the angle between the {101} and {111} forms is 93.51° for the predicted and 93 and 99° for the experimental, the angle between the {101} and {111} forms is 135.35° for the predicted and 131° and 135° for the experimental, and the angle between the {111} and {010} is 131.14° for the predicted and 136° for the experimental.

Figure 4. Predicted morphologies for three different crystal orientations based on attachment energy simulations: (a) SDS; (b) RDS.

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Figure 5. Experimental morphology of (a) SDS, projection of the {100} form, and (b) RDS, projection of the {001} form.

Figure 6. Molecular packing of (a) SDS in relation to the {100} surface and (b) RDS in relation to the {001} surface.

4.5. Correlation between Morphology and Crystal Chemistry. For SDS, Figure 6 demonstrates the molecular packing in relation to the dominant {100} form. This form dominates the morphology due to slow

growth perpendicular to this plane. The molecules are oriented almost perpendicular to the face and grow in a head-to-head and tail-to-tail manner. Consideration of the strongest intermolecular interactions present within the crystal (discussed in the previous section) allows a greater understanding of the resulting morphology. The intermolecular interactions may be split into two groups: those within the oncoming slice (i.e. contributing to the slice energy) and those involved in the attachment of the slice to the crystal (i.e. contributing to the attachment energy) for a specific face. As might be expected, the principal attractive interactions contribute to the slice energy for the {100} form. The interactions contributing to the attachment energy are the weak van der Waals interactions between the hydrocarbon tails and are the principal cause of the slow growth in this direction. For RDS, the molecular packing of the molecules perpendicular to the {101} and {111} forms is such that the growth is faster than that of the {010} and {001} forms. Figure 6 shows the molecular packing in relation to the {001} face. Examination of the intermolecular interactions contributing to the slice/attachment energies was carried out. Consideration of the strongest intermolecular interactions reveals that the most morphologically important form, {001}, had more of the principal attractive intermolecular bonds contributing to the slice energy and more of the principal repulsive intermolecular bonds contributing to the attachment energy than the least morphologically important forms {111}. The larger rubidium ion size has caused a greater separation distance between the metal ion and the sulfate headgroups and, hence, lower atom-atom in-


teraction strengths between the two ions. The larger ion has also resulted in a greater tilt angle between the hydrocarbon chains. The packing of the hydrocarbon chains is more favorable for the RDS system, resulting in a larger attachment energy for the principal face over SDS. This explains the faster growth of the principal face and hence the smaller aspect ratio of the RDS crystal over SDS. A full analysis of the strength and nature of all the interionic interactions in both SDS and RDS crystals has been given by Smith.50 5. Conclusions Refined potential parameters have been determined for RDS and SDS and the resulting intermolecular parameters used to calculate the lattice energies of these systems. Comparison of these values with the experimental “sublimation enthalpies” show reasonable agreement between the calculated and experimental values, suggesting that a certain degree of reliability can be placed on these parameters. These molecular parameters have been utilized to predict the morphology of SDS and RDS. These show agood correlation with the experimental morphologies. The intermolecular bonding within the crystal demonstrates that weak van der Waals interactions between the hydrocarbon tails has resulted in slow growth perpendicular to the principal faces of the crystal. Acknowledgment. This work, which forms part of the doctoral studies50 of L.A.S., has been supported by Unilever Research, which we are most grateful for. We also acknowledge the EPSRC for a number of research grants, resulting in provision of computer modeling facilities and associated software for our group. Glossary θ0 θ R T 0 a, b, c, R, β, γ Å A, B, C ∆Hsub aij dhkl Eatt Ecr Esl Esurf hkl i, j k2, k3, k4 kb, θ, θ0 k, n N, n, n′ q1, q2 r

equilibrium coordinate angle coordinate angle gas constant absolute temperature absolute permittivity of free space crystallographic unit cell parameters angstrom (10-10 m) empirical constants in Buckingham intermolecular potential term sublimination enthalpy empirical constant in two-body Morse intramolecular potential function interplanar lattice spacing attachment energy for crystal face (hkl) crystal lattice energy slice energy for crystal face (hkl) surface energy for crystal crystal plane Miller indices summation variables empirical constants in the two-body harmonic intramolecular potential function empirical constants in the three-body harmonic intramolecular potential function Empirical constants in the four-body torsion intramolecular potential function summation ranges for lattice energy calculation partial electronic charges on two interacting atoms interatomic interaction distance

Crystal Growth & Design, Vol. 5, No. 6, 2005 2171 r0 V Vij, Vkij Z

equilibrium interaction distance crystallographic unit cell volume potential energy of interaction number of molecules/unit cell

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CG058003G

Sodium and Rubidium Dodecyl Sulfates - American Chemical Society

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