Engineering cocrystal thermodynamic stability and eutectic points by micellar solubilization and ionization

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PAPER

Engineering cocrystal thermodynamic stability and eutectic points by micellar

solubilization and ionization†

*

ꢀ

Neal Huang and Naır Rodrıguez-Hornedo

ꢀ

Received 29th March 2011, Accepted 31st May 2011

DOI: 10.1039/c1ce05381g

Pharmaceutical cocrystals are of great interest because of their potential to enhance solubility and

bioavailability of poorly water-soluble drugs. Cocrystal development is however limited by their poor

thermodynamic stability in aqueous environments. The work presented here describes the mechanisms

by which cocrystal stability can be ﬁne-tuned via micellar solubilization and ionization of cocrystal

components. An important feature of cocrystal solution equilibria is the existence of eutectic points

involving coexistence of three phases, a liquid and two solids. The solution composition at the eutectic

points is a critical parameter that deﬁnes the conditions of thermodynamic stability. Equations that

describe the sensitivity of eutectic points and phase diagrams to micellar surfactants and pH are

presented. Predictions are in excellent agreement with the behavior of several carbamazepine cocrystals

in aqueous solutions of sodium lauryl sulfate. Increasing the magnitude of micellar solubilization for

one of the cocrystal components is found to confer greater thermodynamic stability to the cocrystal and

expand its stability region. These ﬁndings provide an unprecedented level of control over cocrystal-

solution phase behavior, and are applicable to multiple additives and solubilization mechanisms that

may be required for the stabilization of highly soluble cocrystals.

regions and to develop mathematical equations that predict

Introduction

cocrystal eutectic point behavior from experimentally accessible

thermodynamic parameters; this enables ﬁne-tuning cocrystal

phase behavior based on a mechanistic understanding of coc-

rystal solution chemistry.

The ability to engineer the thermodynamic stability of cocrystals

has important implications for the control and use of cocrystals

in various industries and for the development of drug delivery

systems in the pharmaceutical industry. Though surfactants have

been widely investigated as a means to increase the solubility of

hydrophobic drugs,^1–4we recently demonstrated that surfactants

can impart thermodynamic stability to cocrystals relative to drug

crystal, and this behavior is dependent on surfactant concen-

tration and pH.^5–7Surfactants that have differential afﬁnities for

cocrystal components have the potential to reverse the thermo-

dynamic stabilities of cocrystal and its components at a surfac-

tant concentration called the critical stabilization concentration

(CSC). The underlying mechanism for the CSC is the enrichment

of the aqueous phase with the most soluble component

(i.e. coformer) as the least soluble cocrystal component (i.e. drug)

is preferentially solubilized by the micelles. A model was devel-

oped that explained cocrystal solubility, CSC, and pH_maxbased

on cocrystal dissociation, component ionization, and micellar

solubilization equilibria.⁷

Eutectic points, also referred to as transition concentrations,

offer an experimentally accessible method to assess cocrystal

solubility and stability regardless of the solubility relationship

between cocrystal and drug.^5,8,9A cocrystal eutectic point is

a point where two solids (one of which is cocrystal) and a solu-

tion coexist in equilibrium.

The solution conditions that favor transformation from co-

crystal to drug (and vice versa) can be quantiﬁed by examining

the solution concentrations of drug and coformer at the eutectic

point as a function of micellar surfactant at a given temperature

and pH. Equations are developed that describe the eutectic

concentrations of drug and coformer in micellar solutions by

considering the equilibria of the partitioning of drug and

coformer between aqueous and micellar pseudophases. The

eutectic concentrations of drug and coformer in micellar solu-

tions are a function of their respective eutectic concentrations in

pure water (or submicellar surfactant concentrations), compo-

nent pK_a(s), solution pH, and K_sfor the individual cocrystal

components.

The purpose of this work is to understand the role of micellar

solubilization and ionization in altering cocrystal stability

A eutectic constant K_eu(ratio of coformer to drug concen-

tration at the eutectic) can be calculated that describes cocrystal

thermodynamic stability relative to drug.¹⁰Eutectic constants are

commonly applied to mixtures of racemic compounds with

Department of Pharmaceutical Sciences, University of Michigan, Ann

Arbor, MI, 48109. E-mail: nrh@umich.edu; Tel: +1-734-763-0101

† Electronic supplementary information (ESI) available. See DOI:

10.1039/c1ce05381g

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enantiomer and were recently adapted to other cocrystal

systems.^11,12This work extends the theoretical framework for

eutectic points and K_euto micellar systems and demonstrates for

the ﬁrst time their ability to tailor regions of stability according

to ionization and micellar solubilization equilibria.

For a 1 : 1 cocrystal RHA whose components are R (non-

ionizable drug) and HA (monoprotic, weakly acidic coformer),

E₁is described by

RHA_solid+ R_solid# R_aq+ HA_aq

(1)

Model equations are derived for cocrystals of CBZ (non-

ionizable, hydrophobic drug) with several ionization properties

and stoichiometries. These cocrystals include 1 : 1 carbamaze-

pine-salicylic acid (CBZ-SLC), 1 : 1 carbamazepine-saccharin

(CBZ-SAC), 2 : 1 carbamazepine-succinic acid (CBZ-SUC), and

2 : 1 carbamazepine-4-aminobenzoic acid monohydrate (CBZ-

4ABA-HYD). Salicylic acid and saccharin are monoprotic weak

acids; salicylic acid has a reported pK_aof 3.0, saccharin has

a range of reported pK_avalues between 1.8 and 2.2.^13–15Succinic

acid is a diprotic weak acid with pK_avalues of of 4.1 and 5.6.¹⁶

4-aminobenzoic acid is amphoteric with pK_avalues of 2.6

and 4.8.¹⁷

and E₂by

RHA_solid+ HA_solid# R_aq+ HA_aq

(2)

The solution phase equilibria that govern cocrystal solubility are

given by

K_sp

RHA_solid

* R_aqþ HA_aq

(3)

(4)

(5)

(6)

(7)

)

K^H_a^A

HA_aq

* A^ꢀþ H^þ

)

aq

K_s^R

R_aqþ M

* R_m

)

Theoretical

K^H_s^A

HA_aqþ M

* HA_m

The work presented here develops a mathematical model to

predict the dependence of cocrystal eutectic points on ionization

and micellar solubilization. This identiﬁes the solution condi-

tions where cocrystal is thermodynamically stable by considering

the partitioning of drug and coformer into micelles. It is based on

relatively simple solution phase equilibria and equilibrium

constants for the cocrystal components that are experimentally

accessible or available in the literature. A quantitative model for

cocrystal solubility was presented previously and demonstrated

that cocrystal solubility relative to drug crystal varies as a func-

tion of surfactant concentration.⁷Knowledge of cocrystal

eutectic points is of critical importance during cocrystal

synthesis, processing, and performance.

K^A_s^ꢀ

A^ꢀþ M

* A^ꢀ

m

aq

where aq refers to aqueous and m refers to micellar. K_spis the

cocrystal solubility product. K_ais the acid dissociation constant.

M is micellar surfactant. K_s^R, K_s^HA, and K_s^Aꢀare the micellar

solubilization constants for R, HA, and A^ꢀrespectively. For the

sake of simplicity this model assumes no solution complexation

between drug and coformer, though theoretical treatments of

such equilibria have been addressed elsewhere.^10,18,19

The equilibrium constants that describe eqn (3)–(7) are given

by

K_sp¼ [R]_aq[HA]_aq

(8)

(9)

½A^ꢀꢁ ½H^þꢁ

aq

K^H_a^A

¼

Cocrystal eutectic point dependence on micellar solubilization

½HAꢁ

aq

Eutectic points as critical indicators of cocrystal solubility have

been discussed thoroughly elsewhere.^5,8The solution composi-

tion at the eutectic is independent of the mass of each phase at

equilibrium, which has several important features: (1) indicates

the thermodynamic stability of cocrystal relative to drug crystal,

(2) enables estimation of cocrystal solubility in solution

compositions where cocrystal is unstable, and (3) provides

insight into solute-solute or solute–solvent interactions between

drug, coformer, and solvent.

½Rꢁ

aq

K_s^R

¼

(10)

(11)

(12)

m

½Rꢁ ½Mꢁ

½HAꢁ

aq

K^H_s^A

m

½HAꢁ ½Mꢁ

½A^ꢀꢁ

aq

ꢀ

K_s^A

m

½A^ꢀꢁ ½Mꢁ

At least two eutectic points exist for a cocrystal, which are

differentiated by the phases at equilibrium. E₁refers to the

eutectic between solid drug, cocrystal, and solution, and E₂refers

to the eutectic between solid coformer, cocrystal, and solution.

Other eutectic points have been reported in the literature, such as

between cocrystals of different stoichiometry.⁹The focus of this

work is on E₁, which is of particular importance to cocrystals of

poorly soluble drugs in aqueous solutions because it describes the

conditions under which a cocrystal can transform to a less

soluble crystalline drug form. The analyses presented here can be

generalized to other solubilization mechanisms such as mixed

micelles or complexation, though the equations may be of

a different nature.

where brackets refer to concentrations with recognition that

under dilute solution conditions they approximate activities. K_s

and K_avalues are assumed to be independent of solution

composition.

Total cocrystal solubility S_RHA,T, in terms of the total drug

concentration at equilibrium [R]_T, is given by the sum of aqueous

and micellar drug in solution,

S_RHA,T¼ [R]_T¼ [R]_aq+ [R]_m

(13)

By considering the equilibrium constants in eqn (8) and (10), eqn

(13) becomes

5410 | CrystEngComm, 2011, 13, 5409–5422

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ꢀ

ꢁ

K_sp

K^H_a^A

½H^þꢁ

þ K^H_s^A½Mꢁ

(23)

½Rꢁ ¼

ð1 þ K^R_s½MꢁÞ

(14)

½Aꢁ

¼

1 þ

T

eu;T

½HAꢁ

S_R;aq

aq

The mass balance on coformer is given by

[A]_T¼ [HA]_aq+ [A^ꢀ]_aq+ [HA]_m+ [A^ꢀ]_m

Substituting eqn (9), (11) and (12) into (15),

Cocrystal stoichiometric solubility can be related to the eutectic

solution concentrations of drug and coformer by combining eqn

(19), (22), and (23) to give

(15)

(16)

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

S_RHA;Tꢂ ¼ ½Rꢁ ½Aꢁ

(24)

eu;T

ꢀ

ꢁ

K^H_a^A

½H^þꢁ

ꢀ

þ K^H_s^A½Mꢁ þ

K^A_s½Mꢁ

Eqn (24) is speciﬁc to cocrystal stoichiometry (1 : 1) but general

for ionization and micellar solubilization properties. For a 2 : 1

cocrystal (e.g. R₂H₂A with drug R and diprotic acid H₂A),

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

½Aꢁ ¼ ½HAꢁ 1 þ

½H^þꢁ

Combining eqn (14) and (16),

T

aq

S_RHA;T¼ ½Rꢁ

½Rꢁ ½Aꢁ

T

eu;T

S_{R H A;T}ꢂ ¼

(25)

2

ꢀ

ꢁ

4

K^H_a^A

½H^þꢁ

K^H_a^A

½H^þꢁ

ꢀ

K_sp

¼

ð1 þ K^R_s½MꢁÞ 1 þ

þ K^H_s^A½Mꢁ þ

K^A_s½Mꢁ (17)

[R]_eu,Tand [A]_eu,Tat a chosen [H⁺] (denoted by [H⁺]_T) can be

rewritten in terms of the drug and coformer concentrations and

[H⁺] at the eutectic in water (denoted by [R]_eu,aq, [A]_eu,aq, and

[H⁺]_aq). Thus

½Aꢁ

T

If the ionized species interacts more favorably with the aqueous

environment than the micellar environment such that K_s^HA

K_s^Aꢀ, eqn (17) can be simpliﬁed to

[

[R]_eu,T¼ [R]_eu,aq(1 + K^R_s[M])

(26)

(27)

ꢀ

ꢁ

K_sp

K^H_a^A

½H^þꢁ

S_RHA;T¼ ½Rꢁ ¼

ð1 þ K^R_s½MꢁÞ 1 þ

þ K^H_s^A½Mꢁ (18)

0

1

T

K^H_a^A

½Aꢁ

T

1 þ

þ K^H_s^A½Mꢁ

K^H_a^A

B

@

C

A

½H^þꢁ

T

unless the ionized species is present at very high

concentrations.^20,21

½Aꢁ

¼ ½Aꢁ

eu;T

eu;aq

1 þ

½H^þꢁ

The total cocrystal solubility in a solution of stoichiometric

concentrations of drug and coformer (S_RHA,T*), is a special case

of eqn (18) when [R]_T¼ [A]_T,

aq

Eqn (26) and (27) show that the full dependence of the cocrystal

eutectic point on pH and surfactant concentration can be

calculated from a eutectic point measurement in water at a single

pH, provided K_sand K_afor the cocrystal components are

known. Eutectic concentrations of drug and coformer for co-

crystals of different stoichiometries and ionization properties are

shown in Table 1.

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ꢀ

ꢁ

K^H_a^A

½H^þꢁ

S_RHA;Tꢂ ¼ K_spð1 þ K^R_s½MꢁÞ 1 þ

þ K^H_s^A½Mꢁ

(19)

A detailed discussion of micellar solubilization and ionization

effects on cocrystal stoichiometric solubilities was presented

previously.^5,7

Fig. 1 shows the predicted dependence of drug and coformer

eutectic concentrations on surfactant concentration for a co-

crystal RHA according to eqn (26) and (27). Different depen-

dencies of [R]_eu,Tand [A]_eu,Ton surfactant concentration are

a consequence of differential solubilization of the cocrystal

components (K_s^R[ K_s^HA). The surfactant concentration

where [R]_eu,T¼ [A]_eu,Tindicates the critical stabilization

concentration (CSC) for cocrystal RHA. At the CSC, a liquid

phase of equal molar ratio as the cocrystal is necessary for

cocrystal to be thermodynamically stable. At the CSC for

a 2 : 1 cocrystal, 0.5[R]_eu,T¼ [A]_eu,T. Drug-rich stoichiometries

require more drug to be solubilized by the micelles to achieve

the coformer enrichment in the aqueous phase that is respon-

sible for the CSC.

At eutectic point E₁the solution is saturated with drug and

cocrystal. E₁is characterized by the solution concentrations of

drug and coformer and is another special case of eqn (18)

when [R]_T¼ S_R,T. The concentration of drug at the eutectic

point, [R]_eu,T, is given by

[R]_eu,T¼ S_R,T

(20)

where S_R,Tis the solubility of drug R in the eutectic micellar

solution. Assuming that the coformer does not affect the solu-

bilization mechanisms of drug (and vice versa), then S_R,Tis

simply the solubility of the drug R in a micellar solution.

The inﬂuence of micellar surfactant concentration on solubi-

lization of hydrophobic drugs is well documented in the litera-

ture and is given by

Though E₂is less discussed in the pharmaceutical cocrystal

literature than other eutectic points, similar methods can be

used to calculate its dependence on surfactant concentration

from eqn (18). At E₂, eqn (20) no longer applies because drug

crystal is not one of the solid phases at equilibrium. Instead,

the relevant solution condition at E₂is that the total coformer

concentration at the eutectic [A]_eu,Tis equal to the total

solubility of the coformer in the eutectic micellar solution

S_R,T¼ S_R,aq(1 + K^R_s[M])

(21)

where S_R,aqis the aqueous solubility of drug R.^1–4,22,23Therefore,

by combining eqn (20) and (21),

[R]_eu,T¼ S_R,aq(1 + K^R_s[M])

(22)

S_A,T

,

The total concentration of coformer at the eutectic point,

[A]_eu,T, is obtained by combining eqn (18) and (22).

[A]_eu,T¼ S_A,T

(28)

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Table 1 Equations that describe drug and coformer eutectic concentrations in micellar solutions at [H⁺]_T, in terms of drug and coformer eutectic

concentrations in pure water at [H⁺]_aq, K_aand K_sof the cocrystal components, and micellar surfactant concentration [M]^a

Drug

eutectic concentration

Coformer

eutectic concentration

Cocrystal

Eqn

(26)

Eqn

(27)

0

1

RHA 1 : 1

nonionizable :

monoprotic

acidic

K_a

½H^þꢁ_T

1 þ

þ K^H_s^A½Mꢁ

K_a

B

C

A

B

[R]_eu,T¼ [R]_eu,aq(1 + K^R_s[M])

½Aꢁ_eu;T¼ ½Aꢁ_eu;aq

B

@

0

1 þ

½H^þꢁ_aq

0

1

HXHA 1 : 1

monoprotic

acidic :

monoprotic

acidic

(32)

(34)

(36)

(38)

(33)

(35)

(37)

(39)

K^H_a^X

½H^þꢁ_T

K^H_a^A

½H^þꢁ_T

1 þ

þ K^H_s^X½Mꢁ

K^H_a^X

½H^þꢁ_aq

1 þ

þ K^H_s^A½Mꢁ

K^H_a^A

B

C

A

B

C

A

B

½Xꢁ_eu;T¼ ½Xꢁ_eu;aq

B

½Aꢁ_eu;T¼ ½Aꢁ_eu;aq

B

@

0

1 þ

½H^þꢁ_aq

1

0

1

BHA 1 : 1

½H^þꢁ_T

K^H_a^A

½H^þꢁ_T

monoprotic basic

: monoprotic

acidic

1 þ

þ K^B_s½Mꢁ

1 þ

þ K^H_s^A½Mꢁ

K^H_a^A

B

C

A

B

@

C

A

K_a^B

B

½Bꢁ_eu;T¼ ½Bꢁ_eu;aq

B

½Aꢁ_eu;T¼ ½Aꢁ_eu;aq

B

½H^þꢁ_aq

@

0

1 þ

K_a^B

½H^þꢁ_aq

1

HA^ꢀ

R₂H₂A 2 : 1

nonionizable :

diprotic acidic

K^H_a^AK^H_a^A

K

2

1 þ

þ

K^H_s^A½Mꢁ

a

2

B

C

A

B

½H^þꢁ_T

B

½Aꢁ_eu;T¼ ½Aꢁ_eu;aq

B

[R]_eu,T¼ [R]_eu,aq(1 + K^R_s[M])

HA^ꢀ

K^H_a^A

½H^þꢁ_aq

K^H_a^A

K

2

@

0

a

1 þ

þ

2

½H^þꢁ_aq

1

R₂HAB 2 : 1

nonionizable :

amphoteric

½H^þꢁ_T

K^H_a^AB

1 þ

þ

K^H_s^AB½Mꢁ

B

@

C

A

H₂AB^þ

a

½H^þꢁ_T

K

[R]_eu,T¼ [R]_eu,aq(1 + K^R_s[M])

½ABꢁ_eu;T¼ ½ABꢁ_eu;aq

½H^þꢁ_aq

K^H_a^AB

½H^þꢁ_aq

1 þ

þ

H₂AB^þ

a

K

a

Subscript aq refers to values measured in submicellar concentrations of surfactant.

Assuming the solubilization mechanisms of drug and coformer

are mutually independent, then S_A,Tis equal to the total solu-

bility of the coformer in micellar solution.

Eutectic constant K_eu

For a cocrystal RHA, at constant temperature and pH, K_euis

deﬁned as

ꢀ

ꢁ

K^H_a^A

½H^þꢁ

þ K^H_s^A½Mꢁ

(29)

a_A;eu

S_A;T¼ S_HA;aq1 þ

K_euh

(40)

a_R;eu

where S_HA,aqis the intrinsic solubility of the weakly acidic

coformer. Eqn (28) and (29) combine to give

where a_A,euand a_R,euare the activities of coformer and drug in

solution at the eutectic point. Eutectic constants have been dis-

cussed in the literature concerning enantiomeric puriﬁcation and

stability of racemic compounds but were recently applied to

cocrystal systems.^10–12

ꢀ

ꢁ

K^H_a^A

½Aꢁ

¼ S_HA;aq1 þ

þ K^H_s^A½Mꢁ

(30)

½H^þꢁ

Substituting (30) into (18) gives [R]_eu,Tat E₂.

eu;T

K_euin the context of cocrystals has been shown to describe

cocrystal thermodynamic stability relative to drug.¹⁰K_euis

determined under equilibrium conditions, though it is not a true

equilibrium constant (such as eqn (3)–(7)). Assuming dilute

conditions where concentrations replace activities,

K_sp

½Rꢁ

¼

ð1 þ K^R_s½MꢁÞ

(31)

eu;T

S_HA;aq

If eqn (30) and (31) are rewritten in terms of [R]_eu,aqand

[A]_eu,aqat E₂, then the same equations as (26) and (27)

are obtained. Thus, eqn (26) and (27) apply to both E₁

and E₂.

½Aꢁ

½Rꢁ

eu;T

K_eu

¼

(41)

eu;T

5412 | CrystEngComm, 2011, 13, 5409–5422

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0

1

K_a

½H^þꢁ

1 þ

ꢀ

ꢁ

1 þ

þ K^H_s^A½Mꢁ

K_a

B

@

C

A

1

T

K_eu;T¼ K_eu;aq

(45)

1 þ K^R_s½Mꢁ

½H^þꢁ

aq

where K_eu,aq¼ [R]_eu,aq/[A]_eu,aq, or the K_euof the cocrystal in

water at [H⁺]_aq. Eqn (45) predicts that K_eu,Tcan either increase or

decrease (as does the cocrystal to drug solubility ratio) as

a function of surfactant concentration, depending on K_s^Rand

K_s^HA

.

Fig. 2 shows the dependence of the cocrystal to drug solubility

ratio and K_eu,Ton surfactant concentration in the absence of

ionization effects. The parameter values used in this simulation

are typical of cocrystals of hydrophobic drugs such as CBZ.

Fig. 2 shows that if the reduction in K_eu,Tis sufﬁcient, a CSC

exists where K_eu,T¼ 1. Equations that describe CSC as a func-

tion of K_euare discussed in a subsequent section. It is notable

that micellar solubilization is most effective in reducing the

cocrystal to drug solubility ratio at surfactant concentrations

very close to the CMC. Therefore, consideration of K_eu,Tplays

an important role in micellar solutions even at surfactant

concentrations far below the CSC.

Fig. 1 Eutectic concentrations of drug ([R]_eu,T) and coformer ([A]_eu,T) as

a function of surfactant concentration under nonionizing conditions.

Predicted according to eqn (26) and (27) for cocrystal RHA at eutectic

point E₁. The CSC for a 1 : 1 cocrystal is given by the surfactant

concentration where [R]_eu,T¼ [A]_eu,T. K_sp¼ 1 mM²(S_RHA,aq/S_R,aq¼ 5),

[R]_eu,aq¼ 0.2 mM, [A]_eu,aq¼ 5 mM, K_s^R¼ 1 mM^ꢀ1, K_s^HA¼ 0, CMC ¼

8 mM.

K

_eu,Tdepends on two main factors: cocrystal solubility relative

to drug in water (calculated from K_eu,aq) and micellar solubili-

zation of cocrystal components (K_s^Rand K_s^HA). Fig. 3 shows the

predicted inﬂuence of cocrystal aqueous solubility and K_s^Ron

K

_eu,Tand the cocrystal to drug solubility ratio according to eqn

K_eucan be related to the ratio of cocrystal stoichiometric

solubility to drug solubility. This can be accomplished when

(43) and (45). Fig. 3 shows that (1) cocrystals with higher

aqueous solubilities relative to drug, or larger K_eu,aq, require

higher surfactant concentrations to achieve the CSC, (2) co-

crystals with high K_s^Rrequire lower surfactant concentrations

to achieve the CSC, and (3) cocrystals highly soluble relative to

drug and/or have high K_s^Rvalues are the most susceptible to

[R]_eu,T¼ S_R,T¼ [R]_aq+ [R]_mand [A]_eu,T¼ [HA]_aq+ [A^ꢀ]_aq

+

[HA]_m+ [A^ꢀ]_m, indicating that ionization and micellar solubi-

lization are the only mechanisms of solubilization. For a 1 : 1

cocrystal (e.g. RHA) eqn (22) and (23) can be substituted into

(41) to yield

0

1

K^H_a^A

1 þ

þ K^H_s^A½Mꢁ

B

C

A

½H^þꢁ

K_{sp B}

K_eu

¼

(42)

B

1 þ K^R_s½Mꢁ

2

@

Eqn (42) can be combined with (19)–(21),

S_R;aq

ꢀ

ꢁ

2

S_RHA;T

S_R;T

ꢂ

K_eu

¼

(43)

which relates K_euto the cocrystal to drug solubility ratio. For

a 2 : 1 cocrystal (e.g. R₂H₂A),

ꢀ

ꢁ

3

1 S_{R H A;T}

ꢂ

2

K_eu

¼

(44)

2

S_R;T

where S_{R H A,T}* is cocrystal R₂H₂A solubility under stoichio-

2

metric conditions in terms of drug concentration.

K_eu# 1 indicates that cocrystal is thermodynamically stable in

stoichiometric solutions of drug and coformer. Likewise, 2 : 1

cocrystals achieve thermodynamic stability at K_eu# 0.5. The

surfactant concentration and pH that achieve K_eu¼ 1 for a 1 : 1

cocrystal (K_eu¼ 0.5 for a 2 : 1 cocrystal) are the CSC and pH_max

respectively.

Fig. 2 Dependence of cocrystal to drug solubility ratio and K_euon

surfactant concentration according to eqn (43) and (45) for a 1 : 1 co-

crystal RHA. K_eu,Tdecreases as surfactant concentration increases,

indicating that the cocrystal to drug solubility ratio is decreasing. CSC

can be estimated from K_eu,aqand K_sfor the cocrystal components.

Simulated under nonionizing conditions, with no interactions beyond

micellar solubilization. K_sp¼ 1 mM², K_eu,aq¼ 25 (S_RHA,aq/S_R,aq¼ 5),

S_R,aq¼ 0.2 mM, K_s^R¼ 1 mM^ꢀ1, K_s^HA¼ 0, and CMC ¼ 8 mM.

K_euin micellar solutions (K_eu,T) at [H⁺]_Tcan be expressed in

terms of K_eumeasured in pure water (K_eu,aq) at [H⁺]_aq

.

Combining eqn (26), (27) and (41),

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Fig. 3 Inﬂuence of cocrystal aqueous solubility and micellar solubilization on K_eu,Tand CSC. (a) impact of cocrystal aqueous solubility (K_eu,aq¼ 4 and

25) when drug solubilization is constant (K_s^R¼ 1 mM^ꢀ1), (b) impact of drug solubilization (K_s^R¼ 1 and 5 mM^ꢀ1) when cocrystal aqueous solubility is

constant (K_eu,aq¼ 25). Curves generated according to eqn (43) and (45) for a 1 : 1 cocrystal RHA with K_s^HA¼ 0, CMC ¼ 8 mM.

changes in K_eu,Tin small concentrations of micellar surfactant.

Changes in K_eu,aq(Fig. 3(a)) can be the result of pH or selection

of a different coformer whose cocrystal is more soluble. Changes

in K_s^R(Fig. 3(b)) can be achieved by surfactant selection.

Fig. 4 shows the predicted K_eu,Tdependence on total surfac-

tant concentration and pH for cocrystal RHA according to eqn

(45), where a cross-section at constant pH is represented by

Fig. 2. K_eu,Tincreases as a function of pH (which is a conse-

quence of K_eu,aqincreasing) and decreases as a function of

surfactant concentration. The intersection of surfaces indicates

the CSC and pH_max, or the surfactant concentrations and pHs

where the cocrystal stoichiometric solubility is equal to the drug

solubility. Together, the CSC and pH_maxvalues identify the

solution conditions where cocrystal and drug are the thermo-

dymically stable phases. Solving eqn (45) for [M] when K_eu,T¼ 1

gives the micellar surfactant concentration at the CSC. Thus, the

CSC at [H⁺]_T(in this case, [H⁺]_T¼ [H⁺]_max) for a 1 : 1 cocrystal

RHA can be written in terms of K_eu,aqat [H⁺]_aq, and is given by

0

1

K^H_a^A

1 þ

B

C

½H^þꢁ

T

K_eu;aq

ꢀ 1

B

@

C

A

K^H_a^A

½H^þꢁ

aq

CSC ¼

þ CMC

(46)

K_eu;aqK^H_s^A

R

!

K_sꢀ

K^H_a^A

1 þ

½H^þꢁ

aq

When K_s^R[ K_s^HA, which is typical for hydrophobic drugs and

hydrophilic coformers, and the pH in micellar solution and water

are equal ([H⁺]_T¼ [H⁺]_aq), eqn (46) simpliﬁes to

K_eu;aqꢀ 1

CSC ¼

þ CMC

(47)

K_s^R

K_eu,aqand [H⁺]_aqalso refer to values in solutions of submicellar

surfactant concentrations. Equations that predict K_eu,Tand CSC

at [H⁺]_Tfrom measurement of K_eu,aqat [H⁺]_aqfor cocrystals of

different stoichiometry and ionization properties are presented in

Table 2.

Effect of micellar solubilization on cocrystal phase stability

regions

Micellar solubilization has the ability to shift the regions of

cocrystal stability by differentially solubilizing drug relative to

coformer. The presented model allows prediction of such

changes in the phase diagram via the eutectic points. Fig. 5

illustrates how differential solubilization of cocrystal compo-

nents results in a shift in the cocrystal stability region. The points

designated by E₁and E₂are the cocrystal eutectic points that

Fig. 4 Dependence of K_eu,Ton total surfactant concentration and pH.

Multicolored surface represents K_eu,Tfor a cocrystal RHA according to

eqn (45). Yellow surface represents K_eu,T¼ 1, where cocrystal and drug

are equally soluble. The intersection points indicate CSC and pH_max

,

values that describe the conditions where cocrystal and drug are ther-

modynamically stable without excess of either component in solution.

K_eu,aq(pH 1.0) ¼ 4, pK_a¼ 3.0, K_s^R¼ 1 mM^ꢀ1, and CMC ¼ 8 mM.

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identify the range of solution compositions where cocrystal is

stable in water (subscript aq) and in a micellar solution (subscript

T). Line E_1,aq-E_1,T, which is generated according to eqn (26) and

(27), shows that increasing surfactant concentration leads to the

eutectic point E₁becoming more enriched with drug.

At the CSC, the eutectic point E₁intersects the stoichiometric

composition line, indicating that RHA becomes congruently

saturating. This shows that a system that is incongruently satu-

rating in pure water can achieve congruent saturation in micellar

solutions. Fig. 5 shows that micellar solubilization can shift or

even widen the range of solution compositions where cocrystal is

the thermodynamically stable phase.

E₂, like E₁, becomes more enriched with drug at the eutectic as

a function of surfactant concentration due to the differential

solubilization of drug over coformer. Eqn (26) and (27) are

applicable to both E₁and E₂. E₁is governed by the drug solu-

bility (eqn (21)) and E₂by the coformer solubility (eqn (29)). In

principle micellar solubilization can cause E₂to intersect the

stoichiometric composition line at a certain concentration of

surfactant, which causes an otherwise congruently saturating

cocrystal to become incongruently saturating. In instances where

micellar solubilization is highly differential in favor of drug, the

concentrations of surfactant required to destabilize a congru-

ently saturating cocrystal may not be experimentally achievable.

Fig. 5 illustrates a simple system where only one cocrystal

stoichiometry exists. The solid phase(s) at equilibrium (cocrystal,

drug, or coformer) is controlled by how E₁and E₂respond to

micellar solubilization. Cocrystal systems that have more than

one stoichiometry can have multiple CSCs, which describe the

conditions where each cocrystal stoichiometry becomes

Fig. 5 Schematic triangular phase diagram of cocrystal RHA and its

components illustrating the inﬂuence of micellar solubilization on

eutectic points and phase stability regions. Differential solubilization of

R results in the solution composition at the eutectic becoming enriched

with drug as surfactant concentration increases. Cocrystals that are

incongruently saturating in the absence of micelles can become congru-

ently saturating in micellar solutions. Dotted line indicates stoichiometric

ratio of cocrystal components.

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congruently saturating. Cocrystals of different stoichiometry are

inﬂuenced differently by the micelles, such that more drug-rich

stoichiometries are solubilized to a much greater extent than

coformer-rich stoichiometries. As such, the eutectic point

between cocrystals of different stoichiometries is expected to

change as a result of micellar solubilization. Our mathematical

models indicate that coformer-rich stoichiometries become more

thermodynamically favorable than drug rich stoichiometries as

surfactant concentration increases (provided drug is preferen-

tially solubilized relative to coformer). Therefore, micellar solu-

bilization can be a tool not only to thermodynamically stabilize

cocrystals but also to select conditions where a particular stoi-

chiometry is favorable.

methanol and 45% water with 0.1% triﬂuoroacetic acid and the

ﬂow rate was 1 mL min^ꢀ1using an isocratic method. Injection

sample volume was 20 or 40 mL. Absorbance of CBZ, SAC, SLC,

SUC, and 4ABA was monitored at 284, 260, 303, 230, and 284

nm, respectively.

X-ray powder diffraction (XRPD)

XRPD diffractograms of solid phases were collected with

a benchtop Rigaku Miniﬂex X-ray diffractometer (Danvers,

ꢁ

MA) using Cu-Ka radiation (l ¼ 1.54 A), a tube voltage of 30

kV, and a tube current of 15 mA. Data were collected from 5 to

40^ꢃat a continuous scan rate of 2.5^ꢃmin^ꢀ1

.

Results

Materials and methods

The model equations presented above predict the dependence of

cocrystal eutectic points on micellar solubilization, which iden-

tiﬁes and enables engineering of the solution compositions where

cocrystal is thermodynamically stable. Eutectic concentrations of

drug and coformer at E₁in micellar solutions are predicted from

eutectic concentrations in water, K_aand K_svalues for the co-

crystal components, solution pH, and surfactant CMC. The

work discussed here focuses on E₁(solid phases at equilibrium

are CBZ cocrystal, CBZD, and solution) because it is the relevant

eutectic point in aqueous media, since it describes the cocrystal

tendency to transform to the less soluble drug. The concepts

discussed in the context of E₁are relevant to other eutectic

points, but E₁better addresses the challenges of cocrystals whose

purpose is to increase the solubility of a hydrophobic drug.

However, consideration of all eutectic points in a cocrystal

system is necessary for complete understanding of the phase

diagram and control of crystallization outcomes.

Materials

Anhydrous monoclinic carbamazepine (CBZ(III); lot no.

057K11612 USP grade) was purchased from Sigma Chemical

Company (St. Louis, MO), stored at 5 ^ꢃC over anhydrous

calcium sulfate and used as received. Salicylic acid (SLC; lot no.

09004LH), saccharin (SAC; lot no. 03111DD), succinic acid

(SUC; lot no. 037K0021), 4-aminobenzoic acid (4ABA; lot no.

068K0698), and sodium lauryl sulfate (SLS; lot no. 104H0667)

were purchased from Sigma Chemical Company (St. Louis, MO)

and used as received. Water used in this study was ﬁltered

through a double deionized puriﬁcation system (Milli Q Plus

Water System from Millipore Co., Bedford, MA).

Cocrystal synthesis

Cocrystals were prepared by the reaction crystallization method

at room temperature by adding CBZ to nearly saturated solu-

tions of coformer.²⁴CBZ-SLC was prepared in acetonitrile,

CBZ-SAC and CBZ-SUC were prepared in ethanol, and CBZ-

4ABA-HYD was prepared in water. CBZ dihydrate (CBZD), the

most stable form of CBZ in water, was prepared from anhydrous

CBZ in water. Solid phases were characterized by XRPD.

The predictions are evaluated for a series of CBZ cocrystals of

different stoichiometries and ionization properties in aqueous

solutions. The cocrystals include 1 : 1 cocrystals with monop-

rotic acids (CBZ-SLC and CBZ-SAC) and 2 : 1 cocrystals with

a diprotic acid (CBZ-SUC) and an amphoteric coformer (CBZ-

4ABA-HYD). The cocrystal stoichiometric solubilities in pure

water were reported previously, and ranged from 1.32 mM for

CBZ-SLC at pH 3.0 to 2.38 mM for CBZ-SUC at pH 3.1 (in

terms of CBZ concentration), or 2.5 to 4.5-fold the aqueous

solubility of CBZD (0.53 mM).^7,25

Measurement of cocrystal eutectic points

Cocrystal eutectic points were mea_ꢃsured as a function of SLS

concentration in water at 25 ꢄ 0.1 C. A detailed discussion of

eutectic point measurements has been discussed elsewhere.^8,1050–

100 mg of cocrystal and 25–50 mg of CBZD were suspended in 3

mL of aqueous SLS solution up to 3 days. pH at equilibrium was

measured but not independently modiﬁed. Cocrystal stoichio-

metric solubilities were determined from eqn (43) and (44). Drug

and coformer concentrations were analyzed by HPLC. Solid

phases at equilibrium were conﬁrmed by XRPD.

pH was not independently adjusted for the studies presented

here but the pH of the eutectic solutions at equilibrium were

measured. pH varied by less than 0.2 units between eutectics

measured in water and in SLS solutions.

Drug and coformer eutectic concentration dependence on SLS

concentration

Fig. 6 shows the solution concentrations of drug and coformer at

the eutectic point E₁as a function of SLS concentration for the

CBZ cocrystals. Fig. 6 shows that drug and coformer concen-

trations increase at different rates with respect to SLS concen-

tration. The CBZ eutectic concentration has a faster rate of

increase than the coformer with respect to SLS concentration,

such that there is a reversal in the relative eutectic concentrations

from coformer-rich in low surfactant concentrations to drug-rich

in high surfactant concentrations. This is in agreement with

High performance liquid chromatography (HPLC)

The solution concentrations of CBZ and coformer were analyzed

by Waters HPLC (Milford, MA) equipped with a UV/vis spec-

trometer detector. Waters’ operation software, Empower 2, was

used to collect and process the data. A C18 Thermo Electron

Corporation column (5 mm, 250 ꢅ 4.6 mm) at ambient temper-

ature (24 ^ꢃC) was used. The mobile phase was composed of 55%

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and vice versa. This ﬁnding is supported by Fig. 8, which

compares the CBZD solubilities at the eutectic and in the absence

of coformer as a function of SLS concentration. The excellent

agreement between CBZ eutectic concentrations and CBZD

solubilities in Fig. 8 shows that the coformers had minimal

impact on the solubilization of CBZ.

The CMC value of 6 mM SLS for CBZ-SAC, CBZ-4ABA-

HYD, and CBZ-SUC are in good agreement with reported CMC

of SLS in saturated CBZ solutions (5.3 mM SLS²⁵). CBZ-SLC

has a CMC value of 8 mM. Our previous cocrystal solubility

studies indicate that SLC exhibits a weak effect on the CMC of

SLS in saturated CBZ solutions, which was reported as 9 mM

SLS.⁷In these studies the magnitude of the changes in CMC as

a result of solutes and solution conditions are generally small

relative to the total surfactant concentrations.

When drug, coformer, and surfactant exhibit solution inter-

actions that affect ionization or micellar solubilization, using

parameters measured for the separate components (K_a, K_s, and

CMC) in the model equations may not be justiﬁed. If necessary,

more rigorous expressions that describe the thermodynamic

parameters as a function of solute and surfactant concentration

may be substituted in place of a constant value.

The CSC can be calculated from the eutectic concentrations of

drug and coformer as a function of SLS concentration in Fig. 7

where the molar ratios of drug and coformer at E₁are equal to

the cocrystal stoichiometry. The CSC indicates the minimum

surfactant concentration such that no excess coformer in solu-

tion is required for the cocrystal to be thermodynamically stable,

thereby creating unfavorable conditions for cocrystal to trans-

form to drug. The CSCs for the 1 : 1 cocrystals CBZ-SLC and

CBZ-SAC are indicated by the surfactant concentration where

[drug]_eu¼ [coformer]_eu, illustrated by the intersection of the drug

and coformer eutectic concentration dependencies. For the 2 : 1

cocrystals CBZ-4ABA-HYD and CBZ-SUC, 0.5[drug]_eu

[coformer]_euat the CSC.

¼

K_eudependence on SLS concentration

Fig. 6 Dependence of eutectic concentrations of CBZ and coformer on

SLS concentration in aqueous solutions. Solid phases at equilibrium are

CBZ cocrystal and CBZD. (a) CBZ-SLC pH 3.0 (b) CBZ-SAC pH 2.2 (c)

CBZ-4ABA-HYD pH 4.0 (d) CBZ-SUC pH 3.1.

The ratio of coformer to drug activities at the eutectic, known as

the eutectic constant K_eu, is an indicator of the thermodynamic

stability of cocrystal and cocrystal component solid phases.

Under dilute conditions where activities are replaced by

concentrations, K_euvalues can be calculated from drug and

predicted behavior according to eqn (26) and (27), which predict

that eutectic concentrations of drug and coformer increase

according to their respective K_svalues.

coformer eutectic concentrations in SLS solutions (Fig. 7). K_eu

>

1 for 1 : 1 cocrystals (> 0.5 for 2 : 1 cocrystals) indicates that

cocrystal is thermodynamically unstable and K_eu# 1 for 1 : 1

cocrystals (# 0.5 for 2 : 1 cocrystals) indicates cocrystal is ther-

modynamically stable. The surfactant concentration and pH

where K_eu¼ 1 for 1 : 1 cocrystals (¼ 0.5 for 2 : 1 cocrystals) are

Fig. 7 shows the predicted and experimental drug and

coformer eutectic concentrations for each cocrystal as a function

of SLS concentration. The predicted lines were generated by

linear regression according to equations in Table 1 where K_s

values and surfactant CMC were allowed to vary; drug and

coformer eutectic concentrations in pure water, solution [H⁺],

and K_avalues remained ﬁxed. Fig. 7 shows very good correlation

between experimental and predicted behavior.

the CSC and pH_max

.

Fig. 9 shows the predicted and experimental K_eudependence

on SLS concentration according to the model equations (Table 2)

using K_sand CMC values in Table 3 and K_eumeasured in pure

water (K_eu,aq). Measured K_euvalues decrease as a function of

SLS concentration, indicating that the cocrystal becomes more

stable relative to drug as SLS concentration increases. If we

assume that solution interactions other than ionization and

micellar solubilization are negligible, decreasing K_euvalues can

be related to decreasing cocrystal to drug solubility ratios (eqn

The K_svalues generated by linear regression (Table 3), are

a measure of the drug and coformer K_svalues in the eutectic

solution, and represent the inﬂuence of coformer on K_s. There is

good agreement between these and the K_svalues of the separate

cocrystal components in aqueous SLS solutions, suggesting that

the presence of coformer negligibly affected drug solubilization

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Fig. 7 Eutectic concentrations of drug and coformer at E₁in aqueous SLS solutions for (a) CBZ-SLC pH 3.0 (b) CBZ-SAC pH 2.2 (c) CBZ-4ABA-

HYD pH 4.0 (d) CBZ-SUC pH 3.1. Lines represent linear regression from equations in Table 1, where K_sand CMC values are allowed to vary (Table 3).

Eutectic concentrations measured in aqueous solutions without SLS, and all other parameters were ﬁxed.

(43) and (44)). The experimental K_eudependence on SLS

concentration is in excellent agreement with the predicted

behavior. This demonstrates that solution conditions where

cocrystal is stable (pH and additive concentration) cannot be

generalized to other solution conditions without considering

ionization and micellar solubilization equilibria, even at low

micellar surfactant concentrations where the CSC is not

achieved.

Table 2. These two methods are complementary to other

methods of evaluating CSC which were studied previously.⁷

Method (1) determines a CSC range between the highest

concentration of surfactant where K_eu> 1 and the lowest

concentration of surfactant where K_eu# 1 for a 1 : 1 cocrystal

(from K_eu> 0.5 to K_eu# 0.5 for 2 : 1 cocrystals). The surfactant

concentrations in Fig. 9 were not selected for the purpose of

narrowing this range, as the kinetics of reaching equilibrium

become slow at concentrations near the CSC. Method (2) is

a calculation based on a eutectic point measured in water, which

avoids the possible kinetic limitations at surfactant concentra-

tions near the CSC.

In this work CSC is evaluated by two methods: (1) K_eu

measured as a function of SLS concentration, and (2) K_eu

calculated from K_eu,aq, [H⁺], K_sand K_afor the cocrystal

components, and surfactant CMC according to equations in

Table 3 Comparison of K_svalues for the drug and coformer measured at saturation when the solid phases at equilibrium are (a) cocrystal and drug at

eutectic point E₁(b) drug or coformer only

K_s(drug)^acocrystal + drug

mM^ꢀ1

K_s(drug)^bdrug only

mM^ꢀ1

K_s(cof)^acocrystal + drug

mM^ꢀ1

K_s(cof)^bcoformer only

mM^ꢀ1

CMC^a

mM

Cocrystal

CBZ-SLC

CBZ-SAC

CBZ4-ABA-

HYD

0.605 ꢄ 0.023

0.541 ꢄ 0.020

0.470 ꢄ 0.009

0.576 ꢄ 0.017^c

0.494 ꢄ 0.012^d

0.107 ꢄ 0.010

0.027 ꢄ 0.002

0.007 ꢄ 0.001

0.001 ꢄ 0.020^e

0.060 ꢄ 0.005

0.013 ꢄ 0.002

<0.010

8

6

CBZ-SUC

0.484 ꢄ 0.009

<0.010

6

a

K_sand CMC determined by linear regression of eutectic concentrations as a function of SLS concentration (Fig. 7) according to equations in Table 1,

where K_sand CMC were allowed to vary and all other parameters remained ﬁxed. ^bK_sdetermined by linear regression of measured solubilities of pure

drug or coformer at saturation as a function of SLS concentration according to eqn (21) and (29). CBZ K_sdemonstrated a weak dependence on SLS

concentration, so K_svalues were determined in a range of SLS concentrations similar to those used in eutectic point experiments (Fig. 7). ^cK_smeasured

d

between 0 mM and 50 mM SLS. K_smeasured between 0 mM and 140 mM SLS. ^eStatistically insigniﬁcant from 0.

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CBZ-SUC shows deviation between the two methods which may

be due to K_eudecreasing very slowly at surfactant concentrations

near the CSC. In Fig. 9(d) the rate of change of K_euwith respect

to SLS concentration is predicted to be very low near the CSC.

This indicates that cocrystal and drug have very similar solubil-

ities, which could limit the kinetics of transformation between

phases. CSC values measured are consistent with previously

reported methods of evaluating CSC.⁷

Engineering cocrystal stability regions

Micellar solubilization provides a mechanism to engineer the

cocrystal stability regions. Fig. 10 shows phase diagrams with the

predicted and experimental eutectic points of CBZ cocrystals as

a function of SLS concentration in a triangular phase diagram.

Predicted lines are generated according to equations in Table 1

with K_sand CMC values in Table 3 and K_eu,aqmeasured

in water. The predicted E₁lines shown are analogous to the

Fig. 8 Comparison of CBZD solubility as a function of SLS concen-

tration ( ) in the absence of coformer and ( ) at the eutectic for four

CBZ cocrystals (CBZ-SLC, CBZ-SAC, CBZ-4ABA-HYD, CBZ-SUC).

Eutectic concentrations show that CBZD solubility is unaffected by the

presence of coformer. Predicted line is drawn according to eqn (21),

S_R,aq¼ 0.53 mM, K_s¼ 0.49 mM^ꢀ1, CMC ¼ 6 mM.

E

_1,aq-E_1,Tline in Fig. 5.

In Fig. 10, the eutectic solution composition at E₁becomes

more enriched in CBZ as micellar solubilization increases. The

predicted lines are generated from equations in Table 1 and K_s

values in Table 3. The experimental E₁values are in excellent

agreement with the predicted behavior. The intersection of the

predicted E₁dependence with the equimolar composition line of

components (dotted line) is the CSC, which describes a solution

composition where drug, cocrystal, and micellar solution are in

CSC values predicted from K_eu,aqmeasurements are in good

agreement with CSC values measured in micellar solutions for

three cocrystals (CBZ-SLC, CBZ-SAC, and CBZ-4ABA-HYD).

Fig. 9 Dependence of K_euon SLS concentration in water for (a) CBZ-SLC pH 3.0 (b) CBZ-SAC pH 2.2 (c) CBZ-4ABA-HYD pH 4.0 (d) CBZ-SUC pH

3.1. Predicted curves and CSCs are generated according to equations in Table 2 using the K_eumeasured in pure water and the K_svalues for drug and

coformer found in Table 1. K_eudependence shows that cocrystal to drug solubility ratios decrease with increasing surfactant concentration. K_euvalues

below the horizontal dotted line (# 1 for 1 : 1 cocrystals and # 0.5 for 2 : 1 cocrystals) indicate the solution contains SLS concentration above the

cocrystal’s CSC.

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Table 4 CSC values determined from (a) measured K_eudependence on SLS and (b) estimated according to equations in Table 2 using measured K_eu,aq

CSC range measured from K_eu

dependence on SLS^amM SLS

CSC calculated from

K_eu,aqmM SLS

b

Cocrystal

pH

CBZ-SLC

CBZ-SAC

CBZ4-ABA-HYD

CBZ-SUC

3.0

2.2

4.0

3.1

9 < CSC < 18

50 < CSC < 55

50 < CSC < 60

160 < CSC

19

42

64

142

a

Range of CSC determined by SLS concentrations where K_eu> 1 to K_eu# 1 for 1 : 1 cocrystals and where K_eu> 0.5 to K_eu# 0.5 for 2 : 1 cocrystals.

Predictions according to equations in Table 2 using measured K_eu,aq(Fig. 9) and K_svalues (Table 3).

b

Fig. 10 Triangular phase diagrams showing predicted and experimental dependence of eutectic point E₁on SLS concentration for (a) CBZ-SLC pH 3.0

(b) CBZ-SAC pH 2.2 (c) CBZ-4ABA-HYD pH 4.0 (d) CBZ-SUC pH 3.1. Surfactant concentrations increase towards the base of the triangle. Predicted

lines generated according to equations in Table 1, K_svalues in Table 3, and eutectic concentrations of cocrystal components measured in pure water.

Micellar solubilization alters the cocrystal regions of stability such that cocrystal is congruently saturating. Dotted lines indicate ratio of cocrystal

components equivalent to cocrystal stoichiometry.

equilibrium with no excess of either cocrystal component in

solution. An incongruently saturating cocrystal below CSC

becomes congruently saturating above CSC.

to the choice of surfactant and pH is shown for several carba-

mazepine cocrystals in aqueous solutions of sodium lauryl sulfate.

Increasing the magnitude of micellar solubilization for one of

the cocrystal components is found to confer greater thermody-

namic stability to the cocrystal and expand its stability region.

This brings a shift in eutectic points and phase stability regions to

solutions of stoichiometry equal to the cocrystal (there is no

excess concentration of either cocrystal component). Thus, co-

crystals which are otherwise unstable can achieve thermody-

namic stability at a given surfactant concentration and pH,

Triangular phase diagrams such as Fig. 10 have utility in

designing solution conditions that either favor or disfavor coc-

rystal formation and stability in solution.

Conclusions

The work presented here describes the mechanisms by which

cocrystal eutectic points can be ﬁne-tuned via micellar solubili-

zation and ionization of cocrystal components. Quantitative

models developed allow for a priori calculation of cocrystal

eutectic points in micellar solutions from a single eutectic point in

pure water, K_sand K_avalues of cocrystal components, and

solution pH. The sensitivity of eutectic points and phase diagrams

regarded as CSC and pH_max

.

The eutectic constant K_euis an important parameter obtained

from the solution composition at the eutectic and is an indicator

of cocrystal solubility and thermodynamic stability relative to

drug. The CSC can be determined from K_eumeasured in micellar

solutions or can be predicted from K_eumeasured in pure water

This journal is ª The Royal Society of Chemistry 2011

CrystEngComm, 2011, 13, 5409–5422 | 5421

View Article Online

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6 N. Huang and N. Rodrıguez-Hornedo, Crystal Growth & Design,

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7 N. Huang and N. Rodrıguez-Hornedo, Submitted to Journal of

(and its associated solution pH) and K_svalues for the cocrystal

components.

ꢀ

Pharmaceutical Sciences, 2011.

ꢀ

8 D. J. Good and N. Rodrıguez-Hornedo, Crystal Growth & Design,

The variation of K_euwith surfactant concentration shows that

cocrystal to drug solubility ratio decreases fastest close to the

CMC. Applications that rely on a large cocrystal solubility

advantage over drug must be cognizant of reductions in the

cocrystal to drug solubility ratio that can result from differential

solubilization of cocrystal components.

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mechanisms that exhibit differential afﬁnities for cocrystal

components. Cocrystals with a high solubility advantage over

drug may require multiple additives and/or solubilization

mechanisms to achive the CSC. Understanding the sensitivity of

cocrystal thermodynamic stability to solution chemistry is crit-

ical for our ability to control, develop, and use cocrystals.

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Acknowledgements

We gratefully acknowledge partial ﬁnancial support from the

Warner-Lambert/Parke Davis Fellowship and the Upjohn

Fellowship from the College of Pharmacy at the University of

Michigan.

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5422 | CrystEngComm, 2011, 13, 5409–5422

This journal is ª The Royal Society of Chemistry 2011

Article Doi

Engineering cocrystal thermodynamic stability and eutectic points by micellar solubilization and ionization

DOI: 10.1039/c1ce05381g

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Article abstract of DOI:10.1039/c1ce05381g

Full text of DOI:10.1039/c1ce05381g

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