7
Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles A. Pérez a , A. Ruíz a , R. Santillán a , J.M. del Río b , M. Corea a, * a SEPI-ESIQIE, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz, Zacatenco, Edificio Z-6, Del. Gustavo A. Madero, C.P. 07738, Mexico Distrito Federal, Mexico b Programa de Aseguramiento de la Producción de Hidrocarburos, Instituto Mexicano del Petróleo, Eje central Lázaro Cárdenas 152, Col. Sn. Bartolo Atepehuacan, C.P. 07730, Mexico Distrito Federal, Mexico article info Article history: Received 8 February 2008 Received in revised form 9 June 2008 Accepted 22 June 2008 Available online 1 July 2008 Keywords: Functional polymers Multilayer latex Carboxylic groups Specific partial properties abstract A series of functionalized multilayer latex particles of P(butyl acrylate–methyl methacry- late–acrylic acid) was synthesized. The total acrylic acid concentration inside particles was varied from 0 to 25 wt.% and the number of particles in the system was held constant. The polymeric particles were studied by means of specific partial volume and specific par- tial compressibility at infinite dilution, which were calculated from density and sound speed measurements. From the behaviour of the partial properties at infinite dilution of the polar and non-polar groups of the polymer chain, it was concluded that the particle swells at low acrylic acids content due to the electrostatic repulsion between the carbox- ylic groups of the polymer chain. From 15 wt.% of acrylic acid up, the particle swells due to the electrostatic repulsion and to the incorporation of water molecules in the bounds of the particle layers. In this way, the hydration is non-homogeneous in the interior of each layer. These results are in agreement with the behaviour of the hydrodynamic radius determined by the quasi-elastic light scattering technique. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Functional groups are usually incorporated into poly- meric latexes by copolymerization with carboxylic acid comonomers [1]. These can impart colloidal stability, freeze–thaw stability, and improve film-forming proper- ties [2–4]. Such monomers can also function as bonding agents in latex-based paper coatings. The carboxylic acid comonomer forms a major component of water-soluble chains on the surface of the latex particle, proving both ste- ric and electrostatic stabilization of the colloid (hence ‘‘electrosteric stabilization”). This surface coating of hydro- philic chains is often referred to as a ‘‘hairy layer” [5]. There are two main applications for this kinds of mate- rials (i) they can provide useful models for fundamental studies in colloidal science, physics and rheology [6]; and (ii) they can be used in a broad range of applications, for example, as binders in paints, adhesives, paper coatings, textiles, etc. [7,8]. However, a new generation of carboxylic latex particles able to respond reversibly to external stimuli, such as tem- perature, pH, ionic strength, solvent nature and external stress has been developed over the past decade [9–11]. These particles have potential technological applications such as supports in the biochemical and biomedical fields [12–14], because the carboxylic groups are able to form amine bonds with the amino groups of bioligands and they are frequently used to achieve protein binding [15,16]. However, the properties of these materials and their activ- ity are affected by the synthesis process, concentration, and location of functional groups inside the particle [1,3,17–22]. In a previous work [23], the swelling phenomena of func- tionalized homogeneous latex particles by means of specific partial thermodynamic properties as a function of the car- boxylic groups concentration was studied. The swelling 1381-5148/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.reactfunctpolym.2008.06.017 * Corresponding author. Tel.: +52 55 57 29 60 00x55286. E-mail addresses: [email protected] (J.M. del Río), [email protected], [email protected] (M. Corea). Reactive & Functional Polymers 68 (2008) 1422–1428 Contents lists available at ScienceDirect Reactive & Functional Polymers journal homepage: www.elsevier.com/locate/react

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Page 1: Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles

Reactive & Functional Polymers 68 (2008) 1422–1428

Contents lists available at ScienceDirect

Reactive & Functional Polymers

journal homepage: www.elsevier .com/locate / react

Partial volume and compressibility at infinite dilutionof functionalized multilayer latex particles

A. Pérez a, A. Ruíz a, R. Santillán a, J.M. del Río b, M. Corea a,*

a SEPI-ESIQIE, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz, Zacatenco, Edificio Z-6, Del. Gustavo A. Madero, C.P. 07738, Mexico Distrito Federal, Mexicob Programa de Aseguramiento de la Producción de Hidrocarburos, Instituto Mexicano del Petróleo, Eje central Lázaro Cárdenas 152, Col. Sn. BartoloAtepehuacan, C.P. 07730, Mexico Distrito Federal, Mexico

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 February 2008Received in revised form 9 June 2008Accepted 22 June 2008Available online 1 July 2008

Keywords:Functional polymersMultilayer latexCarboxylic groupsSpecific partial properties

1381-5148/$ - see front matter � 2008 Elsevier Ltddoi:10.1016/j.reactfunctpolym.2008.06.017

* Corresponding author. Tel.: +52 55 57 29 60 00E-mail addresses: [email protected] (J.M. del R

[email protected] (M. Corea).

A series of functionalized multilayer latex particles of P(butyl acrylate–methyl methacry-late–acrylic acid) was synthesized. The total acrylic acid concentration inside particleswas varied from 0 to 25 wt.% and the number of particles in the system was held constant.The polymeric particles were studied by means of specific partial volume and specific par-tial compressibility at infinite dilution, which were calculated from density and soundspeed measurements. From the behaviour of the partial properties at infinite dilution ofthe polar and non-polar groups of the polymer chain, it was concluded that the particleswells at low acrylic acids content due to the electrostatic repulsion between the carbox-ylic groups of the polymer chain. From 15 wt.% of acrylic acid up, the particle swells due tothe electrostatic repulsion and to the incorporation of water molecules in the bounds of theparticle layers. In this way, the hydration is non-homogeneous in the interior of each layer.These results are in agreement with the behaviour of the hydrodynamic radius determinedby the quasi-elastic light scattering technique.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Functional groups are usually incorporated into poly-meric latexes by copolymerization with carboxylic acidcomonomers [1]. These can impart colloidal stability,freeze–thaw stability, and improve film-forming proper-ties [2–4]. Such monomers can also function as bondingagents in latex-based paper coatings. The carboxylic acidcomonomer forms a major component of water-solublechains on the surface of the latex particle, proving both ste-ric and electrostatic stabilization of the colloid (hence‘‘electrosteric stabilization”). This surface coating of hydro-philic chains is often referred to as a ‘‘hairy layer” [5].

There are two main applications for this kinds of mate-rials (i) they can provide useful models for fundamentalstudies in colloidal science, physics and rheology [6]; and

. All rights reserved.

x55286.ío), [email protected],

(ii) they can be used in a broad range of applications, forexample, as binders in paints, adhesives, paper coatings,textiles, etc. [7,8].

However, a new generation of carboxylic latex particlesable to respond reversibly to external stimuli, such as tem-perature, pH, ionic strength, solvent nature and externalstress has been developed over the past decade [9–11].These particles have potential technological applicationssuch as supports in the biochemical and biomedical fields[12–14], because the carboxylic groups are able to formamine bonds with the amino groups of bioligands and theyare frequently used to achieve protein binding [15,16].However, the properties of these materials and their activ-ity are affected by the synthesis process, concentration,and location of functional groups inside the particle[1,3,17–22].

In a previous work [23], the swelling phenomena of func-tionalized homogeneous latex particles by means of specificpartial thermodynamic properties as a function of the car-boxylic groups concentration was studied. The swelling

Page 2: Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles

Nomenclature

q density (g/cm3)u sound speed (m/s)m1 mass of water (g)m2 mass of non-polar groups (g)m3 mass of polar groups (g)mF mass of polymeric particles (g)mL mass of latex (g)t1 mass fraction of watertF mass fraction of fraction F (polymeric particle)tf2 fraction mass of non-polar groups in the frac-

tion Ftf3 fraction mass of polar groups in the fraction FV volume (cm3)v specific volume (cm3/g)v1 specific partial volume of pure water (cm3/g)vF;1 specific partial volume of fraction F in presence

of water (cm3/g)v2;1,3 specific partial volume of non-polar groups in

presence of water and polar groups (cm3/g)v3;1,2 specific partial volume of polar groups in pres-

ence of water and non-polar groups (cm3/g)vD

2;1;3 specific partial volume of non-polar groups inpresence of water and polar groups at infinitedilution (cm3/g)

vD3;1;2 specific partial volume of polar groups in pres-

ence of water and non-polar groups at infinitedilution (cm3/g)

voF;1 specific partial volume of fraction F in presence

of water at infinite dilution (cm3/g)vo

M specific intrinsic volume of solute molecule atinfinite dilution (cm3/g)

Dvoh specific hydration volume at infinite dilution

(cm3/g)vo

c specific constitutive atomic volume at infinitedilution (cm3/g)

vocav specific volume of cavity at infinite dilution

(cm3/g)nh number of water molecules in the hydration

shellvo

sh specific volume of water in the hydration shell(cm3/g)

voso specific volume of water in the bulk (cm3/g)

k specific adiabatic compressibility (cm3/(bar g))k1 specific adiabatic compressibility of pure water

(cm3/(bar g))ko

F;1 specific partial adiabatic compressibility of frac-tion F in presence of water at infinite dilution(cm3/(bar g))

kocav specific adiabatic compressibility of cavity at

infinite dilution (cm3/(bar g))Dko

h specific adiabatic hydration compressibility atinfinite dilution (cm3/(bar g))

kD2;1;3 specific partial adiabatic compressibility of non-

polar groups in presence of water and polargroups at infinite dilution (cm3/(bar g))

kD3;1;2 specific partial volume of polar groups in pres-

ence of water and non-polar groups at infinitedilution (cm3/(bar g))

P pressure (bar)Ts total solid content (%)

A. Pérez et al. / Reactive & Functional Polymers 68 (2008) 1422–1428 1423

effect and contributions of polar and non-polar groups in-side the particle were determined. The specific partial vol-umes and compressibilities indicated that at lowconcentrations of carboxylic groups, the polar groups werelocated on the surface of particle, whereas at higher concen-tration, polar groups were located progressively from sur-face to interior of it. At the same time, a hydration processin the polymeric particle due to polar groups was found.

In this work, a series of functionalized latex particleswere synthesized by means of emulsion polymerizationtechniques using a multilayer process. The total concentra-tion of carboxylic groups in the particle was varied from 0to 25 wt.%, where the composition of functionalized groupsin each layer was 50, 30 and 20 wt.% of total acrylic acidcontent, respectively. In this way, a concentration gradientof polar groups was generated inside the particle. Theswelling process of these particles was studied using theknowledge of swelling process of the homogeneous parti-cles established in our previous work, because the behaviorof each layer can be described in terms of homogeneousparticles. In this respect, it was found that the hydrationof the particle was located in the bound of each layer. Thatis, the hydration inside the particle was non-homogeneous.In addition, the thermodynamic method employed wasvery sensitive to describe the behavior of polar and non-polar groups inside the particle.

2. Thermodynamics

In order to calculate the specific partial properties in thesystem, the polymeric latex was assumed as a three-compo-nent system: water (component 1), non-polar groups of thepolymer chains (component 2) and carboxylic groups of thepolymer chains (component 3). The polymer particle wasconsidered as a fraction, F, of the system. A fraction of a sys-tem [23] is defined as a thermodynamic entity with internalcomposition. Therefore, for a system composed of a compo-nent and a fraction F; the volume can be expressed as

V ¼ Vðm1;mF; tf3Þ ð1Þ

where m1, is the mass of the water and mF the mass ofpolymeric particle

mF ¼ m2 þm3 ð2Þ

where m2 and m3 are the masses of non-polar and polargroups respectively. The variable tf3 is defined as

tf3 ¼m3

mFð3Þ

and it is a measure of the composition of the fraction. Thespecific partial volume of the polymer particle can be cal-culated as the partial volume of the fraction F as follows[23]:

Page 3: Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles

1424 A. Pérez et al. / Reactive & Functional Polymers 68 (2008) 1422–1428

vF;1 ¼oVomF

� �m1 ;tf3

¼ tf2v2;1;3 þ tf3v3;1;2 ð4Þ

where the limit at the infinite dilution of the fraction is ta-ken as

lim tf ! 0tf3 ¼ tc

f3

vF;1ðtF; tf3Þ ¼ vF;1ð0; tcf3Þ � vo

F;1ðtcf3Þ ð5Þ

being tF the mass fraction of the fraction F. The limits atinfinite dilution of component 2 (non-polar groups) andcomponent 3 (polar groups) are taken as follows [23]:

lim tf ! 0tf3 ¼ tc

f3

v2;1;3ðtF; tf3Þ ¼ v2;1;3ð0; tcf3Þ � vD

2;1;3ðtcf3Þ ð6Þ

and

lim tf ! 0tf3 ¼ tc

f3

v3;1;2ðtF; tf3Þ ¼ v3;1;2ð0; tcf3Þ � vD

3;1;2ðtcf3Þ ð7Þ

In Eqs. (6) and (7) the concentration of the fraction F tendsto zero while its composition is kept constant.

Specific partial properties of fraction F (polymeric parti-cle) at infinite dilution can be interpreted in terms of [24–28]

voF;1 ¼ vo

M þ Dvoh ð8Þ

where voM is the intrinsic volume of the solute molecule, in

which solvent molecules cannot penetrate. In addition, it ispossible to consider that:

voM ¼ vo

c þ vocav ð9Þ

where voc is the specific constitutive atomic volume which

for macromolecules is the sum of van der Waals volumesof the constituent atoms and vo

cav results from the imper-fect atomic packing. The other contribution to vo

F;1 is Dvoh

and it is named as hydration term, which is defined bythe following equation:

Dvoh ¼ nhðvo

sh � vosoÞ ð10Þ

where nh is the number of water molecules in the hydra-tion shell and vo

sh and voso are the specific volumes of water

in the hydration shell and bulk, respectively.In order to calculate the specific partial adiabatic com-

pressibility at infinite dilution [26,29–31], koF;1 is obtained

by substitution of Eq. (9) in Eq. (8) and differentiatingwith respect to pressure (P) at constant entropy (S) andneglecting the variation of the vo

c with respect to thepressure:

koF;1 ¼

ovoF;1

oP

� �S¼ ko

cav þ Dkoh ð11Þ

It is important to point out that voM and vo

cav are positiveand Dvo

h and Dkoh are negative. The swelling process in-

volves the repulsion of charges and a process of hydrationinside the particle. In this way the repulsion betweencharges will increase the terms vo

M and kocav while the pro-

cess of hydration will decrease the terms Dvoh and Dko

h

[23].

3. Experimental

3.1. Materials

The monomers butyl acrylate (BuA), methyl methacry-late (MMA), and acrylic acid (AA) (National Starch & Chem-ical) were commercial grade and were used as received.Sodium dodecylbenzene sulfonate (SDBS) and potassiumpersulfate (from Aldrich) were reactive grade and wereemployed as surfactant and initiator, respectively; bothwere used without purification. The dispersion mediumwas distilled water.

3.2. Latex Preparation

The carboxylated poly(BuA–MMA) samples were pre-pared via emulsion polymerization in a multilayer pro-cess. That is, the particles were prepared by fourconsecutive polymerization sequences, where the second,third and fourth stages were polymerized in the presenceof seed latex particles of poly(BuA). These kinds of parti-cles can be defined as a core–shell particle where the coreis recovered with two or more shell. A schema of evolu-tion of morphology through the synthesis is presentedin Fig. 1.

All reactions were carried out in a semi-continuousreactor consisting of a jacketed rector and a feeding tank.A continuous flow of pre-emulsion material was ensuredby a dosing pump. The reactor consisted of a 1-L stirredglass reactor under a dynamic flow of N2 and at a temper-ature of 70 �C, controlled by a thermal bath. The stirringrate was adjusted to 250 rpm. The latex was synthesizedin three layers. The AA total content in the latex was var-ied from 0 to 25 wt.%. The pH during the reactions stayedat a value lower than 4 after AA was added, this ensurethe incorporation of the acrylic acid in the polymer[19,20,32,33]. The formulation used to prepare latexeswith 5 wt.% of total AA is presented in Table 1, whereeach feeding tank corresponds to quantities of each layerof particle (Fig. 1). In others cases, the total acrylic acidcontent was varied of 10, 15, 20 and 25 wt.% with respectto total monomer concentration. The acrylic acid contentin each layer was 50, 30 and 20 wt.%, respectively, withrespect to the total carboxylic groups. The final solidcontent was determined by means of gravimetrictechniques.

3.3. Gravimetry

The total solid content, Ts, in latexes is defined asTs = tF � 100 where tF = mF/mL being mL the total mass of la-tex (mL = m1 + mF). A series of latexes samples wereweighted and they were put in aluminum trays weightedpreviously obtaining mL. The samples were dried and theywere weighted again. The weights of the trays were sub-strated obtaining mF. Because:

mF ¼ tFmL ð12Þ

the final solid content can be calculated from the slope offits in plots of mF against mL.

Page 4: Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles

Fig. 1. Schema of evolution of morphology of functionalized multilayer latex particles.

Fig. 2. Dry polymer mass as a function of latex mass.

Table 2Total solid content in the latexes synthesized

AA content (wt.%) Mass fraction Total solid content (wt.%)

0 0.0603 ± 0.0018 6.03 ± 0.185 0.07188 ± 0.00046 7.188 ± 0.04610 0.0637 ± 0.0017 6.37 ± 0.1715 0.08010 ± 0.00083 8.010 ± 0.08320 0.07292 ± 0.00052 7.292 ± 0.05225 0.07784 ± 0.00022 7.784 ± 0.022

Table 1Polymerization recipes

Component Content (g)

Reactor (speedor 1st stage)

Feeding tank forlayer 1 (2nd stage)

Feeding tank forlayer 2 (3rd stage)

Feeding tank forlayer 3 (4th stage)

Butyl acrylate 3.6Methyl methacrylate 9 11.0 11.0Acrylic acid 1 0.6 0.4Potassium sulfate 0.14 0.23 0.23 0.24Sodium dodecylbenzene

sulfonate0.02 0.76 0.76 1.0

Water 197.0 99.0 99.0 100.0

A. Pérez et al. / Reactive & Functional Polymers 68 (2008) 1422–1428 1425

3.4. Density and ultrasound speed

A DSA 5000 Anton Paar density and speed of sound ana-lyzer were used. The samples were prepared as follows: astock dispersion of 1.74 wt.% of polymer was made, andit was diluted to concentrations of 0.05, 0.1, 0.15, 0.2,0.25, 0.3 and 0.35 wt.% of polymer. This procedure wasmade for each latex synthesized. The samples were de-gassed before to use. The measurements were made at30, 50 and 70 �C.

3.5. Measurements of particle diameter

The hydrodynamic diameter of carboxylated poly(BuA–MMA) was determined by dynamic light scattering (QELS).All samples were diluted to 10 ppm and measured at 30, 50and 60 �C using a Malvern Autosizer 4800 instrument. Thedistributions of particle size were calculated using theCONTIN program provided by Malvern in the software ofthe equipment.

4. Results and discussion

Fig. 2 shows the dry polymer mass (mF) as function oflatex mass (mL) for 0, 15 and 25 wt.% of acrylic acid. Theslope corresponds to the fraction mass of solids in the latexsamples.

Results of total solid content for 0, 5, 10, 15, 20 and25 wt.% of acrylic acid are presented in Table 2.

The density, q, and the speed of sound, u, of the latexsamples were measured as a function of fraction mass offraction of polymer particles tF and temperature. Valuesof density and sound speed of latex samples measured at

50 �C are shown in panels a and b of Fig. 3. The specific vol-ume of latex samples was calculated from the density databy the following equation:

Page 5: Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles

Fig. 3. (a) Density at 50 �C as a function of tF at different composition of acrylic acid (j 0%, h 5 %, d 10 %, s 15 %,4 20 %, N 20%). (b) Sound speed at 50 �C asa function of mass fraction of fraction F at different compositions of acrylic acid. (c) Specific volume measured at 50 �C as a function of mass fraction ofsolvent at different composition of acrylic acid. (d) Specific compressibility as a function of mass fraction of solvent to different compositions of acrylic acid,measured at 50 �C.

1426 A. Pérez et al. / Reactive & Functional Polymers 68 (2008) 1422–1428

v ¼ 1q

ð13Þ

and the specific adiabatic compressibility was calculatedfrom the experimental density and sound speed data, usingthe following equation:

k ¼ 1qu

� �2

ð14Þ

The specific partial volume and specific partial compress-ibility as a function of the mass fraction of water,t1 = 1�tF, are shown in panels c and d of Fig. 3 at 50 �C.In both cases a linear behavior can be observed indicatingthat the interval of concentrations is in the high dilutionregion [23]. The values of specific partial volume at infinitedilution ðvo

F;1Þ were calculated as the intercept of the linearfit of experimental values of v (Fig. 3c) as a function of t1,taking the following equation:

v ¼ voF;1 þ ðv1 � vo

F;1Þt1 ð15Þ

where v1 is the specific partial volume of water in its purestate. In the same way, ko

F;1 was calculated from the data ofk (Fig. 3d) using the equation:

k ¼ koF;1 þ ðk1 � ko

F;1Þt1 ð16Þ

where k1 is the specific partial compressibility of water inthe pure state. Because the partial properties of the poly-mer particles are obtained at the infinite dilution limit,the interaction between particles are vanished and onlythe interaction between polar and non-polar groups andwater is bearing in mind [23].

Values of voF;1 and ko

F;1 calculated at 30, 50 and 70 �C areshown in Fig. 4. From Fig. 4a, it is observed that vo

F;1 presentsan increment when the acrylic acid content is increased un-til 15 wt.%. This behavior is explained as a gain in the con-tribution of cavity term due to electrostatic repulsioncaused by functional groups inside of particle. When thecarboxylic groups concentration is greater than 15 wt.% afaster drop occurs. This fact can be explained in terms ofan increase in the contribution of the hydration term. Inaddition, vo

F;1 increases with the temperature. In the caseof the specific partial compressibility of the polymeric par-ticle at infinite dilution limit (Fig. 4b) as a function of the ac-rylic acid content, presents a similar behavior than vo

F;1.In both cases, vo

F;1 and koF;1 present a maximum value

when 15 wt.% of acrylic acid content is reached and bothspecific partial properties show an increment when thetemperature arises.

From data in Fig. 4, the limits of Eqs. (6) and (7) for polarand non-polar groups were calculated by means of the fol-lowing equations:

Page 6: Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles

Fig. 5. (a) Specific partial volumes at infinite dilution of polar groupsðvD

3;1;2Þ and non-polar groups ðvD2;1;3Þ as a function of the acrylic acid

content at different temperatures. (b) Specific partial compressibilties atinfinite dilution of polar groups ðkD

3;1;2Þ and non-polar groups ðkD2;1;3Þ as a

function of the carboxylic groups amount.

Fig. 4. (a) Specific partial volume at infinite dilution limit of fraction F as afunction of acrylic acid content at different temperatures. (b) Specificpartial compressibility at infinite dilution limit of fraction F as a functionof carboxylic groups content at different temperatures: j 30 �C, d 50 �C,N 70 �C.

A. Pérez et al. / Reactive & Functional Polymers 68 (2008) 1422–1428 1427

vD2:1;3ðtf3Þ ¼ vo

F;1ðtf3Þ �dvo

F;1

dtf 3

� �� tf3 ð17Þ

vD3:1;2ðtf3Þ ¼ vo

F;1ðtf3Þ þdvo

F;1ðtf3Þdtf3

� �� ð1� tf3Þ ð18Þ

kD2:1;3ðtf3Þ ¼ ko

F;1ðtf3Þ �dko

F;1

dtf3

!� tf3 ð19Þ

kD3:1;2ðtf3Þ ¼ ko

F;1ðtf3Þ þdko

F;1ðtf3Þdtf3

!� ð1� tf3Þ ð20Þ

where tf3 = % AA/100 is a measure of composition of thefraction F (polymeric particle). vD

2;1;3 and vD3;1;2 are the spe-

cific partial volume of non-polar and carboxylic groupsrespectively, whereas kD

2;1;3 and kD3;1;2 are the specific partial

compressibility of non-polar and polar groups.The derivatives of Eqs. (17)–(20) were calculated by

means of numerical methods using the experimentalpoints of Fig. 4. The derivate dvo

F;1=dtf3 for the first pointswas calculated by:

dvoF;1ðt1

f3Þdtf3

¼vo

F;1ðt2f3Þ � vo

F;1ðt1f3Þ

t2f3 � t1

f3

ð21Þ

and for the latest

dvoF;1ðt6

f3Þdtf3

¼vo

F;1ðt6f3Þ � vo

F;1ðt5f3Þ

t6f3 � t5

f3

ð22Þ

For the intermediate points the following equation wasused

dvoF;1ðti

f3Þdtf3

¼vo

F;1ðtiþ1f3 Þ � vo

F;1ðti�1f3 Þ

tiþ1f3 � ti�1

f3

ð23Þ

where i goes from 2 to 5. For the calculation of thedko

F;1=dtf3 analogous Eqs. (21)–(23) were used.Results of specific partial properties for carboxylic and

non-polar groups are shown in Fig. 5. After, interpretingthese results, it is necessary to bear in mind the structure

of the multilayer particle. In a previous work [23] it was re-ported that when tf3 is very low, the carboxylic groups arelocated on the surface of a particle. When the amount ofcarboxylic groups increases, these gradually begin to be lo-cated in the interior of the particle. In this way, in a multi-player particle the carboxylic groups are located in eachlayer, first in the bound and when its amount increases,to the interior of the layer. In panel a of Fig. 5, a slight var-iation of vD

2;1;3 and vD3;1;2 can be observed when 15 wt.% of

acrylic acid concentration is reached inside the polymericparticle. In this point, when the acrylic acid content is in-creased a change in the slope occurs and the specific partialvolume of the polar groups decreases fast until negativevalues. This behavior is a consequence of the hydrationundergone by carboxylic groups of the polymeric chains.For this reason, molecules of water must to be buried inthe bounds of the layers. In the case of specific partial vol-ume of non-polar groups, vD

2;1;3, there is an slight incrementin the slope at the same value of acrylic acid concentration.This fact can be explained in terms of a loss in the hydra-tion in the interior of the layer because water moleculesare located in the bound of the layer. In panel b, kD

2;1;3 andkD

3;1;2 are shown as a function of the acrylic acid contentand their behaviors are similar to that of volume.

The particle hydrodynamic diameter of polymer parti-cles as a function of acrylic acid concentration was mea-sured by quasi-elastic light scattering at 30 and 50 �C.The results are shown in Fig. 6. It is possible to see two dif-ferent behaviors depending on the acrylic acid content.From 0 to 10 wt.% of acrylic acid, the hydrodynamic radiusis similar at two temperatures while from 15 wt.% up, thedifference between temperatures is great. This fact agreeswith the thermodynamic results because, as it was said,at low acrylic acid contents the particle swells increasingcavity contributions due to the electrostatic repulsion ofthe carboxylic groups of the polymer chains. For higher ac-rylic acid contents the electrostatic repulsion is also larger

Page 7: Partial volume and compressibility at infinite dilution of functionalized multilayer latex particles

Fig. 6. Hydrodynamic diameter as a function of acrylic acid. (j 30� C,d 50� C).

1428 A. Pérez et al. / Reactive & Functional Polymers 68 (2008) 1422–1428

and the particle swells now due to the incorporation ofwater molecules in the bounds of the particle layers. In thisregion of acrylic acid content the particle is more sensibleto the temperature due to a mayor separation of the poly-mer chains.

5. Conclusions

For compositions of acrylic acid lower than 15 wt.%, themultilayer latex particle swells due to the electrostaticrepulsion of the carboxylic groups of the polymer particles.At higher acrylic acid content the swelling has two contri-butions. One of them is due to the electrostatic contribu-tion and the other one is due to the water moleculesincorporation in the particle. It is interesting to point outthat with the thermodynamic tools employed in this work,it was possible to detect that the hydration inside the par-ticle is non-homogenous. This phenomenon is only pre-sented in the bounds of the layer particles.

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