Effect of Surface Segregation of Ionic End Groups on Polystyrene

Langmuir 2000, 16, 1279-1284

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Effect of Surface Segregation of Ionic End Groups on Polystyrene Latex Early-Time Interdiffusion S. D. Kim,†,‡,§,| E. M. Boczar,⊥ A. Klein,‡,§,X,# and L. H. Sperling*,‡,§,|,#,∇ Department of Physics, Emulsion Polymers Institute, Polymer Interfaces Center, Center for Polymer Science and Engineering, Materials Research Center, Department of Chemical Engineering, and Department of Materials Science and Engineering, 5 East Packer Avenue, Lehigh University, Bethlehem, Pennsylvania 18015, and Rohm and Haas Company, 727 Norristown Road, Spring House, Pennsylvania 19477 Received June 4, 1999. In Final Form: October 1, 1999 Using a direct energy transfer method, ionic end groups on polystyrene were found to increase the early-time apparent interdiffusion coefficients during film formation. The early-time apparent diffusion coefficients of polystyrene with varying end groups were found to follow the ordering of SO4 > COOH > H. The higher apparent diffusion coefficients are presumably due to the surface segregation of the end groups caused by the polar, aqueous environment during latex synthesis. By titration, 60% of the sulfate end groups and 30% of the carboxyl end groups were found on the latex particle surfaces. The apparent diffusion coefficients at very early times are separable into two additive values: that arising from the polymer chains with chain ends on the latex surface, and that caused by polymer with chain ends buried in the latex interior. The present experiments suggest that the location of the end group is the critical factor determining the initial apparent diffusion coefficients of the polymers rather than the characteristics of the end groups themselves.

Introduction The influence of the variation in polymer chain end groups is of special interest due to the differences in their behavior compared to the central portions of the chain.1 According to reptation theory, polymer chain ends play a significant role in polymer diffusion processes because they “lead” the main chain movement out of its virtual tubes composed of neighboring polymer chains. In industrial practice, polymer chain ends may have various chemical structures depending on the use of initiators, chain transfer agents, or other special chemistries. The location of polymer end groups at interfaces has been studied experimentally2-6 and theoretically.7,8 In the absence of specific interactions9,10 between mers and an interface, the chain ends tends to be segregated at interfaces in order to lower the free energy at the interface. For example, Monte Carlo studies9 of the interface between two polymer melts (Degree of Polymerization of 100, †

Department of Physics. Polymer Interfaces Center. § Center for Polymer Science and Engineering. | Materials Research Center. ⊥ Rohm and Haas Co. X Emulsion Polymers Institute. # Department of Chemical Engineering. ∇ Department of Materials Science and Engineering. ‡

(1) Klein, J. Science 1990, 250, 640. (2) Hunt, M. O.; Belu, A.; Linton, R.; DeSimone, J. M. Macromolecules 1993, 26, 4854. (3) Affrossman, S.; Hartshorne, M.; Kiff, T.; Perthrick, R. A.; Richards, R. W. Macromolecules 1994, 27, 5341. (4) Schaub, T. F.; Kellogg, G. J.; Mayes, A. M.; Kulasekere, R.; Ankner, J. F.; Kaiser, H. Macromolecules 1996, 29, 3982. (5) Botelho de Rego, A. M.; Lopes da Silva, J. D.; Vilar, M. R.; Schott, M.; Petijean, S.; Jerome, R. Macromolecules 1993, 26, 4986. (6) Elman, J. F.; Johs, B. D.; Long, T. E.; Koberstein, J. T. Macromolecules 1994, 27, 5341. (7) Schmidt, I.; Binder, K. J. Phys (Paris) 1985, 46, 1631. (8) Jones, R. A. L.; Kramer, E. J. Polymer 1993, 34, 115. (9) Reiter, J.; Zifferer, G.; Olaj, O. F. Macromolecules 1990, 23, 224. (10) Cifra, P.; Nies, G.; Karasz, F. E. Macromolecules 1994, 27, 1166.

narrow polydispersity) show about twice the relative amount of end groups at the interface compared to the bulk. In the case where there are specific interactions, however, important effects of the end-groups on surface segregation have been found. Elman, et al.,11 studied chain end segregation with neutral, attractive, and repulsive end group systems. The end groups for the air-repulsive carboxyl group systems were depleted at the air interface, while the end groups in systems with air-attractive fluorocarbon chain ends were found higher at the surface than in the bulk. Jalbert et al.12 experimentally and theoretically investigated the surface tension of R,ωfunctional poly(dimethylsiloxanes). They concluded that the end-group segregation is primarily controlled by the surface energy difference between the chain ends and middle chain moieties, while entropic effects are not significant. Surface enrichment of end groups in tetrafluoroethylene-terminated polystyrene4 and surface depletion of end groups in amine-terminated poly(dimethylsiloxane)13 also demonstrated that the specific interactions between end groups and interfaces control the end-group segregation in the polymer. The examples above were cited for systems under equilibrium conditions, with the samples being annealed at a certain temperature above Tg. However, there are cases where the polymer surface is not in an equilibrium state. For example, a cracked surface may have a high concentration of chain ends due to chain scission. The chain ends remain at the surface unless the surfaces are annealed. This nonequilibrium state of having a higher number of chain ends at the surface induces higher crack (11) Elman, J. F.; Johs, B. D.; Long, T. E.; Koberstein, J. T. Macromolecules 1994, 27, 5341. (12) Jalbert, C.; Koberstein, J. T.; Hariharan, A.; Kumar, S. K. Macromolecules 1997, 30, 4481. (13) Jalbert, C. J.; Koberstein, J. T.; Balaji, R.; Bhatia, Q.; Salvati, L., Jr.; Yilgor, I. Macromolecules 1994, 27, 2409.

10.1021/la990709n CCC: $19.00 © 2000 American Chemical Society Published on Web 02/01/2000

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healing rates than the surface previously annealed,14 due to a more rapid interdiffusion. Another practical example of a nonequilibrium system involves latex particles. It is well-known that sulfate end groups of polymer chains are likely to be on the latex particle surface due to their ionic nature.15 During the drying process, interfaces change from polymer/water to polymer/air or polymer/polymer. Therefore, the end groups segregated on the particle surfaces are initially quenched in nonequilibrium states and are exposed to other polymer particles. Polymer interdiffusion in latexes has been extensively investigated recently due to its importance in applications, theory, and the development of new analytical methods. Latex films serve as model systems to study interdiffusion due to their huge interface area per unit volume and their industrial importance. Yoo and co-workers16,17 and Kim and co-workers18 investigated latex film formation by small angle neutron scattering (SANS) methods to understand the interdiffusion process. They measured diffusion coefficients in both anionically polymerized and free-radical-polymerized polystyrene. The diffusion coefficients of latex films from conventional emulsion systems16-18 were an order of magnitude slower than those observed in the anionic miniemulsification system. The apparent slow interdiffusion in the conventional system was attributed to the sulfate end groups and/or the broad molecular weight distribution. Kim and Winnik19 used a direct energy transfer (DET) technique to investigate interdiffusion in poly(butyl methacrylate) latex films made by conventional emulsion polymerization, comparing neutralized and protonated sulfate end groups. The results of this work indicate that the protonated sulfate end groups induced faster interdiffusion. Interdiffusion at short times20 is of special interest because most changes in crack-healing processes, molding, and latex film formation all occur during this time regime. For example, the mechanical strength in a latex film approaches its maximum when the interdiffusion distance is equal to about one radius of gyration, typically less than a few tens of nanometers for most commercial polymers.16,18 Experimental data have shown that at short times, the strength of interfaces depends on annealing time to the one-fourth power during crack healing21 and polymer welding.22 In the present study, polystyrene interdiffusion at latex particle interfaces is investigated using DET, to understand the effect of ionic end groups formed at water/ polymer interfaces on polymer interdiffusion at very early times. (14) Wool, R. P. Polymer Interfaces; Hanser Publisher: New York, 1995. (15) Blackley, D. C. Emulsion Polymerisation; Applied Science Publishers Ltd.: London, 1975; p 172. (16) Yoo, J. N.; Sperling, L. H.; Glinka, C. J.; Klein, A. Macromolecules 1991, 24, 2868. (17) Yoo, J. N.; Sperling, L. H.; Glinka, C. J.; Klein, A. Macromolecules 1990, 23, 3962. (18) Kim, K. D.; Sperling, L. H.; Klein, A.; Hammouda, B. Macromolecules 1994, 27, 6841. (19) Kim, H.-B.; Winnik, M. A. Macromolecules 1994, 27, 1007. (20) Two concepts need to be distinguished: (1) The diffusion coefficient at short-times, where Wool predicts the t1/4 regime to hold. (2) The apparent diffusion coefficient at early times, caused by chain ends being on the surface of latex particles, the present case. Both effects may be present simultaneously. However experimental limitations described in this study precluded their quantitative separation. (21) Hansch, H. H.; Petrovska, D.; Landel, R. F.; Monnerie, L. Polym. Eng. Sci. 1987, 27, 149. (22) Kline, D. B.; Wool, R. P. Polym. Eng. Sci. 1988, 28, 52.

Kim et al. Table 1. Polystyrene Samples for DET Experiments samples

Mn(g/mol)

Mw/Mn

synthesis

H end H end COOH end COOH end SO4 end

72 000 98 000 70 000 94 000 91 000

1.36 1.53 1.39 1.55 1.69

126 000

1.56

stable free radical process stable free radical process stable free radical process stable free radical process emulsion polymerization, fractionation to reduce mol wt distribution emulsion polymerization, fractionation to reduce mol wt distribution

SO4 end

Experimental Section Materials. Styrene monomer (99+% Aldrich) was purified by a column packed with inhibitor remover (Aldrich). For the DET experiment, monomers containing a fluorescent group were synthesized. 9-Anthryl methacrylate (ANMA) was synthesized by reaction of methacryloyl chloride and 9-anthrone in base.23 1-Naphthylethyl methacrylate (NEMA) was prepared by reaction of methacryloyl chloride and 1-naphthylenethanol. Polymerization. Polystyrene, poly(styrene-stat-ANMA), and poly(styrene-stat-NEMA) with a relatively narrow molecular weight distribution were synthesized via a stable free radical process.24 Bulk polymerization was carried out at 125 °C under an argon atmosphere. Benzoyl peroxide and TEMPO (2,2,6,6tetramethyl-1-piperidinyloxy) were used to perform the stable free radical polymerization. 4-Carboxy-TEMPO was used to make carboxyl-terminated polystyrene. All reactions were terminated at a conversion of 50-60% to reduce the broadening of the molecular weight distribution at high conversion. A typical recipe producing Mn ) 70 000 g/mol with a polydispersity index of less than 1.4 consisted of 0.005 mol/L benzoyl peroxide and 0.0065 mol/L TEMPO in styrene monomer. The average molecular weight was controlled by the amount of benzoyl peroxide and TEMPO. Polystyrene with sulfate end groups was prepared via conventional emulsion polymerization. The use of 10 wt % of tetrachloromethane as a retarder to styrene monomer produces polystyrene with one sulfonated end group per chain or none. It was found25,26 that tetrabromomethane and tetrachloromethane which behave as chain transfer agents in homogeneous polymerization function effectively as retarders in the emulsion system. The molecular weight distribution was narrowed by a fractionation technique from solvent/nonsolvent mixtures to remove the high and low molecular weight tails. The polystyrene samples prepared for DET experiments are listed in Table 1. The H end in Table 1 and this paper means polystyrene with no ionic end groups. Fluorescent monomers, ANMA or NEMA, were incorporated into polystyrene for the DET method. The fluorescent comonomer content was 1 wt % in monomer mixture and resulted in 1.5 wt % in the copolymer as measured by IR spectroscopy. Latex Preparation. An artificial miniemulsification27 process was used to prepare latexes with uniform particle sizes. A polymer dispersion is created by ultrasonification and filtration of the water/polymer mixture through a uniform pore size membrane (0.4 µm polycarbonate membrane, Nuclepore). Particle sizes by transmission electron microscopy are 100-120 nm, with a polydispersity of less than 1.3. After solvent was removed by distillation, a fluorescent donor-labeled latex was blended with an acceptor-labeled latex. The two-latex mixture was dried at 50 °C for 1 day, followed by surfactant and cosurfactant removal in a Soxhlet apparatus with methanol and then distilled deionized water. Residual surfactant and cosurfactant contents were (23) Zhao, C.-L.; Wang, Y.; Hruska, Z.; Winnik, M. A. Macromolecules 1990, 23, 4082. (24) Georges, M. K.; Veregin, R. P. N.; Kazmaier, P. M.; Hamer, G. K. Macromolecules 1993, 26, 2987. (25) Whang, B. C.; Lichiti, G.; Gilbert, R. G.; Napper, D. H.; Sangster, D. F. J. Polym. Sci., Polym. Lett. Ed. 1980, 18, 711. (26) Lichiti, G.; Sangster, D. F.; Whang, B. C.; Napper, D. H.; Gilbert, R. G. J. Chem. Soc., Faraday Trans. 1 1982 78, 2129. (27) Mohammadi N.; Kim K. D.; Sperling L. H.; Klein A. J. Colloid Interface Sci. 1993, 157, 124.

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Langmuir, Vol. 16, No. 3, 2000 1281

Table 2. Titration of Ionic End Groups on Latex Particles

end group

Mn (g/mol)

titrated ionic group/PS (µequiv/g)

carboxyl sulfate sulfate

94 000 91 000 126 000

3.2 ( 0.4 6.5 ( 0.6 4.9

fraction of polymer chains with ionic end groups at latex surfacea (%) 30 ( 4 59 ( 4 62

a Fraction of polymer chains with an ionic group at latex surface was calculated with the assumption that no polymer chain has two ionic end groups.

monitored by gel permeation chromatography (GPC) and differential scanning calorimetry (DSC). In another experiment, the presence of ionic groups on the surface of the latex particles was measured by a conductance method.28 Surfactants, including sodium lauryl sulfate, and the counterions were removed by a mixed ionic resin to produce the acid form. The cleaned latex dispersion was titrated by a 0.02 N NaOH water solution, while conductance was monitored. Table 2 shows the titration results of ionic groups at a cleaned latex surface. The fraction of polymer chains which has ionic end groups on the latex surface was calculated with the assumption that no polymer chain has two ionic end groups. The use of 4-carboxyTEMPO in a stable free radical process and the use of a retarder and a persulfate initiator in emulsion polymerization should produce one or less than one ionic end group per polymer chain. Sintering and Film Annealing. A dried latex mixture was pressed under 10 MPa to make a transparent film at a temperature of 100-110 °C for 30 min to 1 h. These conditions were chosen to produce a transparent film with a minimum interdiffusion between latex particles.16 Sample disks with a 1.3 cm diameter and a 0.4 mm thickness were clamped between glass slides to inhibit distortion and were annealed at 115-140 °C. The actual temperature of the samples was directly measured by a thermocouple in contact with the sample surface. From 5 to 10 min was usually needed to reach the desired temperature. DET Measurement and Diffusion Coefficients. Fluorescence spectroscopy has been used to measure the interdiffusion coefficients in latex films.29 Latex particles are labeled with fluorescence donor or acceptor moieties. In this study, naphthyl and anthryl groups are used as fluorescence donor and acceptor, respectively. The naphthyl donor molecules were excited by 280 nm light. The excited donor molecules emit at a characteristic wavelength, near 340 nm, while relaxing to ground state. The fluorescence decay curve of the donor, the number of photons emitted as a function of time, can be described by an exponential decay curve

I(t) ) B exp(-t/τo)

(1)

The quantities I(t), B, and τo are the number of photons at time t, a proportionality constant, and the half-life of the donor emission, respectively. In the presence of acceptor molecules around the donor molecules, there is another mechanism for exited donor molecules to relax to ground state. The excited donor molecules can transfer some energy to the acceptor molecules via a dipole-dipole interaction. Because the donor may transfer to the acceptor molecule without emitting at its characteristic wavelength, this mechanism is called nonradiative direct energy transfer, DET. The efficiency of energy transfer is inversely proportional to the sixth power of the distance between donors and acceptors:

E ) Ro6/(r6 + Ro6)

(2)

where E, Ro, and r are the energy transfer efficiency, the Forster radius, and distance between donor and acceptor molecules, respectively. The Forster radius is a characteristic distance (28) Jayasuriya, R. M.; El-Aasser, M. S.; Vanderhoff, J. W.; Yue, H. J. J. Polym. Sci., Polym. Chem. Ed. 1985, 23, 2819. (29) Wang, Y.; Winnik, M. A. J. Phys. Chem. 1993, 97, 2507.

Figure 1. A typical fluorescence decay curve of naphthyl groups in a polystyrene latex film. The decay curve was fit to an exponential function as described in the text. The bottom figure shows the standard deviation of the fit. between donor and acceptor where the energy transfer efficiency is 50%. Ro for the NEMA/ANMA energy transfer pair is 2.3 nm.30 In DET experiments, the total number of emitted photons at the donor wavelength as a function of annealing times provides a measurement of the polymer interdiffusion between latex particles. The total number of photons is proportional to the area under the fluorescence decay curve. The mixing fraction at time t, Fm(t) defined as follows, provides a measure of the amount of polymer crossing the interface.

Fm(t) ) (A0 - At)/(A0 - A∞)

(3)

Here, A0, At, and A∞ are the area under the curve at time zero, time t, and infinity, respectively. The apparent diffusion coefficients can be obtained, based on a Fickian diffusion model. Arguably, a Fickian diffusion model might not be valid for polymer interdiffusion at short times, namely, less than the reptation time of a polymer chain. Nevertheless, a Fickian model31 is used to describe the concentration profile, C(r,Dt), of the diffusing substance. The Fickian model seems to be the best model up until now to describe the interdiffusion process in latex film. The diffusant is assumed to be uniformly distributed in a sphere of radius R with an initial concentration C0 at time zero and is described by

C(r,Dt) )

(

)

Co R+r R-r erf + erf 2 2xDt 2xDt Co Dt -(R + r)2 -(R - r)2 - exp exp r π 4Dt 4Dt

x (

)

(4)

where D is the diffusion coefficient. The fraction of mixing defined above is related to the concentration profile, C(r,Dt), as follows:29

Fm ) 1 -

3 4πR3

∫ C(r,Dt)4πR R

0

2

dr

(5)

Since the concentration profile is a monotonic function of r, t, and D, the diffusion coefficient can be simply found by varying D for a given Fm(t), t, and R. A BASIC program was written for this purpose. Figure 1 shows a typical decay curve of fluorescence from a naphthyl-labeled polystyrene latex film. A pulsed hydrogen flashlamp selectively excites the naphthalene fluorophore at 280 (30) Berlman, I. B. Energy Transfer Parameters of Aromatic Compounds; Academic Press: New York, 1973; p 309. (31) Crank, J. The Mathematics of Diffusion; Clarendon: Oxford, 1975.

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Figure 2. Fluorescence decay curves of (top to bottom) labeled polystyrene films annealed for 0, 10, 40, and 180 min at 122 °C. The decay time decreases with longer annealing times.

Figure 3. Fraction of mixing as a function of annealing time at 122 °C. Polystyrene of Mn ) 72 000 g/mol with H end (triangles) and polystyrene of Mn ) 70 000 g/mol with carboxyl end groups (circles). Average diffusion coefficients are 3.0 × 10-16 and 1.0 × 10-16 cm2/s for polystyrene with and without carboxyl end groups, respectively. On the basis of the reptation theory,14 the reptation time is approximately 18 and 6 min for H end and carboxyl end PS, respectively. nm. The excitation is focused onto the sample and the emission is monitored at a 90° angle to the excitation, through a Corning O-53 filter. The emission is detected at 340 nm, via a Philips XP2020Q photomultiplier tube operating in a time-correlated single-photon-counting mode. The raw data are first deconvoluted from the instrument response function, which has typically a 2-4 ns width at half-height. Many functions could be applied to analysis of the decay curve; however, a double exponential function built into the instrument software was used because this function produced reasonable χ2 values (e1.5). Figure 2 shows that the fluorescence decay curves of the donor molecules change with annealing times. Longer annealing times induce a faster decay. As annealing time is increased, interdiffusion increases and hence energy transfer also increases. The total number of fluorescence photons was calculated after the decay curves were fit to a double exponential function and integrated. Finally, the fraction of mixing and diffusion coefficients were obtained by eqs 3 and 5.

Results and Discussion Figure 3 shows the diffusion data, in terms of Fm versus time, for polystyrene films with and without carboxyl end groups, annealed at 122 °C. The diffusion coefficients of polystyrene with H end groups are compared with a previous SANS study.18 In the present study, the diffusion coefficients of PS with H end groups were 1.0 × 10-16 cm2/s for Mn ) 72 000 g/mol at 122 °C and 0.4 × 10-16 cm2/s for Mn ) 98 000 g/mol at 126 °C. Since all samples with no functional end groups should obey the Arrhenius

Kim et al.

Figure 4. Fraction of mixing as a function of annealing time at 126 °C. Polystyrene of Mn ) 98 000 g/mol with H ends (triangles) and polystyrene of Mn ) 94 000 g/mol with carboxyl end groups (circles). Average apparent diffusion coefficients are 0.97 × 10-16 and 0.41 × 10-16 cm2/s for polystyrene with and without carboxyl end group, respectively. On the basis of the reptation theory,14 the reptation time is approximately 59 and 26 min for H end and carboxyl end PS, respectively.

equation and reptation theory (D ∼ M-2), the diffusion coefficients can be reduced to the same temperature, 135 °C, and molecular weight (150 000 g/mol). An activation energy of 52 kcal/mol, obtained by Kim et al.,18 was used. The present data show fair agreement between the DET method and SANS results,18 if the differences in methodology and samples are considered. Both studies are done using the same model miniemulsification method to obtain both narrow distributions in particle size and molecular weight. Data reduction in DET experiments is somewhat controversial,32 but the relative comparison based on the same system should be valid. An important point of the data in Figure 3 is that the sample with carboxyl end groups diffuses faster. Figure 3 illustrates that the apparent D value for polystyrene with a carboxyl end group is three times higher than that of H end groups. The trend was also found with higher molecular weight polystyrene, at a higher temperature (Figure 4). Sulfate end groups are commonly introduced in emulsion polymerization through the use of persulfate initiators. Polystyrene with an average of one sulfate end group is the major product in an emulsion polymerization when tetrachloromethane is employed. Figure 5 compares the apparent diffusion coefficients of polystyrene with H, carboxyl, and sulfate end groups, predominantly in the acid form. The data indicate that at early times, sulfate end group polystyrene has the highest diffusion coefficients, followed by carboxyl end groups. However, this difference in diffusion coefficients diminishes as diffusion progresses. This transient difference in apparent diffusion coefficients indicates that the end-group effect on interdiffusion is not due to a change in an average property of a polymer chain, such as the frictional coefficient, chain flexibility, or free volume. If that were the case, the difference should be maintained throughout the diffusion process. The term apparent diffusion coefficient refers to the use of Fickian diffusion concepts at times shorter than the reptation time. Since the latexes are prepared in an aqueous environment, polar end groups of a polymer chain tend to predominate on the surface at synthesis. The surface end (32) (a) Farinha, J. P. S.; Martinho, J. M. G.; Yekta, A.; Winnik, M. A. Macromolecules 1995, 28, 6084. (b) O’Neil, G. A.; Torkelson, J. M. Macromolecules, 1997, 30, 5560.

Polystyrene Latex Interdiffusion

Langmuir, Vol. 16, No. 3, 2000 1283 Table 3. Apparent Diffusion Coefficients Separated into Two Diffusion Coefficients, Dsurface and Dbulka end group

f

carboxyl group sulfate group a

Figure 5. Apparent diffusion coefficient of polystyrene with H (circles, Mn ) 98 000 g/mol), carboxyl (triangles, Mn ) 94 000 g/mol), and sulfate end group (squares, Mn ) 91 000 g/mol and Mn ) 126 000 g/mol) at an annealing temperature of 126 °C. Data were reduced to Mn ) 100 000 g/mol by the relationship, D ∼ M-2. Since molecular weights for all samples are similar, data reduction does not change the trend in this figure.

Dapp (cm2/s)

0.3 0.6

3.3 × 10-16 2.5 × 10-16

1.1 × 2.2 × 10-16

A bulk diffusion coefficient of D ) 50 × 10-18 cm2/s was assumed.

interdiffusion process without chain end segregation at interfaces occurs with a homogeneous concentration of end groups throughout the particle. When chain ends are segregated at an interface, however, a concentration gradient exists, providing an additional driving force for interdiffusion. Such effects on the interdiffusion processes would be expected to be transient, as observed. After a certain period, the surface segregation effect would fail to dominate, and the diffusion coefficients would decrease. Separation of Initial Diffusion Coefficients. Figure 5 describes three apparent diffusion coefficients, for H, carboxyl, and sulfate end groups, which increase with increasing surface coverage of the end groups. The polystyrene latex particles with ionic end groups are composed of two different types of polymer, as indicated by surface titration. The total flux of a mixture of parallel diffusing species can be described by the linear sum of the flux of each species, as long as the different molecules are not coupled. In the present system, polystyrene with and without the surface segregation of the ionic end groups diffuses independently.

Figure 6. A schematic diagram to describe the reptation process of a polymer chain in a latex particle.

j(x,t) ) -Dapp

groups do not have enough time to be randomized because the films were prepared just above the Tg of polystyrene. Although some studies33 have shown that Tg at a polymer surface is lower than that of the bulk, the length scale of the surface in this case is small compared to the polymer chain dimension. To quantify the end-group surface concentration, a titration was carried out for the particles in water. The results indicate that 30% of the carboxyl end groups and 60% of the sulfate end groups are on the particle surface (Table 2). The higher surface segregation of the end groups might account for the differences in interdiffusion. According to theory developed by de Gennes34 and Wool,14 a polymer chain end can be described as initiating the escape from a virtual “tube”, followed by the rest of the chain, as depicted in Figure 6 for a latex particle. The reptation process is described by two steps. The first step, from A to B, involves a chain end moving to the surface of a latex particle. The second step, from B to C, is the movement into another particle. In both steps, the chain end leads the rest of the chain according to the reptation theory. However, if a chain end is already segregated on the surface at the beginning of the diffusion process, at B, the diffusion of the polymer chain only requires the second step. As a consequence, the initial apparent diffusion coefficients of the polymer with a chain end at the surface is higher than that of polymer with chain ends buried in the latex. An alternative explanation for the fast, initial interdiffusion of ionic end-group polystyrene is related to the chemical potential of the diffusion process. The polymer

)

(33) A brief summary is in: Liu Y.; Russell, T. P.; Samant, M. G.; Stohr, J.; Brown, H. R.; Cossy-Favre, A.; Diaz, J. Macromolecules 1997, 30, 7768. (34) de Gennes, P. G. J. Chem. Phys. 1971, 55, 572.

Dsurface (cm2/s)

10-16

∂c ∂x ∂ci

∑i ji(x,t) ) - ∑i Di ∂x

(6)

where j(x,t) is the total flux of all species with a total concentration, c, and apparent diffusion coefficient, D, while ji(x,t), is the flux of a diffusing substance, i, with a concentration, ci, and diffusion coefficient, Di. The data can be described by the linear combination of two independent diffusion coefficients: that arising from polymer chains with end groups on the surface and that arising from polymer with end groups within the latex particle. Polymer with H end groups can serve as the model for polymer without surface end groups, the normal diffusing species, which has a diffusion coefficient of approximately 50 × 10-18 cm2/s. In the shortest time regime of the measurements (30 min), the sulfate- and carboxyl-terminated chains have Dapp values of approximately 220 × 10-18 and 110 × 10-18 cm2/s, respectively, which may be used for the surface end-group chains. Assuming Dsurface is the diffusion of the polymer with chain ends at the surface and that the quantities are describable by two separable diffusion coefficients, their sum can be written:

fDsurface + (1 - f)Dbulk ) Dapp

(7)

where f is the fraction of polymer chains with end groups at the surface and Dbulk, Dsurface, and Dapp are the diffusion coefficients of polymers with end groups in the bulk and at the surface and the total apparent diffusion coefficients obtained by the experiments. Table 3 shows that diffusion coefficients of polystyrene with end groups on the surface, Dsurface, is higher than that in the bulk. In addition, it is immediately observed that the two Dsurface quantities are substantially similar

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Kim et al.

within experimental error. The similar value of Dsurface for two chemically different end groups suggests that the location of the end group is the critical factor in determining the initial diffusion coefficient, more than its chemical nature. While the exact time scale of the measurement and the polydispersity of the sample will influence the absolute magnitude of the D values, the end-group segregation may define the apparent diffusion coefficients. However, the chemical nature of the end group may impact the diffusion process by determining the end-group surface concentration. Surface Segregation of End Groups. On the basis of classical partitioning theories, the volume fraction of end groups on the surface was calculated by Jalbert et al.12 and others35

φ1s )

φ1b exp(-χs) 1 - φ1b + φ1b exp(-χs)

(8)

where φ1s and φ1b represent the volume fraction of end groups at the surface and in the bulk, respectively, and χs is a dimensionless surface interaction parameter between an end group and a repeat unit segment. In this study, φ1b is also equal to the inverse of the degree of polymerization. The model assumes a cubic lattice with a volume, v. The dimensionless interaction parameter is defined by the expression

(9)

where kB represents Boltzmann’s constant, T is the temperature, and ∆U is the surface energy change when a repeat unit at the surface replaces an end group in the bulk. The quantities (γe - γr) and v2/3 are the surface energy of end group, the surface energy of a repeat unit, and the projected area of a unit cubic cell respectively. Equation 9 was used to predict the surface segregation at an air/polymer interface. In contrast, the end-group segregation at a water/polymer interface requires a different approach to determine the surface interaction parameter. The ionic end group and water are miscible, with a negative heat of mixing that cannot be predicted by the surface energy in eq 9. Calculation of the free energy change is described in Supporting Information. The calculation assumes that the heat of mixing between a carboxyl group and water and the interfacial energy between the styrene and water are the source of the free energy change, calculated to be -3.9 kcal/mol. On the basis of the assumption that the thickness of the surface equals the one side of a unit cubic cell, the fraction of end groups segregated at the surface, f, can be obtained by the expression

(

φ1b

v (cm3/mol)

l (nm)

χs

φ1b

φ1s

f

904

99.0

0.549

-1.61

0.00111

0.00547

0.161

Parameters used in the calculation and the results for carboxyl end groups are listed in Table 4. The size of a styrene mer defines the size of a unit cubic cell in this calculation, yielding f ) 0.161. The carboxyl group could be also taken as a unit cell, as in ref 12, resulting in a similar value of f, 0.18. This value is lower than that obtained by titration, 0.30. The calculated values increase if chain connectivity is considered. Literature results9 summarized in the Introduction show that the entropic effect alone (due to the chain connectivity) induces about twice the chain end concentration at the surface, versus the bulk. The results in Table 4 show that the concentration of end groups at the surface is five times higher than that in the bulk. Because of the lack of data for the heat of solution of water and an appropriate analogue for sulfate end groups, such as methyl sulfate, the equilibrium constant could not be estimated for the sulfate system. However, since sulfate end groups are well-known as very strong acids, they should have a higher heat of solution than carboxylic groups. This may lead to a greater surface concentration of end groups, as observed experimentally. Conclusions

(γe - γr)v2/3 kBT

)

φ1s

N

∆U kBT

χs )

f)

Table 4. Summary of Calculation for Surface Segregation of the Carboxyl End Groups at a Water/Polymer Interface at 20 °C

1-

)

(R - l)3 R3

(10)

where R and l represent radius of a latex particle and its surface thickness, respectively. (35) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley-Interscience: New York, 1997; p 390.

Polystyrene interdiffusion in artificial latex films was studied via DET. Polar polymer end groups were found to have an increased early-time apparent interdiffusion coefficient. The polar environment of water induces a high population of ionic end groups on particle surfaces. The surface population of carboxyl and sulfate end groups was measured by a conductance method, yielding about 30% and 60% surface concentrations, respectively. The diffusion coefficients of polystyrene with sulfate end groups shows the fastest interdiffusion at early times, followed by carboxyl end groups, while polystyrene containing H end groups shows the slowest early-time interdiffusion. The higher interdiffusion of polystyrene with ionic end groups is apparently due to the higher end-group surface concentration. The apparent overall diffusion coefficients at short times are separable into two additive values: that caused by the chains with ends on the latex surface and that caused by chains with ends buried in the latex interior. Finally, calculations based on equilibrium thermodynamic relationships suggest that about 18% of the carboxyl end groups are on the surface. Acknowledgment. The authors acknowledge financial support through National Science Foundation Grant No. CTS-9522596. The authors thank Dr. Andrea Kirk and Dr. Patricia Lesko at Rohm and Haas Co. for valuable discussions. Supporting Information Available: The calculation of the free energy change for surface segregation. This material is available free of charge via the Internet at http://pubs.acs.org. LA990709N