Journal ArticleMolecular dynamics simulations of polymer melts at flat and structured surfaces reveal that, for the  former, slow dynamics and increased dynamic heterogeneity for an adsorbed polymer is due to  densification of the polymer in a surface layer, while, for the latter, the energy topography of the  surface plays the dominant role in determining dynamics of interfacial polymer. The dramatic increase in structural relaxation time for polymer melts at the attractive structured surface is largely the result of dynamic heterogeneity induced by the surface and does not resemble dynamics of a bulk melt approaching Tg

Smith, Grant D.

English

The University of Utah: J. Willard Marriott Digital Library

VOLUME 90, NUMBER 22 P H Y S I C A L  R E V I E W  L E T T E R SStructural Relaxation and Dynamic Heterogeneity in a Polymer Melt at Attractive SurfacesGrant D. Smith, Dm itry Bedrov, and Oleg Borodin D e p a rtm en t o f  M a te r ia ls  Science a n d  E n g in eerin g , U n iversity  o f  U tah , 122  South C en tra l C am pus D r iv e ,R oom  304 , S a lt L ake  C ity , U tah  84112, USA (Received 15 January 2003; published 5 June 2003)Molecular dynamics simulations of polymer melts at flat and structured surfaces reveal that, for the former, slow dynamics and increased dynamic heterogeneity for an adsorbed polymer is due to densification of the polymer in a surface layer, while, for the latter, the energy topography of the surface plays the dominant role in determining dynamics of interfacial polymer. The dramatic increase in structural relaxation time for polymer melts at the attractive structured surface is largely the result of dynamic heterogeneity induced by the surface and does not resemble dynamics of a bulk melt approaching Tg.DOI: 10.1103/PhysRevLett.90.226103The dynamics of melt polymers near solid surfaces are of tremendous interest for a wide range of materials including polymer-nanoparticle composites [1] and highly confined polymers [2], Simulation [3,4] and ex­perimental studies [5-7] have shown that the structural relaxation time of melt polymers in the vicinity of solid surfaces with which they have strong, attractive interac­tions can be dramatically greater than that of the corre­sponding bulk polymer at the same thermodynamic conditions. This increase in relaxation time has been associated with an increase in glass transition tempera­ture Tg for interfacial polymer seen in both simulations[3] and experimental studies [1,8].Simulation [3,9,10] and experimental studies [9,11] reveal that attractive interfaces engender density oscilla­tions (layers) in a polymer melt whose amplitude decays rapidly with distance from the surface (e.g., see inset in Fig. 1). Simulations also indicate that the influence of the surface on polymer dynamics is localized to the first few layers of polymer near the surface and is most dramatic for polymer segments adsorbed on the polymer surface (the first polymer layer) [3,4], Hence, understanding the relaxation behavior of polymers in the layer adjacent to an attractive surface is key to understanding the dynamics of interfacial and confined polymers. The fundamental ori­gins of these increased relaxation times for polymers at strongly attractive surfaces remain unclear. Detailed analysis of simulations of roughly spherical nanoparticles in a coarse-grained bead-spring polymer matrix [4] in­dicated that reduced segmental motion along the surface of the particle can be associated with the energy topog­raphy of the nanoparticle surface. In contrast, a recent density functional theory analysis of polymer chains confined between flat, structureless surfaces associated the slowing of polymer dynamics with increased density of the polymer in layers near the surface [12].Recent simulation studies [13] have also revealed the im portant role of dynamic heterogeneity in governing relaxation behavior in polymer melts. Dynamic hetero­geneity, reflected, for example, in an increasingly non-PACS numbers: 68.47.Pe, 61.12.-q, 82.35.GhGaussian character of atomic displacements as tempera­ture decreases toward Tg, can be quantified by the first non-Gaussian correction to the incoherent dynamic struc­ture factor I(q, t) given by [14]I(q, t) =  IGmss(q, t)X{ 1 +  \ [q 2{R{t)2) / 6 f a 2{t) +  ■■■}, whereIGmss(q, t) =  exp[ — q2(R(t)2)/6],a 2(t) 3 (R(t)4) 5 (R (t)2)2 1.(R(t)2) is the mean-square displacement of scattering centers (e.g., monomers) at time t, and q is the magnitude of the scattering vector. Non-Gaussian displacements can result in much slower relaxation, quantified by the rate ofFIG. 1. Incoherent dynamic structure factor of the first poly­mer layer at the structured surface (open squares) and flat surface (open triangles) for eps =  2. Also shown is the dynamic structure factor for the bulk melt. The solid lines are the corresponding dynamic structure factors obtained assuming Gaussian distributed bead displacements. The inset shows the density of polymer beads as a function of distance from the surfaces; vertical lines denote layer boundaries.226103-1 0031-9007/03/90(22)/226103(4)$20.00 © 2003 The American Physical Society 226103-1V o l u m e  9 0 ,  N u m b e r  2 2P H Y S I C A L  R E V I E W  L E T T E R S week ending6 JUNE 2003decay of I(q, t), compared to a more dynamically homo­geneous material with the same intrinsic dynamics quan­tified by (R(t)2).For polymers near attractive surfaces, increased struc­tural relaxation time relative to the bulk melt may be due to a decrease in the rate of intrinsic polymer dynamics for adsorbed polymer segments, an increase in non- Gaussianity (heterogeneity) of monomer displacements for adsorbed polymer, or both. In turn, this (these) ef­fe c ts )  may be a consequence of the energy topography of the surface, densification of the polymer at the surface, or a combination of these effects. In order to help clarify the roles of heterogeneity, surface structure, and polymer densification in the observed slowing of structural relaxa­tion of polymers near attractive surfaces, we have con­ducted simulations of a coarse-grained bead-spring polymer melt confined between attractive structured and structureless (flat) surfaces. The polymer model and simu­lation methodology are described in detail in our pre­vious work [4,10]. Briefly, the systems consisted of 100 polymer chains of 20 beads. All polymer beads interact by a Lennard-Jones potential with a well depth of s pp =  1 with a zero energy at r  =  1 =  <x. The bead- bead bond length was constrained at 0.935. The polymer was confined between parallel surfaces nominally at z =  0 and 10 with periodic boundary conditions in the x and y  directions. The actual spacing between surfaces was adjusted to give a density (beads/cr3) of p  =  0.87 in the center of each film  The atomistic surfaces consisted of two layers of polymer beads in a square array with lattice parameter equal to the diameter of the beads. Polymer-surface (bead-bead) interaction energies s ps =  Spp =  1 and s ps =  2 spp =  2 were investigated. For the flat surfaces the polymer bead-surface potential is given asU(z) =  /\SpJc *' -  c '].where parameter A was adjusted such that the polymer density profiles obtained for structured and flat surfaces were nearly indistinguishable, as shown in Fig. 1. Simu­lations were performed using the simulation package Lucretius [15] at reduced temperature T =  1.0 defined in terms of the well depth for the polymer bead-bead interaction (s pp =  1). Simulations of a bulk melt (3D periodic boundary conditions) were also performed at T  =  1.0, p  =  0.87. All potentials were shifted and trun­cated at 2.5a.  Our integration time step was 5.9 X 10-3 in units of (mcr/spp)1/2 where m is the bead mass, with a total simulation time of approximately 6 X 104 for each system.We have investigated the behavior of incoherent dy­namic structure factor for each layer j  (e.g., see Fig. 1, inset) of the polymer films given asIj (qo> t) =  2“ ^  ( cos[q0Rx>’(t) cos6 ] d d jandus% o, t) =  ex p [^ q 2Q( R f ( t ) 2) / 4 lwhere qo =  l  corresponds to the first peak in the static structure factor for the bulk melt and (Rx?{t)2) is the mean-squared bead displacement of the Nj beads in the jth  layer parallel to the surfaces. Here we investigated only motion parallel to the surface as a division of the material into layers of thickness comparable to 27r/q0 resulting in artifacts in the 3D dynamic structure factor from contribution of motion perpendicular to the layers. The integral was evaluated numerically utilizing 180 equally spaced q  vectors in the xy  plane. The relation­ship for I j ( q 0, t) assumes isotropic motion, while that for l j ’m'ss(q0, t) assumes both isotropic motion and Gaussian- distributed displacements of the scattering centers.Ij(q0, t) for the first polymer layer at structured and flat surfaces for s ps =  2 as well as I(q0, t) for the bulk melt are shown in Fig. 1. Structural relaxation times, defined as the time at which the structure factor decays to 0.1, normalized by the relaxation time of the bulk polymer, are given in Table I for all systems studied. As antici­pated, the structural relaxation time for the polymer near the attractive surfaces (first layer) is much greater than that of the bulk polymer, particularly for the structured surface. Polymer dynamics for layer 2 showed much less influence on the surface and those for layers beyond layer 2 were essentially indistinguishable from the bulk melt. The dynamic structure factor of the film could be represented quite accurately as a weighted sum of contributions from the first two layers with the remainder of the material treated as bulk polymer.Comparison of I ( q 0, t) and I Gaa**{qQ, t) (Fig. 1) or, correspondingly, T/ TGauss5 given in Table I, reveals that heterogeneity, manifested in the non-Gaussianity of bead displacements, makes an insignificant contribution to the structural relaxation time for the bulk melt, con­sistent with the fact that the bulk is well above its glass transition temperature of approximately Tg =  0.35 [ 16]. In contrast, for the adsorbed polymer layer non-Gaussian effects are im portant, particularly for the structured surface, and increase dramatically with the strength of the polymer-surface interaction. For the structured sur­face dynamic heterogeneity induced by the surface playsTABLE I. Normalized structural relaxation times for ad­sorbed and bulk polymer.Relax.timeStructuredSps =  1 ®ps =  2 ef>sFlat1 eps =  2T 8.3Layer 1 2444 1.1 2.2.^Gauss 1.4 53 0.8 1.5T^ TGauss 5.9 46 1.4 1.5^y^GaussBulk melt 1.3226103-2 226103-2V o l u m e  9 0 ,  N u m b e r  2 2 P H Y S I C A L  R E V I E W  L E T T E R Sweek ending6 JUNE 2003a role comparable to that of slower intrinsic dynamics in the dramatically increased structural relaxation time for interfacial polymer. For example, for the structured sur­face with eps =  2, the structural relaxation time is ap­proximately 3 orders of magnitude greater for the first layer than for the bulk ( logr =  3.4), with half of this being due to intrinsically slower dynamics ( logrGauss =  1.7) and half associated with dynamic heterogeneity (lo g r/T Gauss =  1.7).Dynamic heterogeneity in the adsorbed polymer layer was further investigated by comparing the magnitude of a 2(t), the mean-square bead displacement (Rxy(t)2), and the distribution of bead displacements P(Rxy) for polymer segments in the first layer at t =  tmax, the time corre­sponding to the maximum in a 2(t), for each system studied. Values of tmax, (Rxy(tmax)2), and a 2(tmax) are tabu­lated in Table II. For bulk polymer melts tmax corresponds to the caging time, i.e., the time scale upon which seg­ments begin to move beyond the cage of their neighbors. The caging time increases with decreasing temperature and is expected to diverge as Tg approached [13,17], As our bulk melt is well above Tg, tmax is small and the cor­responding a 2(tmax) is modest. Table II shows that tmax and a 2 (tmax) are greater for the adsorbed polymer and in ­crease with increasing strength of the polymer-surface interaction, particularly for the structured surface.We can gain insight into the fundamental roles of surface energy topography and polymer densification on the dynamics of adsorbed polymer by comparing values of (Rxy(tmax)2) given in Table II for each system. For the flat surface (Rxy(tmax)2) values correspond to that for the bulk melt, revealing that caging effects in the first poly­mer layer of the flat interface are occurring on the same length scale as those in the bulk melt. This indicates that densification of the first layer in the flat surface is promot­ing neighbor caging sim ilar to that observed in the bulk melt with decreasing temperature and, hence, leads to reduced dynamics and increased heterogeneity sim ilar to that observed in bulk polymers approaching the glass transition temperature [13]. In contrast, a structured surface with the same polymer density profile as a flat surface exhibits much stronger caging effects as mani-TABLE II. Comparison of non-Gaussian properties of bead displacements for adsorbed polymers.Systema m^ax a 2(*max) ybBulk 0.47 0.35 0.096s Sps =  1 1.89 0.68 0.225 0.80S -  s ps =  2 13.3 3.03 0.086 0.95s ~  ®ps 3 496 10.2 0.027 1.00f  ~  ®ps 1 0.59 0.35 0.122 0.80/  -  eps =  2 1.18 0.37 0.137 0.95fested in dramatically longer caging (and hence struc­tural relaxation times) and greater non-Gaussianity [large a 2{tm&x) }  than observed for the flat surface. For the structured surface the length scale of the caging decreases with increasing strength of the polymer-surface interaction. To further illustrate this effect, we performed additional simulations for a structured surface at eps =  3 (see Table II). Here the caging length scale reflects the amplitude of vibration of adsorbed polymer beads within energy wells on the structured surface, which become deeper (leading to reduced vibrational am pli­tudes) with the increase of strength of the polymer- surface interaction.The above analysis indicates that the reduced dynamics and increased heterogeneity for polymer segments ad­sorbed on the structured surface are due to polymer beads becoming trapped within energy wells on the surface that become increasingly deep with increasing eps. These effects are much stronger than density-induced neighbor caging observed for the flat surface. We concluded that the densification of the surface layer p e r  se, responsible for slowing dynamics and increased heterogeneity for ad­sorbed polymers at the flat surface, is unim portant for the structured surface. This is further illustrated in Fig. 2, which shows clearly the much longer relaxation time for the structured surface at the same surface density as a flat surface and the significantly different scaling of relaxa­tion time with density for the structured and flat surfaces.We can gain insight into the relaxation mechanism polymer segments adsorbed on the structured surface by investigating the distribution of bead displacements P(Rxy) at tmax, shown in Fig. 3 for each system studied. Also shown is P(Rxy) for the corresponding Gauss­ian distributions [yielding the same ((Rxy)2) as the actual distributions] for each system. The distributions for adsorbed polymer at the flat surface show deviation from Gaussian behavior but do not show any indication of the emergence of a second peak. Similar behavior isav =  structured surface, /  =  flat surface.bSurfaee density of beads (number of beads in the first layer perunit surface area).FIG. 2. Structural relaxation time for the first polymer layer for structured and flat surfaces as a function of bead surface density in the first layer.226103-3 226103-3V o l u m e  9 0 ,  N u m b e r  2 2P H Y S I C A L  R E V I E W  L E T T E R S week ending6 J UNE 20030.0 0,2 0.4 0.6 0.8 1.0 1.2 1.4 1.6RxyFIG. 3. Distribution of bead displacements at times corre­sponding to the maximum in a 2(t) for (a) the structured surface and (b) the fiat surface. Lines show the corresponding Gaussian distributions (/?"’) yielding equivalent (Rxy(tm.dJ 2).observed for segment distributions in bulk polymer melts approaching Tg [131. Much more dramatic deviations from Gaussian behavior are manifested for the structured surface. Particularly for the larger polymer-surface inter­action energies, there is a clear two-peak structure to the distributions. The first peak reflects segments that remain trapped in their cages (surface energy wells) on the caging time scale, while the second peak, which is m ani­fested on a length scale corresponding to the surface structure, reflects segments which have left their origi­nal well for neighboring wells. Sim ilar behavior was observed in our recent simulations of micelle forming telechelic polymer solutions, where on the caging time scale the majority of attractive polymer ends remained trapped within their original micelle but where also a clear contribution from those who had migrated to neigh­boring micelles could also be observed [171.In summary, our molecular dynamics simulation study of the dynamics of polymers at attractive interfaces re­veals that slowed structural relaxation compared to the bulk melt polymer is due to both slower intrinsic dynam ­ics for the adsorbed polymer and increased dynamic heterogeneity within the adsorbed polymer layer. For the structureless surface, the influence of the interface on the dynamics of adsorbed polymer can be associated with increased neighbor caging due to densification of polymer within the adsorbed layer. The slower intrinsic dynamics and increasing dynamic heterogeneity with increasing strength of the surface-polymer attraction for the flat surface resembles behavior observed for bulkpolymer melts with decreasing temperature. In contrast, for the structured surface, simulations indicate that den­sification of the polymer in the adsorbed layer is not fundamentally responsible for the dramatically slowed dynamics and increased dynamic heterogeneity of the adsorbed polymer compared to both the bulk polymer and polymer adsorbed to the flat surface. Rather, the specific topography of the surface plays a dominant role, with polymer segments becoming caged within sur­face energy wells and relaxation that occurs by migration of segments to neighboring energy wells.The authors gratefully acknowledge support of NASA through Grant No. NAG-12319 as well as the Department of Energy through Grant No. DEFG0301ER45914 and University of Utah Center for the Simulation of Acci­dental Fires and Explosions (C-SAFE) for support of this work.[1] G. Tsagaropoulos and A. Eiseberg, Macromolecules 28, 396 (1995); 28, 6067 (1995).[2] Polymer Surfaces, Interfaces, and Thin Films, edited by A. Karim and S. Kumar (World Scientific, Singapore, 2000).[3] F. W. Starr, T. B. Schr0der, and S. C. Glotzer, Phys. Rev. E 64, 021802 (2001); Macromolecules 35, 4481 (2002).[4] G. D. Smith, D. Bedrov, L. Li, and O. Byutner, J. Chem. Phys. 117, 9478 (2002).[5] S. Gagliardi, V. Arrighi, R. Ferguson, and M. T. F. Telling, Physica (Amsterdam) 301B, 110 (2001).[6] Gy. Torok, V.T. Lebedev, L. Cser, D. N. Orlova, Gy. Kali, A. 1. Sibilev, V. L. Alexeev, V. A. Bershtein, V. P. Budtov, V. N. Zgonnik, L.V. Vinogradova, and E. Yu. Melenevskaya, Physica (Amsterdam) 297B, 45 (2001).[7] E.K Lin, R. Kolb, S. K  Satija, and W.L. Wu, Macro­molecules 32, 3753 (1999).[8] W.E. Wallace, J.H  van Zanten, and W.L. Wu, Phys. Rev. E 52, 3329 (1995); J.H. van Zanten, W.E. Wallace, and W.L. Wu, Phys. Rev. E 53, 2053 (1996).[9] D. Y. Yoon, M. Vacatello, and G. D. Smith, in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, edited by K Binder (Oxford, New York, 1995).[10] J. S. Smith, D. Bedrov, and G. D. Smith, Compos. Sci. Technol. (to be published).[11] Y. Yang, K Hill, and J.G. Harris, Langmuir 9, 1983 (1993).[12] J. D. McCoy and J.G. Curro, J. Chem. Phys. 116, 9154 (2002).[13] G.D. Smith, W. Paul, M. Monkenbusch, and D. Richter, J. Chem. Phys. 114, 4285 (2001); G. D. Smith, O. Borodin, and W. Paul, J. Chem. Phys. 117, 10350 (2002); G. D. Smith, W. Paul, and D. Bedrov (to be published).[14] W. van Megan, T. C. Mortensen, S. R Williams, and J. Muller, Phys. Rev. E 58, 6073 (1998).[15] http://lucretius.mse.utah.edu[16] C. Bennemann, W. Paul, K Binder, and B. Diinweg, Phys. Rev. E 57, 843 (1998).[17] D. Bedrov, G.D. Smith, and J.F  Douglas, Europhys. Lett. 59, 384 (2002).2 2 6 1 0 3 -4 2 2 6 1 0 3 -4

Structural relaxation and dynamic hetrogeneity in a polymer melt at attractive surfaces

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Structural relaxation and dynamic hetrogeneity in a polymer melt at attractive surfaces

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